Daily Papers

Large Language Models (LLMs), such as the GPT-4 and LLaMA families, have demonstrated considerable success across diverse tasks, including multiple-choice questions (MCQs). However, these models exhibit a positional bias, particularly an even worse anchored bias in the GPT-2 family, where they consistently favour the first choice 'A' in MCQs during inference. This anchored bias challenges the integrity of GPT-2's decision-making process, as it skews performance based on the position rather than the content of the choices in MCQs. In this study, we utilise the mechanistic interpretability approach to identify the internal modules within GPT-2 models responsible for this bias. We focus on the Multi-Layer Perceptron (MLP) layers and attention heads, using the "logit lens" method to trace and modify the specific value vectors that contribute to the bias. By updating these vectors within MLP and recalibrating attention patterns to neutralise the preference for the first choice 'A', we effectively mitigate the anchored bias. Our interventions not only mitigate the bias but also improve the overall MCQ prediction accuracy for the GPT-2 family across various datasets. This work represents the first comprehensive mechanistic analysis of anchored bias in MCQs within the GPT-2 models, introducing targeted, minimal-intervention strategies that significantly enhance GPT2 model robustness and accuracy in MCQs. Our code is available at https://github.com/ruizheliUOA/Anchored_Bias_GPT2.

Chain-of-Thought (CoT) prompting has significantly enhanced the reasoning abilities of large language models. However, recent studies have shown that models can still perform complex reasoning tasks even when the CoT is replaced with filler(hidden) characters (e.g., "..."), leaving open questions about how models internally process and represent reasoning steps. In this paper, we investigate methods to decode these hidden characters in transformer models trained with filler CoT sequences. By analyzing layer-wise representations using the logit lens method and examining token rankings, we demonstrate that the hidden characters can be recovered without loss of performance. Our findings provide insights into the internal mechanisms of transformer models and open avenues for improving interpretability and transparency in language model reasoning.

The rapid development of Large Multimodal Models (LMMs) has significantly advanced multimodal understanding by harnessing the language abilities of Large Language Models (LLMs) and integrating modality-specific encoders. However, LMMs are plagued by hallucinations that limit their reliability and adoption. While traditional methods to detect and mitigate these hallucinations often involve costly training or rely heavily on external models, recent approaches utilizing internal model features present a promising alternative. In this paper, we critically assess the limitations of the state-of-the-art training-free technique, the logit lens, in handling generalized visual hallucinations. We introduce a refined method that leverages contextual token embeddings from middle layers of LMMs. This approach significantly improves hallucination detection and grounding across diverse categories, including actions and OCR, while also excelling in tasks requiring contextual understanding, such as spatial relations and attribute comparison. Our novel grounding technique yields highly precise bounding boxes, facilitating a transition from Zero-Shot Object Segmentation to Grounded Visual Question Answering. Our contributions pave the way for more reliable and interpretable multimodal models.

As language models become more powerful and sophisticated, it is crucial that they remain trustworthy and reliable. There is concerning preliminary evidence that models may attempt to deceive or keep secrets from their operators. To explore the ability of current techniques to elicit such hidden knowledge, we train a Taboo model: a language model that describes a specific secret word without explicitly stating it. Importantly, the secret word is not presented to the model in its training data or prompt. We then investigate methods to uncover this secret. First, we evaluate non-interpretability (black-box) approaches. Subsequently, we develop largely automated strategies based on mechanistic interpretability techniques, including logit lens and sparse autoencoders. Evaluation shows that both approaches are effective in eliciting the secret word in our proof-of-concept setting. Our findings highlight the promise of these approaches for eliciting hidden knowledge and suggest several promising avenues for future work, including testing and refining these methods on more complex model organisms. This work aims to be a step towards addressing the crucial problem of eliciting secret knowledge from language models, thereby contributing to their safe and reliable deployment.

The use of deep neural networks in real-world applications require well-calibrated networks with confidence scores that accurately reflect the actual probability. However, it has been found that these networks often provide over-confident predictions, which leads to poor calibration. Recent efforts have sought to address this issue by focal loss to reduce over-confidence, but this approach can also lead to under-confident predictions. While different variants of focal loss have been explored, it is difficult to find a balance between over-confidence and under-confidence. In our work, we propose a new loss function by focusing on dual logits. Our method not only considers the ground truth logit, but also take into account the highest logit ranked after the ground truth logit. By maximizing the gap between these two logits, our proposed dual focal loss can achieve a better balance between over-confidence and under-confidence. We provide theoretical evidence to support our approach and demonstrate its effectiveness through evaluations on multiple models and datasets, where it achieves state-of-the-art performance. Code is available at https://github.com/Linwei94/DualFocalLoss

A key challenge of modern machine learning systems is to achieve Out-of-Distribution (OOD) generalization -- generalizing to target data whose distribution differs from that of source data. Despite its significant importance, the fundamental question of ``what are the most effective algorithms for OOD generalization'' remains open even under the standard setting of covariate shift. This paper addresses this fundamental question by proving that, surprisingly, classical Maximum Likelihood Estimation (MLE) purely using source data (without any modification) achieves the minimax optimality for covariate shift under the well-specified setting. That is, no algorithm performs better than MLE in this setting (up to a constant factor), justifying MLE is all you need. Our result holds for a very rich class of parametric models, and does not require any boundedness condition on the density ratio. We illustrate the wide applicability of our framework by instantiating it to three concrete examples -- linear regression, logistic regression, and phase retrieval. This paper further complement the study by proving that, under the misspecified setting, MLE is no longer the optimal choice, whereas Maximum Weighted Likelihood Estimator (MWLE) emerges as minimax optimal in certain scenarios.

Risk parity, also known as equal risk contribution, has recently gained increasing attention as a portfolio allocation method. However, solving portfolio weights must resort to numerical methods as the analytic solution is not available. This study improves two existing iterative methods: the cyclical coordinate descent (CCD) and Newton methods. We enhance the CCD method by simplifying the formulation using a correlation matrix and imposing an additional rescaling step. We also suggest an improved initial guess inspired by the CCD method for the Newton method. Numerical experiments show that the improved CCD method performs the best and is approximately three times faster than the original CCD method, saving more than 40% of the iterations.

Leveraging the models' outputs, specifically the logits, is a common approach to estimating the test accuracy of a pre-trained neural network on out-of-distribution (OOD) samples without requiring access to the corresponding ground truth labels. Despite their ease of implementation and computational efficiency, current logit-based methods are vulnerable to overconfidence issues, leading to prediction bias, especially under the natural shift. In this work, we first study the relationship between logits and generalization performance from the view of low-density separation assumption. Our findings motivate our proposed method MaNo which (1) applies a data-dependent normalization on the logits to reduce prediction bias, and (2) takes the L_p norm of the matrix of normalized logits as the estimation score. Our theoretical analysis highlights the connection between the provided score and the model's uncertainty. We conduct an extensive empirical study on common unsupervised accuracy estimation benchmarks and demonstrate that MaNo achieves state-of-the-art performance across various architectures in the presence of synthetic, natural, or subpopulation shifts.

Most of the existing Out-Of-Distribution (OOD) detection algorithms depend on single input source: the feature, the logit, or the softmax probability. However, the immense diversity of the OOD examples makes such methods fragile. There are OOD samples that are easy to identify in the feature space while hard to distinguish in the logit space and vice versa. Motivated by this observation, we propose a novel OOD scoring method named Virtual-logit Matching (ViM), which combines the class-agnostic score from feature space and the In-Distribution (ID) class-dependent logits. Specifically, an additional logit representing the virtual OOD class is generated from the residual of the feature against the principal space, and then matched with the original logits by a constant scaling. The probability of this virtual logit after softmax is the indicator of OOD-ness. To facilitate the evaluation of large-scale OOD detection in academia, we create a new OOD dataset for ImageNet-1K, which is human-annotated and is 8.8x the size of existing datasets. We conducted extensive experiments, including CNNs and vision transformers, to demonstrate the effectiveness of the proposed ViM score. In particular, using the BiT-S model, our method gets an average AUROC 90.91% on four difficult OOD benchmarks, which is 4% ahead of the best baseline. Code and dataset are available at https://github.com/haoqiwang/vim.

This paper proposes a new framework to detect, segment, and estimate the localization of the eyes from a periocular Near-Infra-Red iris image under alcohol consumption. The purpose of the system is to measure the fitness for duty. Fitness systems allow us to determine whether a person is physically or psychologically able to perform their tasks. Our framework is based on an object detector trained from scratch to detect both eyes from a single image. Then, two efficient networks were used for semantic segmentation; a Criss-Cross attention network and DenseNet10, with only 122,514 and 210,732 parameters, respectively. These networks can find the pupil, iris, and sclera. In the end, the binary output eye mask is used for pupil and iris diameter estimation with high precision. Five state-of-the-art algorithms were used for this purpose. A mixed proposal reached the best results. A second contribution is establishing an alcohol behavior curve to detect the alcohol presence utilizing a stream of images captured from an iris instance. Also, a manually labeled database with more than 20k images was created. Our best method obtains a mean Intersection-over-Union of 94.54% with DenseNet10 with only 210,732 parameters and an error of only 1-pixel on average.

Kahneman & Tversky's prospect theory tells us that humans perceive random variables in a biased but well-defined manner; for example, humans are famously loss-averse. We show that objectives for aligning LLMs with human feedback implicitly incorporate many of these biases -- the success of these objectives (e.g., DPO) over cross-entropy minimization can partly be ascribed to them being human-aware loss functions (HALOs). However, the utility functions these methods attribute to humans still differ from those in the prospect theory literature. Using a Kahneman-Tversky model of human utility, we propose a HALO that directly maximizes the utility of generations instead of maximizing the log-likelihood of preferences, as current methods do. We call this approach Kahneman-Tversky Optimization (KTO), and it matches or exceeds the performance of preference-based methods at scales from 1B to 30B. Crucially, KTO does not need preferences -- only a binary signal of whether an output is desirable or undesirable for a given input. This makes it far easier to use in the real world, where preference data is scarce and expensive.

Domain shift remains a persistent challenge in deep-learning-based computer vision, often requiring extensive model modifications or large labeled datasets to address. Inspired by human visual perception, which adjusts input quality through corrective lenses rather than over-training the brain, we propose Lens, a novel camera sensor control method that enhances model performance by capturing high-quality images from the model's perspective rather than relying on traditional human-centric sensor control. Lens is lightweight and adapts sensor parameters to specific models and scenes in real-time. At its core, Lens utilizes VisiT, a training-free, model-specific quality indicator that evaluates individual unlabeled samples at test time using confidence scores without additional adaptation costs. To validate Lens, we introduce ImageNet-ES Diverse, a new benchmark dataset capturing natural perturbations from varying sensor and lighting conditions. Extensive experiments on both ImageNet-ES and our new ImageNet-ES Diverse show that Lens significantly improves model accuracy across various baseline schemes for sensor control and model modification while maintaining low latency in image captures. Lens effectively compensates for large model size differences and integrates synergistically with model improvement techniques. Our code and dataset are available at github.com/Edw2n/Lens.git.

Block coordinate descent (BCD) methods are widely used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can significantly improve the progress made by each BCD iteration. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with sparse dependencies between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active-set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization.

Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.

We generalise an existing construction of Bayesian Lenses to admit lenses between pairs of objects where the backwards object is dependent on states on the forwards object (interpreted as probability distributions). This gives a natural setting for studying stochastic maps with Bayesian inverses restricted to the points supported by a given prior. In order to state this formally we develop a proposed definition by Fritz of a support object in a Markov category and show that these give rise to a section into the category of dependent Bayesian lenses encoding a more canonical notion of Bayesian inversion.

With the advance of AI, road object detection has been a prominent topic in computer vision, mostly using perspective cameras. Fisheye lens provides omnidirectional wide coverage for using fewer cameras to monitor road intersections, however with view distortions. To our knowledge, there is no existing open dataset prepared for traffic surveillance on fisheye cameras. This paper introduces an open FishEye8K benchmark dataset for road object detection tasks, which comprises 157K bounding boxes across five classes (Pedestrian, Bike, Car, Bus, and Truck). In addition, we present benchmark results of State-of-The-Art (SoTA) models, including variations of YOLOv5, YOLOR, YOLO7, and YOLOv8. The dataset comprises 8,000 images recorded in 22 videos using 18 fisheye cameras for traffic monitoring in Hsinchu, Taiwan, at resolutions of 1080times1080 and 1280times1280. The data annotation and validation process were arduous and time-consuming, due to the ultra-wide panoramic and hemispherical fisheye camera images with large distortion and numerous road participants, particularly people riding scooters. To avoid bias, frames from a particular camera were assigned to either the training or test sets, maintaining a ratio of about 70:30 for both the number of images and bounding boxes in each class. Experimental results show that YOLOv8 and YOLOR outperform on input sizes 640times640 and 1280times1280, respectively. The dataset will be available on GitHub with PASCAL VOC, MS COCO, and YOLO annotation formats. The FishEye8K benchmark will provide significant contributions to the fisheye video analytics and smart city applications.

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a target space (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the SSO algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for SSO when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of SSO.

Text-to-image diffusion models (T2I) use a latent representation of a text prompt to guide the image generation process. However, the process by which the encoder produces the text representation is unknown. We propose the Diffusion Lens, a method for analyzing the text encoder of T2I models by generating images from its intermediate representations. Using the Diffusion Lens, we perform an extensive analysis of two recent T2I models. Exploring compound prompts, we find that complex scenes describing multiple objects are composed progressively and more slowly compared to simple scenes; Exploring knowledge retrieval, we find that representation of uncommon concepts requires further computation compared to common concepts, and that knowledge retrieval is gradual across layers. Overall, our findings provide valuable insights into the text encoder component in T2I pipelines.

Conjoint analysis, an application of factorial experimental design, is a popular tool in social science research for studying multidimensional preferences. In such experiments in the political analysis context, respondents are asked to choose between two hypothetical political candidates with randomly selected features, which can include partisanship, policy positions, gender and race. We consider the problem of identifying optimal candidate profiles. Because the number of unique feature combinations far exceeds the total number of observations in a typical conjoint experiment, it is impossible to determine the optimal profile exactly. To address this identification challenge, we derive an optimal stochastic intervention that represents a probability distribution of various attributes aimed at achieving the most favorable average outcome. We first consider an environment where one political party optimizes their candidate selection. We then move to the more realistic case where two political parties optimize their own candidate selection simultaneously and in opposition to each other. We apply the proposed methodology to an existing candidate choice conjoint experiment concerning vote choice for US president. We find that, in contrast to the non-adversarial approach, expected outcomes in the adversarial regime fall within range of historical electoral outcomes, with optimal strategies suggested by the method more likely to match the actual observed candidates compared to strategies derived from a non-adversarial approach. These findings indicate that incorporating adversarial dynamics into conjoint analysis may yield unique insight into social science data from experiments.

We focus on the classification problem with a separable dataset, one of the most important and classical problems from machine learning. The standard approach to this task is logistic regression with gradient descent (LR+GD). Recent studies have observed that LR+GD can find a solution with arbitrarily large step sizes, defying conventional optimization theory. Our work investigates this phenomenon and makes three interconnected key observations about LR+GD with large step sizes. First, we find a remarkably simple explanation of why LR+GD with large step sizes solves the classification problem: LR+GD reduces to a batch version of the celebrated perceptron algorithm when the step size gamma to infty. Second, we observe that larger step sizes lead LR+GD to higher logistic losses when it tends to the perceptron algorithm, but larger step sizes also lead to faster convergence to a solution for the classification problem, meaning that logistic loss is an unreliable metric of the proximity to a solution. Surprisingly, high loss values can actually indicate faster convergence. Third, since the convergence rate in terms of loss function values of LR+GD is unreliable, we examine the iteration complexity required by LR+GD with large step sizes to solve the classification problem and prove that this complexity is suboptimal. To address this, we propose a new method, Normalized LR+GD - based on the connection between LR+GD and the perceptron algorithm - with much better theoretical guarantees.

Moment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods of moments, include the prominent generalized method of moments (GMM) which has recently gained attention in causal inference. GMM is a special case of the broader family of empirical likelihood estimators which are based on approximating a population distribution by means of minimizing a varphi-divergence to an empirical distribution. However, the use of varphi-divergences effectively limits the candidate distributions to reweightings of the data samples. We lift this long-standing limitation and provide a method of moments that goes beyond data reweighting. This is achieved by defining an empirical likelihood estimator based on maximum mean discrepancy which we term the kernel method of moments (KMM). We provide a variant of our estimator for conditional moment restrictions and show that it is asymptotically first-order optimal for such problems. Finally, we show that our method achieves competitive performance on several conditional moment restriction tasks.

Randomized controlled trials (RCTs) are considered the gold standard for estimating the average treatment effect (ATE) of interventions. One use of RCTs is to study the causes of global poverty -- a subject explicitly cited in the 2019 Nobel Memorial Prize awarded to Duflo, Banerjee, and Kremer "for their experimental approach to alleviating global poverty." Because the ATE is a population summary, anti-poverty experiments often seek to unpack the effect variation around the ATE by conditioning (CATE) on tabular variables such as age and ethnicity that were measured during the RCT data collection. Although such variables are key to unpacking CATE, using only such variables may fail to capture historical, geographical, or neighborhood-specific contributors to effect variation, as tabular RCT data are often only observed near the time of the experiment. In global poverty research, when the location of the experiment units is approximately known, satellite imagery can provide a window into such factors important for understanding heterogeneity. However, there is no method that specifically enables applied researchers to analyze CATE from images. In this paper, using a deep probabilistic modeling framework, we develop such a method that estimates latent clusters of images by identifying images with similar treatment effects distributions. Our interpretable image CATE model also includes a sensitivity factor that quantifies the importance of image segments contributing to the effect cluster prediction. We compare the proposed methods against alternatives in simulation; also, we show how the model works in an actual RCT, estimating the effects of an anti-poverty intervention in northern Uganda and obtaining a posterior predictive distribution over effects for the rest of the country where no experimental data was collected. We make all models available in open-source software.

In anomaly segmentation for complex driving scenes, state-of-the-art approaches utilize anomaly scoring functions to calculate anomaly scores. For these functions, accurately predicting the logits of inlier classes for each pixel is crucial for precisely inferring the anomaly score. However, in real-world driving scenarios, the diversity of scenes often results in distorted manifolds of pixel embeddings in the space. This effect is not conducive to directly using the pixel embeddings for the logit prediction during inference, a concern overlooked by existing methods. To address this problem, we propose a novel method called Random Walk on Pixel Manifolds (RWPM). RWPM utilizes random walks to reveal the intrinsic relationships among pixels to refine the pixel embeddings. The refined pixel embeddings alleviate the distortion of manifolds, improving the accuracy of anomaly scores. Our extensive experiments show that RWPM consistently improve the performance of the existing anomaly segmentation methods and achieve the best results. Code is available at: https://github.com/ZelongZeng/RWPM.

We study the problem of estimating the distribution of the return of a policy using an offline dataset that is not generated from the policy, i.e., distributional offline policy evaluation (OPE). We propose an algorithm called Fitted Likelihood Estimation (FLE), which conducts a sequence of Maximum Likelihood Estimation (MLE) and has the flexibility of integrating any state-of-the-art probabilistic generative models as long as it can be trained via MLE. FLE can be used for both finite-horizon and infinite-horizon discounted settings where rewards can be multi-dimensional vectors. Our theoretical results show that for both finite-horizon and infinite-horizon discounted settings, FLE can learn distributions that are close to the ground truth under total variation distance and Wasserstein distance, respectively. Our theoretical results hold under the conditions that the offline data covers the test policy's traces and that the supervised learning MLE procedures succeed. Experimentally, we demonstrate the performance of FLE with two generative models, Gaussian mixture models and diffusion models. For the multi-dimensional reward setting, FLE with diffusion models is capable of estimating the complicated distribution of the return of a test policy.

Strongly lensed variable quasars can serve as precise cosmological probes, provided that time delays between the image fluxes can be accurately measured. A number of methods have been proposed to address this problem. In this paper, we explore in detail a new approach based on kernel regression estimates, which is able to estimate a single time delay given several datasets for the same quasar. We develop realistic artificial data sets in order to carry out controlled experiments to test of performance of this new approach. We also test our method on real data from strongly lensed quasar Q0957+561 and compare our estimates against existing results.

Ensuring reliable confidence scores from deep networks is of pivotal importance in critical decision-making systems, notably in the medical domain. While recent literature on calibrating deep segmentation networks has led to significant progress, their uncertainty is usually modeled by leveraging the information of individual pixels, which disregards the local structure of the object of interest. In particular, only the recent Spatially Varying Label Smoothing (SVLS) approach addresses this issue by softening the pixel label assignments with a discrete spatial Gaussian kernel. In this work, we first present a constrained optimization perspective of SVLS and demonstrate that it enforces an implicit constraint on soft class proportions of surrounding pixels. Furthermore, our analysis shows that SVLS lacks a mechanism to balance the contribution of the constraint with the primary objective, potentially hindering the optimization process. Based on these observations, we propose a principled and simple solution based on equality constraints on the logit values, which enables to control explicitly both the enforced constraint and the weight of the penalty, offering more flexibility. Comprehensive experiments on a variety of well-known segmentation benchmarks demonstrate the superior performance of the proposed approach.

Pre-training foundation models on large-scale datasets demonstrates exceptional performance. However, recent research questions this traditional notion, exploring whether an increase in pre-training data always leads to enhanced model performance. To address this issue, data-effective learning approaches have been introduced. However, current methods in this area lack a clear standard for sample selection. Our experiments reveal that by maximizing V-information, sample selection can be framed as an optimization problem, enabling effective improvement in model performance even with fewer samples. Under this guidance, we develop an optimal data-effective learning method (OptiDEL) to maximize V-information. The OptiDEL method generates hard samples to achieve or even exceed the performance of models trained on the full dataset while using substantially less data. We compare the OptiDEL method with state-of-the-art approaches finding that OptiDEL consistently outperforms existing approaches across different datasets, with foundation models trained on only 5% of the pre-training data surpassing the performance of those trained on the full dataset.

For a data-generating process for random variables that can be described with a linear structural equation model, we consider a situation in which (i) a set of covariates satisfying the back-door criterion cannot be observed or (ii) such a set can be observed, but standard statistical estimation methods cannot be applied to estimate causal effects because of multicollinearity/high-dimensional data problems. We propose a novel two-stage penalized regression approach, the penalized covariate-mediator selection operator (PCM Selector), to estimate the causal effects in such scenarios. Unlike existing penalized regression analyses, when a set of intermediate variables is available, PCM Selector provides a consistent or less biased estimator of the causal effect. In addition, PCM Selector provides a variable selection procedure for intermediate variables to obtain better estimation accuracy of the causal effects than does the back-door criterion.

In recent years, many interpretability methods have been proposed to help interpret the internal states of Transformer-models, at different levels of precision and complexity. Here, to analyze encoder-decoder Transformers, we propose a simple, new method: DecoderLens. Inspired by the LogitLens (for decoder-only Transformers), this method involves allowing the decoder to cross-attend representations of intermediate encoder layers instead of using the final encoder output, as is normally done in encoder-decoder models. The method thus maps previously uninterpretable vector representations to human-interpretable sequences of words or symbols. We report results from the DecoderLens applied to models trained on question answering, logical reasoning, speech recognition and machine translation. The DecoderLens reveals several specific subtasks that are solved at low or intermediate layers, shedding new light on the information flow inside the encoder component of this important class of models.

There is a growing gap between the impressive results of deep image generative models and classical algorithms that offer theoretical guarantees. The former suffer from mode collapse or memorization issues, limiting their application to scientific data. The latter require restrictive assumptions such as log-concavity to escape the curse of dimensionality. We partially bridge this gap by introducing conditionally strongly log-concave (CSLC) models, which factorize the data distribution into a product of conditional probability distributions that are strongly log-concave. This factorization is obtained with orthogonal projectors adapted to the data distribution. It leads to efficient parameter estimation and sampling algorithms, with theoretical guarantees, although the data distribution is not globally log-concave. We show that several challenging multiscale processes are conditionally log-concave using wavelet packet orthogonal projectors. Numerical results are shown for physical fields such as the varphi^4 model and weak lensing convergence maps with higher resolution than in previous works.

We address the problem of synthesizing multi-view optical illusions: images that change appearance upon a transformation, such as a flip or rotation. We propose a simple, zero-shot method for obtaining these illusions from off-the-shelf text-to-image diffusion models. During the reverse diffusion process, we estimate the noise from different views of a noisy image, and then combine these noise estimates together and denoise the image. A theoretical analysis suggests that this method works precisely for views that can be written as orthogonal transformations, of which permutations are a subset. This leads to the idea of a visual anagram--an image that changes appearance under some rearrangement of pixels. This includes rotations and flips, but also more exotic pixel permutations such as a jigsaw rearrangement. Our approach also naturally extends to illusions with more than two views. We provide both qualitative and quantitative results demonstrating the effectiveness and flexibility of our method. Please see our project webpage for additional visualizations and results: https://dangeng.github.io/visual_anagrams/

Although contrastive learning methods have shown prevailing performance on a variety of representation learning tasks, they encounter difficulty when the training dataset is long-tailed. Many researchers have combined contrastive learning and a logit adjustment technique to address this problem, but the combinations are done ad-hoc and a theoretical background has not yet been provided. The goal of this paper is to provide the background and further improve the performance. First, we show that the fundamental reason contrastive learning methods struggle with long-tailed tasks is that they try to maximize the mutual information maximization between latent features and input data. As ground-truth labels are not considered in the maximization, they are not able to address imbalances between class labels. Rather, we interpret the long-tailed recognition task as a mutual information maximization between latent features and ground-truth labels. This approach integrates contrastive learning and logit adjustment seamlessly to derive a loss function that shows state-of-the-art performance on long-tailed recognition benchmarks. It also demonstrates its efficacy in image segmentation tasks, verifying its versatility beyond image classification.

MATSim (Multi-Agent Transport Simulation Toolkit) is an open source large-scale agent-based transportation planning project applied to various areas like road transport, public transport, freight transport, regional evacuation, etc. BEAM (Behavior, Energy, Autonomy, and Mobility) framework extends MATSim to enable powerful and scalable analysis of urban transportation systems. The agents from the BEAM simulation exhibit 'mode choice' behavior based on multinomial logit model. In our study, we consider eight mode choices viz. bike, car, walk, ride hail, driving to transit, walking to transit, ride hail to transit, and ride hail pooling. The 'alternative specific constants' for each mode choice are critical hyperparameters in a configuration file related to a particular scenario under experimentation. We use the 'Urbansim-10k' BEAM scenario (with 10,000 population size) for all our experiments. Since these hyperparameters affect the simulation in complex ways, manual calibration methods are time consuming. We present a parallel Bayesian optimization method with early stopping rule to achieve fast convergence for the given multi-in-multi-out problem to its optimal configurations. Our model is based on an open source HpBandSter package. This approach combines hierarchy of several 1D Kernel Density Estimators (KDE) with a cheap evaluator (Hyperband, a single multidimensional KDE). Our model has also incorporated extrapolation based early stopping rule. With our model, we could achieve a 25% L1 norm for a large-scale BEAM simulation in fully autonomous manner. To the best of our knowledge, our work is the first of its kind applied to large-scale multi-agent transportation simulations. This work can be useful for surrogate modeling of scenarios with very large populations.

We introduce a new class of algorithms, Stochastic Generalized Method of Moments (SGMM), for estimation and inference on (overidentified) moment restriction models. Our SGMM is a novel stochastic approximation alternative to the popular Hansen (1982) (offline) GMM, and offers fast and scalable implementation with the ability to handle streaming datasets in real time. We establish the almost sure convergence, and the (functional) central limit theorem for the inefficient online 2SLS and the efficient SGMM. Moreover, we propose online versions of the Durbin-Wu-Hausman and Sargan-Hansen tests that can be seamlessly integrated within the SGMM framework. Extensive Monte Carlo simulations show that as the sample size increases, the SGMM matches the standard (offline) GMM in terms of estimation accuracy and gains over computational efficiency, indicating its practical value for both large-scale and online datasets. We demonstrate the efficacy of our approach by a proof of concept using two well known empirical examples with large sample sizes.

We characterize the statistical efficiency of knowledge transfer through n samples from a teacher to a probabilistic student classifier with input space mathcal S over labels mathcal A. We show that privileged information at three progressive levels accelerates the transfer. At the first level, only samples with hard labels are known, via which the maximum likelihood estimator attains the minimax rate {|{mathcal S||{mathcal A}|}/{n}}. The second level has the teacher probabilities of sampled labels available in addition, which turns out to boost the convergence rate lower bound to {{|{mathcal S}||{mathcal A}|}/{n}}. However, under this second data acquisition protocol, minimizing a naive adaptation of the cross-entropy loss results in an asymptotically biased student. We overcome this limitation and achieve the fundamental limit by using a novel empirical variant of the squared error logit loss. The third level further equips the student with the soft labels (complete logits) on {mathcal A} given every sampled input, thereby provably enables the student to enjoy a rate {|{mathcal S}|}/{n} free of |{mathcal A}|. We find any Kullback-Leibler divergence minimizer to be optimal in the last case. Numerical simulations distinguish the four learners and corroborate our theory.

Online continual learning aims to continuously train neural networks from a continuous data stream with a single pass-through data. As the most effective approach, the rehearsal-based methods replay part of previous data. Commonly used predictors in existing methods tend to generate biased dot-product logits that prefer to the classes of current data, which is known as a bias issue and a phenomenon of forgetting. Many approaches have been proposed to overcome the forgetting problem by correcting the bias; however, they still need to be improved in online fashion. In this paper, we try to address the bias issue by a more straightforward and more efficient method. By decomposing the dot-product logits into an angle factor and a norm factor, we empirically find that the bias problem mainly occurs in the angle factor, which can be used to learn novel knowledge as cosine logits. On the contrary, the norm factor abandoned by existing methods helps remember historical knowledge. Based on this observation, we intuitively propose to leverage the norm factor to balance the new and old knowledge for addressing the bias. To this end, we develop a heuristic approach called unbias experience replay (UER). UER learns current samples only by the angle factor and further replays previous samples by both the norm and angle factors. Extensive experiments on three datasets show that UER achieves superior performance over various state-of-the-art methods. The code is in https://github.com/FelixHuiweiLin/UER.

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.

Neural Radiance Field (NeRF) has achieved superior performance for novel view synthesis by modeling the scene with a Multi-Layer Perception (MLP) and a volume rendering procedure, however, when fewer known views are given (i.e., few-shot view synthesis), the model is prone to overfit the given views. To handle this issue, previous efforts have been made towards leveraging learned priors or introducing additional regularizations. In contrast, in this paper, we for the first time provide an orthogonal method from the perspective of network structure. Given the observation that trivially reducing the number of model parameters alleviates the overfitting issue, but at the cost of missing details, we propose the multi-input MLP (mi-MLP) that incorporates the inputs (i.e., location and viewing direction) of the vanilla MLP into each layer to prevent the overfitting issue without harming detailed synthesis. To further reduce the artifacts, we propose to model colors and volume density separately and present two regularization terms. Extensive experiments on multiple datasets demonstrate that: 1) although the proposed mi-MLP is easy to implement, it is surprisingly effective as it boosts the PSNR of the baseline from 14.73 to 24.23. 2) the overall framework achieves state-of-the-art results on a wide range of benchmarks. We will release the code upon publication.

Finding the mode of a high dimensional probability distribution D is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when D is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known. In this work, we significantly generalize a result of (LeeLiMusco:2021) on mode approximation for Gaussian mixture models. We develop randomized dimensionality reduction methods for mixtures involving a broader class of kernels, including the popular logistic, sigmoid, and generalized Gaussian kernels. As in Lee et al.'s work, our dimensionality reduction results yield quasi-polynomial algorithms for mode finding with multiplicative accuracy (1-epsilon) for any epsilon > 0. Moreover, when combined with gradient descent, they yield efficient practical heuristics for the problem. In addition to our positive results, we prove a hardness result for box kernels, showing that there is no polynomial time algorithm for finding the mode of a kernel density estimate, unless P = NP. Obtaining similar hardness results for kernels used in practice (like Gaussian or logistic kernels) is an interesting future direction.

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on it, and finally may make a purchase; estimating the probability of purchases is difficult because of their rarity. We show both theoretically and through data experiments that the more abundant data in earlier steps may be leveraged to improve estimation of probabilities of rare events. We present PRESTO, a relaxation of the proportional odds model for ordinal regression. Instead of estimating weights for one separating hyperplane that is shifted by separate intercepts for each of the estimated Bayes decision boundaries between adjacent pairs of categorical responses, we estimate separate weights for each of these transitions. We impose an L1 penalty on the differences between weights for the same feature in adjacent weight vectors in order to shrink towards the proportional odds model. We prove that PRESTO consistently estimates the decision boundary weights under a sparsity assumption. Synthetic and real data experiments show that our method can estimate rare probabilities in this setting better than both logistic regression on the rare category, which fails to borrow strength from more abundant categories, and the proportional odds model, which is too inflexible.

It is believed that in knowledge distillation (KD), the role of the teacher is to provide an estimate for the unknown Bayes conditional probability distribution (BCPD) to be used in the student training process. Conventionally, this estimate is obtained by training the teacher using maximum log-likelihood (MLL) method. To improve this estimate for KD, in this paper we introduce the concept of conditional mutual information (CMI) into the estimation of BCPD and propose a novel estimator called the maximum CMI (MCMI) method. Specifically, in MCMI estimation, both the log-likelihood and CMI of the teacher are simultaneously maximized when the teacher is trained. Through Eigen-CAM, it is further shown that maximizing the teacher's CMI value allows the teacher to capture more contextual information in an image cluster. Via conducting a thorough set of experiments, we show that by employing a teacher trained via MCMI estimation rather than one trained via MLL estimation in various state-of-the-art KD frameworks, the student's classification accuracy consistently increases, with the gain of up to 3.32\%. This suggests that the teacher's BCPD estimate provided by MCMI method is more accurate than that provided by MLL method. In addition, we show that such improvements in the student's accuracy are more drastic in zero-shot and few-shot settings. Notably, the student's accuracy increases with the gain of up to 5.72\% when 5\% of the training samples are available to the student (few-shot), and increases from 0\% to as high as 84\% for an omitted class (zero-shot). The code is available at https://github.com/iclr2024mcmi/ICLRMCMI.

Over-parameterized deep networks trained using gradient-based optimizers are a popular choice for solving classification and ranking problems. Without appropriately tuned ell_2 regularization or weight decay, such networks have the tendency to make output scores (logits) and network weights large, causing training loss to become too small and the network to lose its adaptivity (ability to move around) in the parameter space. Although regularization is typically understood from an overfitting perspective, we highlight its role in making the network more adaptive and enabling it to escape more easily from weights that generalize poorly. To provide such a capability, we propose a method called Logit Attenuating Weight Normalization (LAWN), that can be stacked onto any gradient-based optimizer. LAWN controls the logits by constraining the weight norms of layers in the final homogeneous sub-network. Empirically, we show that the resulting LAWN variant of the optimizer makes a deep network more adaptive to finding minimas with superior generalization performance on large-scale image classification and recommender systems. While LAWN is particularly impressive in improving Adam, it greatly improves all optimizers when used with large batch sizes

Lenses are a well-established structure for modelling bidirectional transformations, such as the interactions between a database and a view of it. Lenses may be symmetric or asymmetric, and may be composed, forming the morphisms of a monoidal category. More recently, the notion of a learner has been proposed: these provide a compositional way of modelling supervised learning algorithms, and again form the morphisms of a monoidal category. In this paper, we show that the two concepts are tightly linked. We show both that there is a faithful, identity-on-objects symmetric monoidal functor embedding a category of asymmetric lenses into the category of learners, and furthermore there is such a functor embedding the category of learners into a category of symmetric lenses.

This paper proposes a new loss function for adversarial training. Since adversarial training has difficulties, e.g., necessity of high model capacity, focusing on important data points by weighting cross-entropy loss has attracted much attention. However, they are vulnerable to sophisticated attacks, e.g., Auto-Attack. This paper experimentally reveals that the cause of their vulnerability is their small margins between logits for the true label and the other labels. Since neural networks classify the data points based on the logits, logit margins should be large enough to avoid flipping the largest logit by the attacks. Importance-aware methods do not increase logit margins of important samples but decrease those of less-important samples compared with cross-entropy loss. To increase logit margins of important samples, we propose switching one-vs-the-rest loss (SOVR), which switches from cross-entropy to one-vs-the-rest loss for important samples that have small logit margins. We prove that one-vs-the-rest loss increases logit margins two times larger than the weighted cross-entropy loss for a simple problem. We experimentally confirm that SOVR increases logit margins of important samples unlike existing methods and achieves better robustness against Auto-Attack than importance-aware methods.

Gaze redirection is the task of changing the gaze to a desired direction for a given monocular eye patch image. Many applications such as videoconferencing, films, games, and generation of training data for gaze estimation require redirecting the gaze, without distorting the appearance of the area surrounding the eye and while producing photo-realistic images. Existing methods lack the ability to generate perceptually plausible images. In this work, we present a novel method to alleviate this problem by leveraging generative adversarial training to synthesize an eye image conditioned on a target gaze direction. Our method ensures perceptual similarity and consistency of synthesized images to the real images. Furthermore, a gaze estimation loss is used to control the gaze direction accurately. To attain high-quality images, we incorporate perceptual and cycle consistency losses into our architecture. In extensive evaluations we show that the proposed method outperforms state-of-the-art approaches in terms of both image quality and redirection precision. Finally, we show that generated images can bring significant improvement for the gaze estimation task if used to augment real training data.

Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often involves non-convex and high-dimensional objective functions, imposing difficult computational and statistical challenges. The classic expectation-maximization (EM) algorithm is a computationally thrifty iterative method that maximizes a surrogate function minorizing the log-likelihood of observed data in each iteration, which however suffers from bad local maxima even in the special case of the standard Gaussian mixture model with common isotropic covariance matrices. On the other hand, recent studies reveal that the unique global solution of a semidefinite programming (SDP) relaxed K-means achieves the information-theoretically sharp threshold for perfectly recovering the cluster labels under the standard Gaussian mixture model. In this paper, we extend the SDP approach to a general setting by integrating cluster labels as model parameters and propose an iterative likelihood adjusted SDP (iLA-SDP) method that directly maximizes the exact observed likelihood in the presence of data heterogeneity. By lifting the cluster assignment to group-specific membership matrices, iLA-SDP avoids centroids estimation -- a key feature that allows exact recovery under well-separateness of centroids without being trapped by their adversarial configurations. Thus iLA-SDP is less sensitive than EM to initialization and more stable on high-dimensional data. Our numeric experiments demonstrate that iLA-SDP can achieve lower mis-clustering errors over several widely used clustering methods including K-means, SDP and EM algorithms.

Post-hoc out-of-distribution (OOD) detection has garnered intensive attention in reliable machine learning. Many efforts have been dedicated to deriving score functions based on logits, distances, or rigorous data distribution assumptions to identify low-scoring OOD samples. Nevertheless, these estimate scores may fail to accurately reflect the true data density or impose impractical constraints. To provide a unified perspective on density-based score design, we propose a novel theoretical framework grounded in Bregman divergence, which extends distribution considerations to encompass an exponential family of distributions. Leveraging the conjugation constraint revealed in our theorem, we introduce a ConjNorm method, reframing density function design as a search for the optimal norm coefficient p against the given dataset. In light of the computational challenges of normalization, we devise an unbiased and analytically tractable estimator of the partition function using the Monte Carlo-based importance sampling technique. Extensive experiments across OOD detection benchmarks empirically demonstrate that our proposed ConjNorm has established a new state-of-the-art in a variety of OOD detection setups, outperforming the current best method by up to 13.25% and 28.19% (FPR95) on CIFAR-100 and ImageNet-1K, respectively.

We study the problem of estimating the time delay between two signals representing delayed, irregularly sampled and noisy versions of the same underlying pattern. We propose and demonstrate an evolutionary algorithm for the (hyper)parameter estimation of a kernel-based technique in the context of an astronomical problem, namely estimating the time delay between two gravitationally lensed signals from a distant quasar. Mixed types (integer and real) are used to represent variables within the evolutionary algorithm. We test the algorithm on several artificial data sets, and also on real astronomical observations of quasar Q0957+561. By carrying out a statistical analysis of the results we present a detailed comparison of our method with the most popular methods for time delay estimation in astrophysics. Our method yields more accurate and more stable time delay estimates: for Q0957+561, we obtain 419.6 days for the time delay between images A and B. Our methodology can be readily applied to current state-of-the-art optical monitoring data in astronomy, but can also be applied in other disciplines involving similar time series data.

A sample of 60,410 bona fide optical quasars with astrometric proper motions in Gaia EDR3 and spectroscopic redshifts above 0.5 in an oval 8400 square degree area of the sky is constructed. Using orthogonal Zernike functions of polar coordinates, the proper motion fields are fitted in a weighted least-squares adjustment of the entire sample and of six equal bins of sorted redshifts. The overall fit with 37 Zernike functions reveals a statistically significant pattern, which is likely to be of instrumental origin. The main feature of this pattern is a chain of peaks and dips mostly in the R.A. component with an amplitude of 25~muas yr^{-1}. This field is subtracted from each of the six analogous fits for quasars grouped by redshifts covering the range 0.5 through 7.03, with median values 0.72, 1.00, 1.25, 1.52, 1.83, 2.34. The resulting residual patterns are noisier, with formal uncertainties up to 8~muas yr^{-1} in the central part of the area. We detect a single high-confidence Zernike term for R.A. proper motion components of quasars with redshifts around 1.52 representing a general gradient of 30 muas yr^{-1} over 150degr on the sky. We do not find any small- or medium-scale systemic variations of the residual proper motion field as functions of redshift above the 2.5,sigma significance level.

Single-view novel view synthesis, the task of generating images from new viewpoints based on a single reference image, is an important but challenging task in computer vision. Recently, Denoising Diffusion Probabilistic Model (DDPM) has become popular in this area due to its strong ability to generate high-fidelity images. However, current diffusion-based methods directly rely on camera pose matrices as viewing conditions, globally and implicitly introducing 3D constraints. These methods may suffer from inconsistency among generated images from different perspectives, especially in regions with intricate textures and structures. In this work, we present Light Field Diffusion (LFD), a conditional diffusion-based model for single-view novel view synthesis. Unlike previous methods that employ camera pose matrices, LFD transforms the camera view information into light field encoding and combines it with the reference image. This design introduces local pixel-wise constraints within the diffusion models, thereby encouraging better multi-view consistency. Experiments on several datasets show that our LFD can efficiently generate high-fidelity images and maintain better 3D consistency even in intricate regions. Our method can generate images with higher quality than NeRF-based models, and we obtain sample quality similar to other diffusion-based models but with only one-third of the model size.

This paper extends the classic theory of convex optimization to the minimization of functions that are equal to the negated logarithm of what we term as a sum-log-concave function, i.e., a sum of log-concave functions. In particular, we show that such functions are in general not convex but still satisfy generalized convexity inequalities. These inequalities unveil the key importance of a certain vector that we call the cross-gradient and that is, in general, distinct from the usual gradient. Thus, we propose the Cross Gradient Descent (XGD) algorithm moving in the opposite direction of the cross-gradient and derive a convergence analysis. As an application of our sum-log-concave framework, we introduce the so-called checkered regression method relying on a sum-log-concave function. This classifier extends (multiclass) logistic regression to non-linearly separable problems since it is capable of tessellating the feature space by using any given number of hyperplanes, creating a checkerboard-like pattern of decision regions.

While likelihood-based generative models, particularly diffusion and autoregressive models, have achieved remarkable fidelity in visual generation, the maximum likelihood estimation (MLE) objective inherently suffers from a mode-covering tendency that limits the generation quality under limited model capacity. In this work, we propose Direct Discriminative Optimization (DDO) as a unified framework that bridges likelihood-based generative training and the GAN objective to bypass this fundamental constraint. Our key insight is to parameterize a discriminator implicitly using the likelihood ratio between a learnable target model and a fixed reference model, drawing parallels with the philosophy of Direct Preference Optimization (DPO). Unlike GANs, this parameterization eliminates the need for joint training of generator and discriminator networks, allowing for direct, efficient, and effective finetuning of a well-trained model to its full potential beyond the limits of MLE. DDO can be performed iteratively in a self-play manner for progressive model refinement, with each round requiring less than 1% of pretraining epochs. Our experiments demonstrate the effectiveness of DDO by significantly advancing the previous SOTA diffusion model EDM, reducing FID scores from 1.79/1.58 to new records of 1.30/0.97 on CIFAR-10/ImageNet-64 datasets, and by consistently improving both guidance-free and CFG-enhanced FIDs of visual autoregressive models on ImageNet 256times256.

In observational studies, balancing covariates in different treatment groups is essential to estimate treatment effects. One of the most commonly used methods for such purposes is weighting. The performance of this class of methods usually depends on strong regularity conditions for the underlying model, which might not hold in practice. In this paper, we investigate weighting methods from a functional estimation perspective and argue that the weights needed for covariate balancing could differ from those needed for treatment effects estimation under low regularity conditions. Motivated by this observation, we introduce a new framework of weighting that directly targets the treatment effects estimation. Unlike existing methods, the resulting estimator for a treatment effect under this new framework is a simple kernel-based U-statistic after applying a data-driven transformation to the observed covariates. We characterize the theoretical properties of the new estimators of treatment effects under a nonparametric setting and show that they are able to work robustly under low regularity conditions. The new framework is also applied to several numerical examples to demonstrate its practical merits.

Automated model selection is often proposed to users to choose which machine learning model (or method) to apply to a given regression task. In this paper, we show that combining different regression models can yield better results than selecting a single ('best') regression model, and outline an efficient method that obtains optimally weighted convex linear combination from a heterogeneous set of regression models. More specifically, in this paper, a heuristic weight optimization, used in a preceding conference paper, is replaced by an exact optimization algorithm using convex quadratic programming. We prove convexity of the quadratic programming formulation for the straightforward formulation and for a formulation with weighted data points. The novel weight optimization is not only (more) exact but also more efficient. The methods we develop in this paper are implemented and made available via github-open source. They can be executed on commonly available hardware and offer a transparent and easy to interpret interface. The results indicate that the approach outperforms model selection methods on a range of data sets, including data sets with mixed variable type from drug discovery applications.

When asked to summarize articles or answer questions given a passage, large language models (LLMs) can hallucinate details and respond with unsubstantiated answers that are inaccurate with respect to the input context. This paper describes a simple approach for detecting such contextual hallucinations. We hypothesize that contextual hallucinations are related to the extent to which an LLM attends to information in the provided context versus its own generations. Based on this intuition, we propose a simple hallucination detection model whose input features are given by the ratio of attention weights on the context versus newly generated tokens (for each attention head). We find that a linear classifier based on these lookback ratio features is as effective as a richer detector that utilizes the entire hidden states of an LLM or a text-based entailment model. The lookback ratio-based detector -- Lookback Lens -- is found to transfer across tasks and even models, allowing a detector that is trained on a 7B model to be applied (without retraining) to a larger 13B model. We further apply this detector to mitigate contextual hallucinations, and find that a simple classifier-guided decoding approach is able to reduce the amount of hallucination, for example by 9.6% in the XSum summarization task.

We study preferential Bayesian optimization (BO) where reliable feedback is limited to pairwise comparison called duels. An important challenge in preferential BO, which uses the preferential Gaussian process (GP) model to represent flexible preference structure, is that the posterior distribution is a computationally intractable skew GP. The most widely used approach for preferential BO is Gaussian approximation, which ignores the skewness of the true posterior. Alternatively, Markov chain Monte Carlo (MCMC) based preferential BO is also proposed. In this work, we first verify the accuracy of Gaussian approximation, from which we reveal the critical problem that the predictive probability of duels can be inaccurate. This observation motivates us to improve the MCMC-based estimation for skew GP, for which we show the practical efficiency of Gibbs sampling and derive the low variance MC estimator. However, the computational time of MCMC can still be a bottleneck in practice. Towards building a more practical preferential BO, we develop a new method that achieves both high computational efficiency and low sample complexity, and then demonstrate its effectiveness through extensive numerical experiments.

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

Considering the increased workload in pathology laboratories today, automated tools such as artificial intelligence models can help pathologists with their tasks and ease the workload. In this paper, we are proposing a segmentation model (DRU-Net) that can provide a delineation of human non-small cell lung carcinomas and an augmentation method that can improve classification results. The proposed model is a fused combination of truncated pre-trained DenseNet201 and ResNet101V2 as a patch-wise classifier followed by a lightweight U-Net as a refinement model. We have used two datasets (Norwegian Lung Cancer Biobank and Haukeland University Hospital lung cancer cohort) to create our proposed model. The DRU-Net model achieves an average of 0.91 Dice similarity coefficient. The proposed spatial augmentation method (multi-lens distortion) improved the network performance by 3%. Our findings show that choosing image patches that specifically include regions of interest leads to better results for the patch-wise classifier compared to other sampling methods. The qualitative analysis showed that the DRU-Net model is generally successful in detecting the tumor. On the test set, some of the cases showed areas of false positive and false negative segmentation in the periphery, particularly in tumors with inflammatory and reactive changes.

We revisit the flat-sky approximation for evaluating the angular power spectra of projected random fields by retaining information about the correlations along the line of sight. With broad, overlapping radial window functions, these line-of-sight correlations are suppressed and are ignored in the Limber approximation. However, retaining the correlations is important for narrow window functions or unequal-time spectra but introduces significant computational difficulties due to the highly oscillatory nature of the integrands involved. We deal with the integral over line-of-sight wave-modes in the flat-sky approximation analytically, using the FFTlog expansion of the 3D power spectrum. This results in an efficient computational method, which is a substantial improvement compared to any full-sky approaches. We apply our results to galaxy clustering (with and without redshift-space distortions), CMB lensing and galaxy lensing observables. For clustering, we find excellent agreement with the full-sky results on large (percent-level agreement) and intermediate or small (subpercent agreement) scales, dramatically out-performing the Limber approximation for both wide and narrow window functions, and in equal- and unequal-time cases. In the case of lensing, we show on the full sky that the angular power spectrum of the convergence can be very well approximated by projecting the 3D Laplacian (rather than the correct angular Laplacian) of the gravitational potential, even on large scales. Combining this approximation with our flat-sky techniques provides an efficient and accurate evaluation of the CMB lensing angular power spectrum on all scales.

We consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this end, we propose an algorithm referred to as Pessimistic ASsortment opTimizAtion (PASTA for short) designed based on the principle of pessimism, that can correctly identify the optimal assortment by only requiring the offline data to cover the optimal assortment under general settings. In particular, we establish a regret bound for the offline assortment optimization problem under the celebrated multinomial logit model. We also propose an efficient computational procedure to solve our pessimistic assortment optimization problem. Numerical studies demonstrate the superiority of the proposed method over the existing baseline method.

Several popular computer vision (CV) datasets, specifically employed for Object Detection (OD) in autonomous driving tasks exhibit biases due to a range of factors including weather and lighting conditions. These biases may impair a model's generalizability, rendering it ineffective for OD in novel and unseen datasets. Especially, in autonomous driving, it may prove extremely high risk and unsafe for the vehicle and its surroundings. This work focuses on understanding these datasets better by identifying such "good-weather" bias. Methods to mitigate such bias which allows the OD models to perform better and improve the robustness are also demonstrated. A simple yet effective OD framework for studying bias mitigation is proposed. Using this framework, the performance on popular datasets is analyzed and a significant difference in model performance is observed. Additionally, a knowledge transfer technique and a synthetic image corruption technique are proposed to mitigate the identified bias. Finally, using the DAWN dataset, the findings are validated on the OD task, demonstrating the effectiveness of our techniques in mitigating real-world "good-weather" bias. The experiments show that the proposed techniques outperform baseline methods by averaged fourfold improvement.

Backward Filtering Forward Guiding (BFFG) is a bidirectional algorithm proposed in Mider et al. [2021] and studied more in depth in a general setting in Van der Meulen and Schauer [2022]. In category theory, optics have been proposed for modelling systems with bidirectional data flow. We connect BFFG with optics and prove that different ways of composing the building blocks of BFFG correspond to equivalent optics.

This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear system Atheta = b for which A and b can only be accessed through random estimates {({bf A}_n, {bf b}_n): n in N^*}. Our analysis is based on new results regarding moments and high probability bounds for products of matrices which are shown to be tight. We derive high probability bounds on the performance of LSA under weaker conditions on the sequence {({bf A}_n, {bf b}_n): n in N^*} than previous works. However, in contrast, we establish polynomial concentration bounds with order depending on the stepsize. We show that our conclusions cannot be improved without additional assumptions on the sequence of random matrices {{bf A}_n: n in N^*}, and in particular that no Gaussian or exponential high probability bounds can hold. Finally, we pay a particular attention to establishing bounds with sharp order with respect to the number of iterations and the stepsize and whose leading terms contain the covariance matrices appearing in the central limit theorems.

Counterfactual explanations is one of the post-hoc methods used to provide explainability to machine learning models that have been attracting attention in recent years. Most examples in the literature, address the problem of generating post-hoc explanations for black-box machine learning models after the rejection of a loan application. In contrast, in this work, we investigate mathematical programming formulations for scorecard models, a type of interpretable model predominant within the banking industry for lending. The proposed mixed-integer programming formulations combine objective functions to ensure close, realistic and sparse counterfactuals using multi-objective optimization techniques for a binary, probability or continuous outcome. Moreover, we extend these formulations to generate multiple optimal counterfactuals simultaneously while guaranteeing diversity. Experiments on two real-world datasets confirm that the presented approach can generate optimal diverse counterfactuals addressing desired properties with assumable CPU times for practice use.

We investigate the theoretical foundations of classifier-free guidance (CFG). CFG is the dominant method of conditional sampling for text-to-image diffusion models, yet unlike other aspects of diffusion, it remains on shaky theoretical footing. In this paper, we disprove common misconceptions, by showing that CFG interacts differently with DDPM (Ho et al., 2020) and DDIM (Song et al., 2021), and neither sampler with CFG generates the gamma-powered distribution p(x|c)^gamma p(x)^{1-gamma}. Then, we clarify the behavior of CFG by showing that it is a kind of predictor-corrector method (Song et al., 2020) that alternates between denoising and sharpening, which we call predictor-corrector guidance (PCG). We prove that in the SDE limit, CFG is actually equivalent to combining a DDIM predictor for the conditional distribution together with a Langevin dynamics corrector for a gamma-powered distribution (with a carefully chosen gamma). Our work thus provides a lens to theoretically understand CFG by embedding it in a broader design space of principled sampling methods.

Building 3D perception systems for autonomous vehicles that do not rely on high-density LiDAR is a critical research problem because of the expense of LiDAR systems compared to cameras and other sensors. Recent research has developed a variety of camera-only methods, where features are differentiably "lifted" from the multi-camera images onto the 2D ground plane, yielding a "bird's eye view" (BEV) feature representation of the 3D space around the vehicle. This line of work has produced a variety of novel "lifting" methods, but we observe that other details in the training setups have shifted at the same time, making it unclear what really matters in top-performing methods. We also observe that using cameras alone is not a real-world constraint, considering that additional sensors like radar have been integrated into real vehicles for years already. In this paper, we first of all attempt to elucidate the high-impact factors in the design and training protocol of BEV perception models. We find that batch size and input resolution greatly affect performance, while lifting strategies have a more modest effect -- even a simple parameter-free lifter works well. Second, we demonstrate that radar data can provide a substantial boost to performance, helping to close the gap between camera-only and LiDAR-enabled systems. We analyze the radar usage details that lead to good performance, and invite the community to re-consider this commonly-neglected part of the sensor platform.

Machine learning (ML) holds great potential for accurately forecasting treatment outcomes over time, which could ultimately enable the adoption of more individualized treatment strategies in many practical applications. However, a significant challenge that has been largely overlooked by the ML literature on this topic is the presence of informative sampling in observational data. When instances are observed irregularly over time, sampling times are typically not random, but rather informative -- depending on the instance's characteristics, past outcomes, and administered treatments. In this work, we formalize informative sampling as a covariate shift problem and show that it can prohibit accurate estimation of treatment outcomes if not properly accounted for. To overcome this challenge, we present a general framework for learning treatment outcomes in the presence of informative sampling using inverse intensity-weighting, and propose a novel method, TESAR-CDE, that instantiates this framework using Neural CDEs. Using a simulation environment based on a clinical use case, we demonstrate the effectiveness of our approach in learning under informative sampling.

Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are fine-tuned for the application at hand. Although this tuning process can require large computational costs, recent work has shown that these costs can be reduced by line search methods that iteratively adjust the stepsize. We propose an alternative approach to stochastic line search by using a new algorithm based on forward step model building. This model building step incorporates second-order information that allows adjusting not only the stepsize but also the search direction. Noting that deep learning model parameters come in groups (layers of tensors), our method builds its model and calculates a new step for each parameter group. This novel diagonalization approach makes the selected step lengths adaptive. We provide convergence rate analysis, and experimentally show that the proposed algorithm achieves faster convergence and better generalization in well-known test problems. More precisely, SMB requires less tuning, and shows comparable performance to other adaptive methods.

Denoisers play a central role in many applications, from noise suppression in low-grade imaging sensors, to empowering score-based generative models. The latter category of methods makes use of Tweedie's formula, which links the posterior mean in Gaussian denoising (\ie the minimum MSE denoiser) with the score of the data distribution. Here, we derive a fundamental relation between the higher-order central moments of the posterior distribution, and the higher-order derivatives of the posterior mean. We harness this result for uncertainty quantification of pre-trained denoisers. Particularly, we show how to efficiently compute the principal components of the posterior distribution for any desired region of an image, as well as to approximate the full marginal distribution along those (or any other) one-dimensional directions. Our method is fast and memory-efficient, as it does not explicitly compute or store the high-order moment tensors and it requires no training or fine tuning of the denoiser. Code and examples are available on the project webpage in https://hilamanor.github.io/GaussianDenoisingPosterior/ .

While diffusion models can learn complex distributions, sampling requires a computationally expensive iterative process. Existing distillation methods enable efficient sampling, but have notable limitations, such as performance degradation with very few sampling steps, reliance on training data access, or mode-seeking optimization that may fail to capture the full distribution. We propose EM Distillation (EMD), a maximum likelihood-based approach that distills a diffusion model to a one-step generator model with minimal loss of perceptual quality. Our approach is derived through the lens of Expectation-Maximization (EM), where the generator parameters are updated using samples from the joint distribution of the diffusion teacher prior and inferred generator latents. We develop a reparametrized sampling scheme and a noise cancellation technique that together stabilizes the distillation process. We further reveal an interesting connection of our method with existing methods that minimize mode-seeking KL. EMD outperforms existing one-step generative methods in terms of FID scores on ImageNet-64 and ImageNet-128, and compares favorably with prior work on distilling text-to-image diffusion models.

We present a new methodology for detecting out-of-distribution (OOD) images by utilizing norms of the score estimates at multiple noise scales. A score is defined to be the gradient of the log density with respect to the input data. Our methodology is completely unsupervised and follows a straight forward training scheme. First, we train a deep network to estimate scores for levels of noise. Once trained, we calculate the noisy score estimates for N in-distribution samples and take the L2-norms across the input dimensions (resulting in an NxL matrix). Then we train an auxiliary model (such as a Gaussian Mixture Model) to learn the in-distribution spatial regions in this L-dimensional space. This auxiliary model can now be used to identify points that reside outside the learned space. Despite its simplicity, our experiments show that this methodology significantly outperforms the state-of-the-art in detecting out-of-distribution images. For example, our method can effectively separate CIFAR-10 (inlier) and SVHN (OOD) images, a setting which has been previously shown to be difficult for deep likelihood models.

We describe a novel attribution method which is grounded in Sensitivity Analysis and uses Sobol indices. Beyond modeling the individual contributions of image regions, Sobol indices provide an efficient way to capture higher-order interactions between image regions and their contributions to a neural network's prediction through the lens of variance. We describe an approach that makes the computation of these indices efficient for high-dimensional problems by using perturbation masks coupled with efficient estimators to handle the high dimensionality of images. Importantly, we show that the proposed method leads to favorable scores on standard benchmarks for vision (and language models) while drastically reducing the computing time compared to other black-box methods -- even surpassing the accuracy of state-of-the-art white-box methods which require access to internal representations. Our code is freely available: https://github.com/fel-thomas/Sobol-Attribution-Method

There is a long history, as well as a recent explosion of interest, in statistical and generative modeling approaches based on score functions -- derivatives of the log-likelihood of a distribution. In seminal works, Hyv\"arinen proposed vanilla score matching as a way to learn distributions from data by computing an estimate of the score function of the underlying ground truth, and established connections between this method and established techniques like Contrastive Divergence and Pseudolikelihood estimation. It is by now well-known that vanilla score matching has significant difficulties learning multimodal distributions. Although there are various ways to overcome this difficulty, the following question has remained unanswered -- is there a natural way to sample multimodal distributions using just the vanilla score? Inspired by a long line of related experimental works, we prove that the Langevin diffusion with early stopping, initialized at the empirical distribution, and run on a score function estimated from data successfully generates natural multimodal distributions (mixtures of log-concave distributions).

Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension. By updating the directional and radial components of chain iterates separately, we obtain a family of samplers that mimic polar slice sampling, and yet can be implemented efficiently. Numerical experiments in a variety of settings indicate that our proposed algorithm outperforms the two most closely related approaches, elliptical slice sampling (Murray et al., 2010) and hit-and-run uniform slice sampling (MacKay, 2003). We prove the well-definedness and convergence of our methods under suitable assumptions on the target distribution.

For observational studies, we study the sensitivity of causal inference when treatment assignments may depend on unobserved confounders. We develop a loss minimization approach for estimating bounds on the conditional average treatment effect (CATE) when unobserved confounders have a bounded effect on the odds ratio of treatment selection. Our approach is scalable and allows flexible use of model classes in estimation, including nonparametric and black-box machine learning methods. Based on these bounds for the CATE, we propose a sensitivity analysis for the average treatment effect (ATE). Our semi-parametric estimator extends/bounds the augmented inverse propensity weighted (AIPW) estimator for the ATE under bounded unobserved confounding. By constructing a Neyman orthogonal score, our estimator of the bound for the ATE is a regular root-n estimator so long as the nuisance parameters are estimated at the o_p(n^{-1/4}) rate. We complement our methodology with optimality results showing that our proposed bounds are tight in certain cases. We demonstrate our method on simulated and real data examples, and show accurate coverage of our confidence intervals in practical finite sample regimes with rich covariate information.

Climbing grades are used to classify a climbing route based on its perceived difficulty, and have come to play a central role in the sport of rock climbing. Recently, the first statistically rigorous method for estimating climbing grades from whole-history ascent data was described, based on the dynamic Bradley-Terry model for games between players of time-varying ability. In this paper, we implement inference under the whole-history rating model using Markov chain Monte Carlo and apply the method to a curated data set made up of climbers who climb regularly. We use these data to get an estimate of the model's fundamental scale parameter m, which defines the proportional increase in difficulty associated with an increment of grade. We show that the data conform to assumptions that the climbing grade scale is a logarithmic scale of difficulty, like decibels or stellar magnitude. We estimate that an increment in Ewbank, French and UIAA climbing grade systems corresponds to 2.1, 2.09 and 2.13 times increase in difficulty respectively, assuming a logistic model of probability of success as a function of grade. Whereas we find that the Vermin scale for bouldering (V-grade scale) corresponds to a 3.17 increase in difficulty per grade increment. In addition, we highlight potential connections between the logarithmic properties of climbing grade scales and the psychophysical laws of Weber and Fechner.

This paper presents a novel preconditioning strategy for the classic 8-point algorithm (8-PA) for estimating an essential matrix from 360-FoV images (i.e., equirectangular images) in spherical projection. To alleviate the effect of uneven key-feature distributions and outlier correspondences, which can potentially decrease the accuracy of an essential matrix, our method optimizes a non-rigid transformation to deform a spherical camera into a new spatial domain, defining a new constraint and a more robust and accurate solution for an essential matrix. Through several experiments using random synthetic points, 360-FoV, and fish-eye images, we demonstrate that our normalization can increase the camera pose accuracy by about 20% without significantly overhead the computation time. In addition, we present further benefits of our method through both a constant weighted least-square optimization that improves further the well known Gold Standard Method (GSM) (i.e., the non-linear optimization by using epipolar errors); and a relaxation of the number of RANSAC iterations, both showing that our normalization outcomes a more reliable, robust, and accurate solution.

Optics and lenses are abstract categorical gadgets that model systems with bidirectional data flow. In this paper we observe that the denotational definition of optics - identifying two optics as equivalent by observing their behaviour from the outside - is not suitable for operational, software oriented approaches where optics are not merely observed, but built with their internal setups in mind. We identify operational differences between denotationally isomorphic categories of cartesian optics and lenses: their different composition rule and corresponding space-time tradeoffs, positioning them at two opposite ends of a spectrum. With these motivations we lift the existing categorical constructions and their relationships to the 2-categorical level, showing that the relevant operational concerns become visible. We define the 2-category 2-Optic(C) whose 2-cells explicitly track optics' internal configuration. We show that the 1-category Optic(C) arises by locally quotienting out the connected components of this 2-category. We show that the embedding of lenses into cartesian optics gets weakened from a functor to an oplax functor whose oplaxator now detects the different composition rule. We determine the difficulties in showing this functor forms a part of an adjunction in any of the standard 2-categories. We establish a conjecture that the well-known isomorphism between cartesian lenses and optics arises out of the lax 2-adjunction between their double-categorical counterparts. In addition to presenting new research, this paper is also meant to be an accessible introduction to the topic.

In this paper, we present a self-calibrating framework that jointly optimizes camera parameters, lens distortion and 3D Gaussian representations, enabling accurate and efficient scene reconstruction. In particular, our technique enables high-quality scene reconstruction from Large field-of-view (FOV) imagery taken with wide-angle lenses, allowing the scene to be modeled from a smaller number of images. Our approach introduces a novel method for modeling complex lens distortions using a hybrid network that combines invertible residual networks with explicit grids. This design effectively regularizes the optimization process, achieving greater accuracy than conventional camera models. Additionally, we propose a cubemap-based resampling strategy to support large FOV images without sacrificing resolution or introducing distortion artifacts. Our method is compatible with the fast rasterization of Gaussian Splatting, adaptable to a wide variety of camera lens distortion, and demonstrates state-of-the-art performance on both synthetic and real-world datasets.

In this work we propose a blackbox intervention method for visual dialog models, with the aim of assessing the contribution of individual linguistic or visual components. Concretely, we conduct structured or randomized interventions that aim to impair an individual component of the model, and observe changes in task performance. We reproduce a state-of-the-art visual dialog model and demonstrate that our methodology yields surprising insights, namely that both dialog and image information have minimal contributions to task performance. The intervention method presented here can be applied as a sanity check for the strength and robustness of each component in visual dialog systems.

The recent trend towards Personalized Federated Learning (PFL) has garnered significant attention as it allows for the training of models that are tailored to each client while maintaining data privacy. However, current PFL techniques primarily focus on modeling the conditional distribution heterogeneity (i.e. concept shift), which can result in suboptimal performance when the distribution of input data across clients diverges (i.e. covariate shift). Additionally, these techniques often lack the ability to adapt to unseen data, further limiting their effectiveness in real-world scenarios. To address these limitations, we propose a novel approach, FedGMM, which utilizes Gaussian mixture models (GMM) to effectively fit the input data distributions across diverse clients. The model parameters are estimated by maximum likelihood estimation utilizing a federated Expectation-Maximization algorithm, which is solved in closed form and does not assume gradient similarity. Furthermore, FedGMM possesses an additional advantage of adapting to new clients with minimal overhead, and it also enables uncertainty quantification. Empirical evaluations on synthetic and benchmark datasets demonstrate the superior performance of our method in both PFL classification and novel sample detection.

The 3D Gaussian Splatting (3DGS) gained its popularity recently by combining the advantages of both primitive-based and volumetric 3D representations, resulting in improved quality and efficiency for 3D scene rendering. However, 3DGS is not alias-free, and its rendering at varying resolutions could produce severe blurring or jaggies. This is because 3DGS treats each pixel as an isolated, single point rather than as an area, causing insensitivity to changes in the footprints of pixels. Consequently, this discrete sampling scheme inevitably results in aliasing, owing to the restricted sampling bandwidth. In this paper, we derive an analytical solution to address this issue. More specifically, we use a conditioned logistic function as the analytic approximation of the cumulative distribution function (CDF) in a one-dimensional Gaussian signal and calculate the Gaussian integral by subtracting the CDFs. We then introduce this approximation in the two-dimensional pixel shading, and present Analytic-Splatting, which analytically approximates the Gaussian integral within the 2D-pixel window area to better capture the intensity response of each pixel. Moreover, we use the approximated response of the pixel window integral area to participate in the transmittance calculation of volume rendering, making Analytic-Splatting sensitive to the changes in pixel footprint at different resolutions. Experiments on various datasets validate that our approach has better anti-aliasing capability that gives more details and better fidelity.

Many social and environmental phenomena are associated with macroscopic changes in the built environment, captured by satellite imagery on a global scale and with daily temporal resolution. While widely used for prediction, these images and especially image sequences remain underutilized for causal inference, especially in the context of randomized controlled trials (RCTs), where causal identification is established by design. In this paper, we develop and compare a set of general tools for analyzing Conditional Average Treatment Effects (CATEs) from temporal satellite data that can be applied to any RCT where geographical identifiers are available. Through a simulation study, we analyze different modeling strategies for estimating CATE in sequences of satellite images. We find that image sequence representation models with more parameters generally yield a greater ability to detect heterogeneity. To explore the role of model and data choice in practice, we apply the approaches to two influential RCTs -- Banerjee et al. (2015), a poverty study in Cusco, Peru, and Bolsen et al. (2014), a water conservation experiment in Georgia, USA. We benchmark our image sequence models against image-only, tabular-only, and combined image-tabular data sources, summarizing practical implications for investigators in a multivariate analysis. Land cover classifications over satellite images facilitate interpretation of what image features drive heterogeneity. We also show robustness to data and model choice of satellite-based generalization of the RCT results to larger geographical areas outside the original. Overall, this paper shows how satellite sequence data can be incorporated into the analysis of RCTs, and provides evidence about the implications of data, model, and evaluation metric choice for causal analysis.

Despite the recent advances in the field of computational Schr\"odinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal solver which plays the role of simple-yet-effective baseline for SB just like, e.g., k-means method in clustering, logistic regression in classification or Sinkhorn algorithm in discrete optimal transport. We address this issue and propose a novel fast and simple SB solver. Our development is a smart combination of two ideas which recently appeared in the field: (a) parameterization of the Schr\"odinger potentials with sum-exp quadratic functions and (b) viewing the log-Schr\"odinger potentials as the energy functions. We show that combined together these ideas yield a lightweight, simulation-free and theoretically justified SB solver with a simple straightforward optimization objective. As a result, it allows solving SB in moderate dimensions in a matter of minutes on CPU without a painful hyperparameter selection. Our light solver resembles the Gaussian mixture model which is widely used for density estimation. Inspired by this similarity, we also prove an important theoretical result showing that our light solver is a universal approximator of SBs. Furthemore, we conduct the analysis of the generalization error of our light solver. The code for our solver can be found at https://github.com/ngushchin/LightSB

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

Geolocating images of a ground-level scene entails estimating the location on Earth where the picture was taken, in absence of GPS or other location metadata. Typically, methods are evaluated by measuring the Great Circle Distance (GCD) between a predicted location and ground truth. However, this measurement is limited because it only evaluates a single point, not estimates of regions or score heatmaps. This is especially important in applications to rural, wilderness and under-sampled areas, where finding the exact location may not be possible, and when used in aggregate systems that progressively narrow down locations. In this paper, we introduce a novel metric, Recall vs Area (RvA), which measures the accuracy of estimated distributions of locations. RvA treats image geolocation results similarly to document retrieval, measuring recall as a function of area: For a ranked list of (possibly non-contiguous) predicted regions, we measure the accumulated area required for the region to contain the ground truth coordinate. This produces a curve similar to a precision-recall curve, where "precision" is replaced by square kilometers area, allowing evaluation of performance for different downstream search area budgets. Following directly from this view of the problem, we then examine a simple ensembling approach to global-scale image geolocation, which incorporates information from multiple sources to help address domain shift, and can readily incorporate multiple models, attribute predictors, and data sources. We study its effectiveness by combining the geolocation models GeoEstimation and the current SOTA GeoCLIP, with attribute predictors based on ORNL LandScan and ESA-CCI Land Cover. We find significant improvements in image geolocation for areas that are under-represented in the training set, particularly non-urban areas, on both Im2GPS3k and Street View images.

In this research, we compare four different evaluation methods in coevolution on the Majority Function problem. The size of the problem is selected such that evaluation against all possible test cases is feasible. Two measures are used for the comparisons, i.e., the objective fitness derived from evaluating solutions against all test cases, and the objective fitness correlation (OFC), which is defined as the correlation coefficient between subjective and objective fitness. The results of our experiments suggest that a combination of average score and weighted informativeness may provide a more accurate evaluation in coevolution. In order to confirm this difference, a series of t-tests on the preference between each pair of the evaluation methods is performed. The resulting significance is affirmative, and the tests for two quality measures show similar preference on four evaluation methods. %This study is the first time OFC is actually computed on a real problem. Experiments on Majority Function problems with larger sizes and Parity problems are in progress, and their results will be added in the final version.

Training state-of-the-art vision models has become prohibitively expensive for researchers and practitioners. For the sake of accessibility and resource reuse, it is important to focus on adapting these models to a variety of downstream scenarios. An interesting and practical paradigm is online test-time adaptation, according to which training data is inaccessible, no labelled data from the test distribution is available, and adaptation can only happen at test time and on a handful of samples. In this paper, we investigate how test-time adaptation methods fare for a number of pre-trained models on a variety of real-world scenarios, significantly extending the way they have been originally evaluated. We show that they perform well only in narrowly-defined experimental setups and sometimes fail catastrophically when their hyperparameters are not selected for the same scenario in which they are being tested. Motivated by the inherent uncertainty around the conditions that will ultimately be encountered at test time, we propose a particularly "conservative" approach, which addresses the problem with a Laplacian Adjusted Maximum-likelihood Estimation (LAME) objective. By adapting the model's output (not its parameters), and solving our objective with an efficient concave-convex procedure, our approach exhibits a much higher average accuracy across scenarios than existing methods, while being notably faster and have a much lower memory footprint. The code is available at https://github.com/fiveai/LAME.

This study addresses the issue observed in Large Vision Language Models (LVLMs), where excessive attention on a few image tokens, referred to as blind tokens, leads to hallucinatory responses in tasks requiring fine-grained understanding of visual objects. We found that tokens receiving lower attention weights often hold essential information for identifying nuanced object details -- ranging from merely recognizing object existence to identifying their attributes (color, position, etc.) and understanding their relationships. To counteract the over-emphasis on blind tokens and to accurately respond to user queries, we introduce a technique called Attentional Vision Calibration (AVC). During the decoding phase, AVC identifies blind tokens by analyzing the image-related attention distribution. It then dynamically adjusts the logits for the next token prediction by contrasting the logits conditioned on the original visual tokens with those conditioned on the blind tokens. This effectively lowers the dependency on blind tokens and promotes a more balanced consideration of all tokens. We validate AVC on benchmarks such as POPE, MME, and AMBER, where it consistently outperforms existing decoding techniques in mitigating object hallucinations in LVLMs.

We consider identification of average treatment effects on the treated (ATT) within the difference-in-differences (DiD) framework in the presence of endogenous sample selection. First, we establish that the usual DiD estimand fails to recover meaningful treatment effects, even if selection and treatment assignment are independent. Next, we partially identify the ATT for individuals who are always observed post-treatment regardless of their treatment status, and derive bounds on this parameter under different sets of assumptions about the relationship between sample selection and treatment assignment. Extensions to the repeated cross-section and two-by-two comparisons in the staggered adoption case are explored. Furthermore, we provide identification results for the ATT of three additional empirically relevant latent groups by incorporating outcome mean dominance assumptions which have intuitive appeal in applications. Finally, two empirical illustrations demonstrate the approach's usefulness by revisiting (i) the effect of a job training program on earnings(Calonico & Smith, 2017) and (ii) the effect of a working-from-home policy on employee performance (Bloom, Liang, Roberts, & Ying, 2015).

The presence of distribution shifts poses a significant challenge for deploying modern machine learning models in real-world applications. This work focuses on the target shift problem in a regression setting (Zhang et al., 2013; Nguyen et al., 2016). More specifically, the target variable y (also known as the response variable), which is continuous, has different marginal distributions in the training source and testing domain, while the conditional distribution of features x given y remains the same. While most literature focuses on classification tasks with finite target space, the regression problem has an infinite dimensional target space, which makes many of the existing methods inapplicable. In this work, we show that the continuous target shift problem can be addressed by estimating the importance weight function from an ill-posed integral equation. We propose a nonparametric regularized approach named ReTaSA to solve the ill-posed integral equation and provide theoretical justification for the estimated importance weight function. The effectiveness of the proposed method has been demonstrated with extensive numerical studies on synthetic and real-world datasets.

The inspiral, merger, and ringdown of Massive Black Hole Binaries (MBHBs) is one the main sources of Gravitational Waves (GWs) for the future Laser Interferometer Space Antenna (LISA), an ESA-led mission in the implementation phase. It is expected that LISA will detect these systems throughout the entire observable universe. Robust and efficient data analysis algorithms are necessary to detect and estimate physical parameters for these systems. In this work, we explore the application of Sequential Neural Likelihood, a simulation-based inference algorithm, to detect and characterize MBHB GW signals in synthetic LISA data. We describe in detail the different elements of the method, their performance and possible alternatives that can be used to enhance the performance. Instead of sampling from the conventional likelihood function, which requires a forward simulation for each evaluation, this method constructs a surrogate likelihood that is ultimately described by a neural network trained from a dataset of simulations of the MBHB signals and noise. One important advantage of this method is that, given that the likelihood is independent of the priors, we can iteratively train models that target specific observations in a fraction of the time and computational cost that other traditional and machine learning-based strategies would require. Because of the iterative nature of the method, we are able to train models to obtain qualitatively similar posteriors with less than 2\% of the simulator calls that Markov Chain Monte Carlo methods would require. We compare these posteriors with those obtained from Markov Chain Monte Carlo techniques and discuss the differences that appear, in particular in relation with the important role that data compression has in the modular implementation of the method that we present. We also discuss different strategies to improve the performance of the algorithms.

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may ask whether composing the inversions of the component processes gives the same belief update as the inversion of the whole. We answer this question affirmatively, showing that the relevant compositional structure is precisely that of the lens pattern, and that we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a corresponding fibred category. We define a general notion of (mixed) Bayesian lens, and discuss the (un)lawfulness of these lenses when their contravariant components are exact Bayesian inversions. We prove our main result both abstractly and concretely, for both discrete and continuous states, taking care to illustrate the common structures.

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers, which is commonly used in the optimization literature due to its fast convergence. In contrast to distributed optimization, distributed sampling allows for uncertainty quantification in Bayesian inference tasks. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. For our theoretical results, we use convex optimization tools to establish a fundamental inequality on the generated local sample iterates. This inequality enables us to show convergence of the distribution associated with these iterates to the underlying target distribution in Wasserstein distance. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.

Mixture-of-experts (MoE) model incorporates the power of multiple submodels via gating functions to achieve greater performance in numerous regression and classification applications. From a theoretical perspective, while there have been previous attempts to comprehend the behavior of that model under the regression settings through the convergence analysis of maximum likelihood estimation in the Gaussian MoE model, such analysis under the setting of a classification problem has remained missing in the literature. We close this gap by establishing the convergence rates of density estimation and parameter estimation in the softmax gating multinomial logistic MoE model. Notably, when part of the expert parameters vanish, these rates are shown to be slower than polynomial rates owing to an inherent interaction between the softmax gating and expert functions via partial differential equations. To address this issue, we propose using a novel class of modified softmax gating functions which transform the input value before delivering them to the gating functions. As a result, the previous interaction disappears and the parameter estimation rates are significantly improved.

The flat lensless camera design reduces the camera size and weight significantly. In this design, the camera lens is replaced by another optical element that interferes with the incoming light. The image is recovered from the raw sensor measurements using a reconstruction algorithm. Yet, the quality of the reconstructed images is not satisfactory. To mitigate this, we propose utilizing a pre-trained diffusion model with a control network and a learned separable transformation for reconstruction. This allows us to build a prototype flat camera with high-quality imaging, presenting state-of-the-art results in both terms of quality and perceptuality. We demonstrate its ability to leverage also textual descriptions of the captured scene to further enhance reconstruction. Our reconstruction method which leverages the strong capabilities of a pre-trained diffusion model can be used in other imaging systems for improved reconstruction results.

In this paper, we introduce a novel predict-and-optimize method for profit-driven churn prevention. We frame the task of targeting customers for a retention campaign as a regret minimization problem. The main objective is to leverage individual customer lifetime values (CLVs) to ensure that only the most valuable customers are targeted. In contrast, many profit-driven strategies focus on churn probabilities while considering average CLVs. This often results in significant information loss due to data aggregation. Our proposed model aligns with the guidelines of Predict-and-Optimize (PnO) frameworks and can be efficiently solved using stochastic gradient descent methods. Results from 12 churn prediction datasets underscore the effectiveness of our approach, which achieves the best average performance compared to other well-established strategies in terms of average profit.

We present a deeply integrated method of exploiting low-cost gyroscopes to improve general purpose feature tracking. Most previous methods use gyroscopes to initialize and bound the search for features. In contrast, we use them to regularize the tracking energy function so that they can directly assist in the tracking of ambiguous and poor-quality features. We demonstrate that our simple technique offers significant improvements in performance over conventional template-based tracking methods, and is in fact competitive with more complex and computationally expensive state-of-the-art trackers, but at a fraction of the computational cost. Additionally, we show that the practice of initializing template-based feature trackers like KLT (Kanade-Lucas-Tomasi) using gyro-predicted optical flow offers no advantage over using a careful optical-only initialization method, suggesting that some deeper level of integration, like the method we propose, is needed in order to realize a genuine improvement in tracking performance from these inertial sensors.

Modern astronomical surveys are producing datasets of unprecedented size and richness, increasing the potential for high-impact scientific discovery. This possibility, coupled with the challenge of exploring a large number of sources, has led to the development of novel machine-learning-based anomaly detection approaches, such as Astronomaly. For the first time, we test the scalability of Astronomaly by applying it to almost 4 million images of galaxies from the Dark Energy Camera Legacy Survey. We use a trained deep learning algorithm to learn useful representations of the images and pass these to the anomaly detection algorithm isolation forest, coupled with Astronomaly's active learning method, to discover interesting sources. We find that data selection criteria have a significant impact on the trade-off between finding rare sources such as strong lenses and introducing artefacts into the dataset. We demonstrate that active learning is required to identify the most interesting sources and reduce artefacts, while anomaly detection methods alone are insufficient. Using Astronomaly, we find 1635 anomalies among the top 2000 sources in the dataset after applying active learning, including eight strong gravitational lens candidates, 1609 galaxy merger candidates, and 18 previously unidentified sources exhibiting highly unusual morphology. Our results show that by leveraging the human-machine interface, Astronomaly is able to rapidly identify sources of scientific interest even in large datasets.

To achieve the highest perceptual quality, state-of-the-art diffusion models are optimized with objectives that typically look very different from the maximum likelihood and the Evidence Lower Bound (ELBO) objectives. In this work, we reveal that diffusion model objectives are actually closely related to the ELBO. Specifically, we show that all commonly used diffusion model objectives equate to a weighted integral of ELBOs over different noise levels, where the weighting depends on the specific objective used. Under the condition of monotonic weighting, the connection is even closer: the diffusion objective then equals the ELBO, combined with simple data augmentation, namely Gaussian noise perturbation. We show that this condition holds for a number of state-of-the-art diffusion models. In experiments, we explore new monotonic weightings and demonstrate their effectiveness, achieving state-of-the-art FID scores on the high-resolution ImageNet benchmark.

We consider the task of evaluating policies of algorithmic resource allocation through randomized controlled trials (RCTs). Such policies are tasked with optimizing the utilization of limited intervention resources, with the goal of maximizing the benefits derived. Evaluation of such allocation policies through RCTs proves difficult, notwithstanding the scale of the trial, because the individuals' outcomes are inextricably interlinked through resource constraints controlling the policy decisions. Our key contribution is to present a new estimator leveraging our proposed novel concept, that involves retrospective reshuffling of participants across experimental arms at the end of an RCT. We identify conditions under which such reassignments are permissible and can be leveraged to construct counterfactual trials, whose outcomes can be accurately ascertained, for free. We prove theoretically that such an estimator is more accurate than common estimators based on sample means -- we show that it returns an unbiased estimate and simultaneously reduces variance. We demonstrate the value of our approach through empirical experiments on synthetic, semi-synthetic as well as real case study data and show improved estimation accuracy across the board.

Wide-angle lenses are commonly used in perception tasks requiring a large field of view. Unfortunately, these lenses produce significant distortions making conventional models that ignore the distortion effects unable to adapt to wide-angle images. In this paper, we present a novel transformer-based model that automatically adapts to the distortion produced by wide-angle lenses. We leverage the physical characteristics of such lenses, which are analytically defined by the radial distortion profile (assumed to be known), to develop a distortion aware radial swin transformer (DarSwin). In contrast to conventional transformer-based architectures, DarSwin comprises a radial patch partitioning, a distortion-based sampling technique for creating token embeddings, and an angular position encoding for radial patch merging. We validate our method on classification tasks using synthetically distorted ImageNet data and show through extensive experiments that DarSwin can perform zero-shot adaptation to unseen distortions of different wide-angle lenses. Compared to other baselines, DarSwin achieves the best results (in terms of Top-1 accuracy) with significant gains when trained on bounded levels of distortions (very-low, low, medium, and high) and tested on all including out-of-distribution distortions. The code and models are publicly available at https://lvsn.github.io/darswin/

Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation~(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. However, as found in previous works, NCE may perform poorly in many tasks due to its flat loss landscape and slow convergence. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models from the perspective of compositional optimization. To tackle the partition function, a noise distribution is introduced such that the log partition function can be written as a compositional function whose inner function can be estimated with stochastic samples. Hence, the objective can be optimized by stochastic compositional optimization algorithms. Despite being a simple method, we demonstrate that it is more favorable than NCE by (1) establishing a fast convergence rate and quantifying its dependence on the noise distribution through the variance of stochastic estimators; (2) developing better results for one-dimensional Gaussian mean estimation by showing our objective has a much favorable loss landscape and hence our method enjoys faster convergence; (3) demonstrating better performance on multiple applications, including density estimation, out-of-distribution detection, and real image generation.

Supervised learning datasets may contain multiple cues that explain the training set equally well, i.e., learning any of them would lead to the correct predictions on the training data. However, many of them can be spurious, i.e., lose their predictive power under a distribution shift and consequently fail to generalize to out-of-distribution (OOD) data. Recently developed "diversification" methods (Lee et al., 2023; Pagliardini et al., 2023) approach this problem by finding multiple diverse hypotheses that rely on different features. This paper aims to study this class of methods and identify the key components contributing to their OOD generalization abilities. We show that (1) diversification methods are highly sensitive to the distribution of the unlabeled data used for diversification and can underperform significantly when away from a method-specific sweet spot. (2) Diversification alone is insufficient for OOD generalization. The choice of the used learning algorithm, e.g., the model's architecture and pretraining, is crucial. In standard experiments (classification on Waterbirds and Office-Home datasets), using the second-best choice leads to an up to 20\% absolute drop in accuracy. (3) The optimal choice of learning algorithm depends on the unlabeled data and vice versa i.e. they are co-dependent. (4) Finally, we show that, in practice, the above pitfalls cannot be alleviated by increasing the number of diverse hypotheses, the major feature of diversification methods. These findings provide a clearer understanding of the critical design factors influencing the OOD generalization abilities of diversification methods. They can guide practitioners in how to use the existing methods best and guide researchers in developing new, better ones.