stat.ML

arXiv:2501.00119v1 Announce Type: cross Abstract: A/B tests, also known as randomized controlled experiments (RCTs), are the gold standard for evaluating the impact of new policies, products, or decisions. However, these tests can be costly in terms of time and resources, potentially exposing users, customers, or other test subjects (units) to inferior options. This paper explores practical considerations in applying methodologies inspired by "synthetic control" as an alternative to traditional A/B testing in settings with very large numbers of units, involving up to hundreds of millions of units, which is common in modern applications such as e-commerce and ride-sharing platforms. This method is particularly valuable in settings where the treatment affects only a subset of units, leaving many units unaffected. In these scenarios, synthetic control methods leverage data from unaffected units to estimate counterfactual outcomes for treated units. After the treatment is implemented, these estimates can be compared to actual outcomes to measure the treatment effect. A key challenge in creating accurate counterfactual outcomes is interpolation bias, a well-documented phenomenon that occurs when control units differ significantly from treated units. To address this, we propose a two-phase approach: first using nearest neighbor matching based on unit covariates to select similar control units, then applying supervised learning methods suitable for high-dimensional data to estimate counterfactual outcomes. Testing using six large-scale experiments demonstrates that this approach successfully improves estimate accuracy. However, our analysis reveals that machine learning bias -- which arises from methods that trade off bias for variance reduction -- can impact results and affect conclusions about treatment effects. We document this bias in large-scale experimental settings and propose effective de-biasing techniques to address this challenge.

arXiv:2501.00755v1 Announce Type: cross Abstract: Causal inference in observational studies with high-dimensional covariates presents significant challenges. We introduce CausalBGM, an AI-powered Bayesian generative modeling approach that captures the causal relationship among covariates, treatment, and outcome variables. The core innovation of CausalBGM lies in its ability to estimate the individual treatment effect (ITE) by learning individual-specific distributions of a low-dimensional latent feature set (e.g., latent confounders) that drives changes in both treatment and outcome. This approach not only effectively mitigates confounding effects but also provides comprehensive uncertainty quantification, offering reliable and interpretable causal effect estimates at the individual level. CausalBGM adopts a Bayesian model and uses a novel iterative algorithm to update the model parameters and the posterior distribution of latent features until convergence. This framework leverages the power of AI to capture complex dependencies among variables while adhering to the Bayesian principles. Extensive experiments demonstrate that CausalBGM consistently outperforms state-of-the-art methods, particularly in scenarios with high-dimensional covariates and large-scale datasets. Its Bayesian foundation ensures statistical rigor, providing robust and well-calibrated posterior intervals. By addressing key limitations of existing methods, CausalBGM emerges as a robust and promising framework for advancing causal inference in modern applications in fields such as genomics, healthcare, and social sciences. CausalBGM is maintained at the website https://causalbgm.readthedocs.io/.

arXiv:2501.00762v1 Announce Type: new Abstract: Graph neural networks (GNNs) have achieved remarkable empirical success in processing and representing graph-structured data across various domains. However, a significant challenge known as "oversmoothing" persists, where vertex features become nearly indistinguishable in deep GNNs, severely restricting their expressive power and practical utility. In this work, we analyze the asymptotic oversmoothing rates of deep GNNs with and without residual connections by deriving explicit convergence rates for a normalized vertex similarity measure. Our analytical framework is grounded in the multiplicative ergodic theorem. Furthermore, we demonstrate that adding residual connections effectively mitigates or prevents oversmoothing across several broad families of parameter distributions. The theoretical findings are strongly supported by numerical experiments.

arXiv:2501.00015v1 Announce Type: cross Abstract: (Pseudo)random sampling, a costly yet widely used method in (probabilistic) machine learning and Markov Chain Monte Carlo algorithms, remains unfeasible on a truly large scale due to unmet computational requirements. We introduce an energy-efficient algorithm for uniform Float16 sampling, utilizing a room-temperature stochastic magnetic tunnel junction device to generate truly random floating-point numbers. By avoiding expensive symbolic computation and mapping physical phenomena directly to the statistical properties of the floating-point format and uniform distribution, our approach achieves a higher level of energy efficiency than the state-of-the-art Mersenne-Twister algorithm by a minimum factor of 9721 and an improvement factor of 5649 compared to the more energy-efficient PCG algorithm. Building on this sampling technique and hardware framework, we decompose arbitrary distributions into many non-overlapping approximative uniform distributions along with convolution and prior-likelihood operations, which allows us to sample from any 1D distribution without closed-form solutions. We provide measurements of the potential accumulated approximation errors, demonstrating the effectiveness of our method.

arXiv:2501.00389v1 Announce Type: cross Abstract: We study the momentum-based minimization of a diffuse perimeter functional on Euclidean spaces and on graphs with applications to semi-supervised classification tasks in machine learning. While the gradient flow in the task at hand is a parabolic partial differential equation, the momentum-method corresponds to a damped hyperbolic PDE, leading to qualitatively and quantitatively different trajectories. Using a convex-concave splitting-based FISTA-type time discretization, we demonstrate empirically that momentum can lead to faster convergence if the time step size is large but not too large. With large time steps, the PDE analysis offers only limited insight into the geometric behavior of solutions and typical hyperbolic phenomena like loss of regularity are not be observed in sample simulations.

arXiv:2501.00754v1 Announce Type: cross Abstract: The learner's ability to generate a hypothesis that closely approximates the target function is crucial in machine learning. Achieving this requires sufficient data; however, unauthorized access by an eavesdropping learner can lead to security risks. Thus, it is important to ensure the performance of the "authorized" learner by limiting the quality of the training data accessible to eavesdroppers. Unlike previous studies focusing on encryption or access controls, we provide a theorem to ensure superior learning outcomes exclusively for the authorized learner with quantum label encoding. In this context, we use the probably-approximately-correct (PAC) learning framework and introduce the concept of learning probability to quantitatively assess learner performance. Our theorem allows the condition that, given a training dataset, an authorized learner is guaranteed to achieve a certain quality of learning outcome, while eavesdroppers are not. Notably, this condition can be constructed based only on the authorized-learning-only measurable quantities of the training data, i.e., its size and noise degree. We validate our theoretical proofs and predictions through convolutional neural networks (CNNs) image classification learning.

arXiv:2501.00623v1 Announce Type: new Abstract: In this article, we present a model for analyzing the cooccurrence count data derived from practical fields such as user-item or item-item data from online shopping platform, cooccurring word-word pairs in sequences of texts. Such data contain important information for developing recommender systems or studying relevance of items or words from non-numerical sources. Different from traditional regression models, there are no observations for covariates. Additionally, the cooccurrence matrix is typically of so high dimension that it does not fit into a computer's memory for modeling. We extract numerical data by defining windows of cooccurrence using weighted count on the continuous scale. Positive probability mass is allowed for zero observations. We present Shared parameter Alternating Tweedie (SA-Tweedie) model and an algorithm to estimate the parameters. We introduce a learning rate adjustment used along with the Fisher scoring method in the inner loop to help the algorithm stay on track of optimizing direction. Gradient descent with Adam update was also considered as an alternative method for the estimation. Simulation studies and an application showed that our algorithm with Fisher scoring and learning rate adjustment outperforms the other two methods. Pseudo-likelihood approach with alternating parameter update was also studied. Numerical studies showed that the pseudo-likelihood approach is not suitable in our shared parameter alternating regression models with unobserved covariates.

arXiv:2501.00677v1 Announce Type: new Abstract: Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable non-convex approach, coined Learned Robust Matrix Completion (LRMC), for large-scale RMC problems. LRMC enjoys low computational complexity with linear convergence. Motivated by the proposed theorem, the free parameters of LRMC can be effectively learned via deep unfolding to achieve optimum performance. Furthermore, this paper proposes a flexible feedforward-recurrent-mixed neural network framework that extends deep unfolding from fix-number iterations to infinite iterations. The superior empirical performance of LRMC is verified with extensive experiments against state-of-the-art on synthetic datasets and real applications, including video background subtraction, ultrasound imaging, face modeling, and cloud removal from satellite imagery.

arXiv:2501.00891v1 Announce Type: new Abstract: The contextual multi-armed bandit (MAB) problem is crucial in sequential decision-making. A line of research, known as online clustering of bandits, extends contextual MAB by grouping similar users into clusters, utilizing shared features to improve learning efficiency. However, existing algorithms, which rely on the upper confidence bound (UCB) strategy, struggle to gather adequate statistical information to accurately identify unknown user clusters. As a result, their theoretical analyses require several strong assumptions about the "diversity" of contexts generated by the environment, leading to impractical settings, complicated analyses, and poor practical performance. Removing these assumptions has been a long-standing open problem in the clustering of bandits literature. In this paper, we provide two solutions to this open problem. First, following the i.i.d. context generation setting in existing studies, we propose two novel algorithms, UniCLUB and PhaseUniCLUB, which incorporate enhanced exploration mechanisms to accelerate cluster identification. Remarkably, our algorithms require substantially weaker assumptions while achieving regret bounds comparable to prior work. Second, inspired by the smoothed analysis framework, we propose a more practical setting that eliminates the requirement for i.i.d. context generation used in previous studies, thus enhancing the performance of existing algorithms for online clustering of bandits. Our technique can be applied to both graph-based and set-based clustering of bandits frameworks. Extensive evaluations on both synthetic and real-world datasets demonstrate that our proposed algorithms consistently outperform existing approaches.

arXiv:2501.01291v1 Announce Type: new Abstract: Conventional Multi-Armed Bandit (MAB) algorithms are designed for stationary environments, where the reward distributions associated with the arms do not change with time. In many applications, however, the environment is more accurately modeled as being nonstationary. In this work, piecewise stationary MAB (PS-MAB) environments are investigated, in which the reward distributions associated with a subset of the arms change at some change-points and remain stationary between change-points. Our focus is on the asymptotic analysis of PS-MABs, for which practical algorithms based on change detection (CD) have been previously proposed. Our goal is to modularize the design and analysis of such CD-based Bandit (CDB) procedures. To this end, we identify the requirements for stationary bandit algorithms and change detectors in a CDB procedure that are needed for the modularization. We assume that the rewards are sub-Gaussian. Under this assumption and a condition on the separation of the change-points, we show that the analysis of CDB procedures can indeed be modularized, so that regret bounds can be obtained in a unified manner for various combinations of change detectors and bandit algorithms. Through this analysis, we develop new modular CDB procedures that are order-optimal. We compare the performance of our modular CDB procedures with various other methods in simulations.

arXiv:2501.00277v1 Announce Type: cross Abstract: Modern AI algorithms require labeled data. In real world, majority of data are unlabeled. Labeling the data are costly. this is particularly true for some areas requiring special skills, such as reading radiology images by physicians. To most efficiently use expert's time for the data labeling, one promising approach is human-in-the-loop active learning algorithm. In this work, we propose a novel active learning framework with significant potential for application in modern AI systems. Unlike the traditional active learning methods, which only focus on determining which data point should be labeled, our framework also introduces an innovative perspective on incorporating different query scheme. We propose a model to integrate the information from different types of queries. Based on this model, our active learning frame can automatically determine how the next question is queried. We further developed a data driven exploration and exploitation framework into our active learning method. This method can be embedded in numerous active learning algorithms. Through simulations on five real-world datasets, including a highly complex real image task, our proposed active learning framework exhibits higher accuracy and lower loss compared to other methods.

arXiv:2501.00382v1 Announce Type: cross Abstract: This paper advances empirical demand analysis by integrating multimodal product representations derived from artificial intelligence (AI). Using a detailed dataset of toy cars on \textit{Amazon.com}, we combine text descriptions, images, and tabular covariates to represent each product using transformer-based embedding models. These embeddings capture nuanced attributes, such as quality, branding, and visual characteristics, that traditional methods often struggle to summarize. Moreover, we fine-tune these embeddings for causal inference tasks. We show that the resulting embeddings substantially improve the predictive accuracy of sales ranks and prices and that they lead to more credible causal estimates of price elasticity. Notably, we uncover strong heterogeneity in price elasticity driven by these product-specific features. Our findings illustrate that AI-driven representations can enrich and modernize empirical demand analysis. The insights generated may also prove valuable for applied causal inference more broadly.

arXiv:2501.00632v1 Announce Type: cross Abstract: This article considers the impact of different thresholding methods to the Nearest Shrunken Centroid algorithm, which is popularly referred as the Prediction Analysis of Microarrays (PAM) for high-dimensional classification. PAM uses soft thresholding to achieve high computational efficiency and high classification accuracy but in the price of retaining too many features. When applied to microarray human cancers, PAM selected 2611 features on average from 10 multi-class datasets. Such a large number of features make it difficult to perform follow up study. One reason behind this problem is the soft thresholding, which is known to produce biased parameter estimate in regression analysis. In this article, we extend the PAM algorithm with two other thresholding methods, hard and order thresholding, and a deep search algorithm to achieve better thresholding parameter estimate. The modified algorithms are extensively tested and compared to the original one based on real data and Monte Carlo studies. In general, the modification not only gave better cancer status prediction accuracy, but also resulted in more parsimonious models with significantly smaller number of features.

arXiv:2501.00744v1 Announce Type: cross Abstract: Generative models are ubiquitous in modern artificial intelligence (AI) applications. Recent advances have led to a variety of generative modeling approaches that are capable of synthesizing highly realistic samples. Despite these developments, evaluating the distributional match between the synthetic samples and the target distribution in a statistically principled way remains a core challenge. We focus on evaluating image generative models, where studies often treat human evaluation as the gold standard. Commonly adopted metrics, such as the Fr\'echet Inception Distance (FID), do not sufficiently capture the differences between the learned and target distributions, because the assumption of normality ignores differences in the tails. We propose the Embedded Characteristic Score (ECS), a comprehensive metric for evaluating the distributional match between the learned and target sample distributions, and explore its connection with moments and tail behavior. We derive natural properties of ECS and show its practical use via simulations and an empirical study.

arXiv:2501.00381v1 Announce Type: new Abstract: As AI systems become increasingly autonomous, aligning their decision-making to human preferences is essential. In domains like autonomous driving or robotics, it is impossible to write down the reward function representing these preferences by hand. Inverse reinforcement learning (IRL) offers a promising approach to infer the unknown reward from demonstrations. However, obtaining human demonstrations can be costly. Active IRL addresses this challenge by strategically selecting the most informative scenarios for human demonstration, reducing the amount of required human effort. Where most prior work allowed querying the human for an action at one state at a time, we motivate and analyse scenarios where we collect longer trajectories. We provide an information-theoretic acquisition function, propose an efficient approximation scheme, and illustrate its performance through a set of gridworld experiments as groundwork for future work expanding to more general settings.

arXiv:2501.00555v1 Announce Type: new Abstract: Large language models (LLMs) are empowering decision-making in several applications, including tool or API usage and answering multiple-choice questions (MCQs). However, they often make overconfident, incorrect predictions, which can be risky in high-stakes settings like healthcare and finance. To mitigate these risks, recent works have used conformal prediction (CP), a model-agnostic framework for distribution-free uncertainty quantification. CP transforms a \emph{score function} into prediction sets that contain the true answer with high probability. While CP provides this coverage guarantee for arbitrary scores, the score quality significantly impacts prediction set sizes. Prior works have relied on LLM logits or other heuristic scores, lacking quality guarantees. We address this limitation by introducing CP-OPT, an optimization framework to learn scores that minimize set sizes while maintaining coverage. Furthermore, inspired by the Monty Hall problem, we extend CP's utility beyond uncertainty quantification to improve accuracy. We propose \emph{conformal revision of questions} (CROQ) to revise the problem by narrowing down the available choices to those in the prediction set. The coverage guarantee of CP ensures that the correct choice is in the revised question prompt with high probability, while the smaller number of choices increases the LLM's chances of answering it correctly. Experiments on MMLU, ToolAlpaca, and TruthfulQA datasets with Gemma-2, Llama-3 and Phi-3 models show that CP-OPT significantly reduces set sizes while maintaining coverage, and CROQ improves accuracy over the standard inference, especially when paired with CP-OPT scores. Together, CP-OPT and CROQ offer a robust framework for improving both the safety and accuracy of LLM-driven decision-making.

arXiv:2501.00628v1 Announce Type: new Abstract: High-dimensional sparse matrix data frequently arise in various applications. A notable example is the weighted word-word co-occurrence count data, which summarizes the weighted frequency of word pairs appearing within the same context window. This type of data typically contains highly skewed non-negative values with an abundance of zeros. Another example is the co-occurrence of item-item or user-item pairs in e-commerce, which also generates high-dimensional data. The objective is to utilize this data to predict the relevance between items or users. In this paper, we assume that items or users can be represented by unknown dense vectors. The model treats the co-occurrence counts as arising from zero-inflated Gamma random variables and employs cosine similarity between the unknown vectors to summarize item-item relevance. The unknown values are estimated using the shared parameter alternating zero-inflated Gamma regression models (SA-ZIG). Both canonical link and log link models are considered. Two parameter updating schemes are proposed, along with an algorithm to estimate the unknown parameters. Convergence analysis is presented analytically. Numerical studies demonstrate that the SA-ZIG using Fisher scoring without learning rate adjustment may fail to fi nd the maximum likelihood estimate. However, the SA-ZIG with learning rate adjustment performs satisfactorily in our simulation studies.

arXiv:2501.00664v1 Announce Type: new Abstract: Generative models hold great potential, but only if one can trust the evaluation of the data they generate. We show that many commonly used quality scores for comparing two-dimensional distributions of synthetic vs. ground-truth data give better results than they should, a phenomenon we call the "grade inflation problem." We show that the correlation score, Jaccard score, earth-mover's score, and Kullback-Leibler (relative-entropy) score all suffer grade inflation. We propose that any score that values all datapoints equally, as these do, will also exhibit grade inflation; we refer to such scores as "equipoint" scores. We introduce the concept of "equidensity" scores, and present the Eden score, to our knowledge the first example of such a score. We found that Eden avoids grade inflation and agrees better with human perception of goodness-of-fit than the equipoint scores above. We propose that any reasonable equidensity score will avoid grade inflation. We identify a connection between equidensity scores and R\'enyi entropy of negative order. We conclude that equidensity scores are likely to outperform equipoint scores for generative models, and for comparing low-dimensional distributions more generally.

arXiv:2501.00817v1 Announce Type: new Abstract: Learning parity functions is a canonical problem in learning theory, which although computationally tractable, is not amenable to standard learning algorithms such as gradient-based methods. This hardness is usually explained via statistical query lower bounds [Kearns, 1998]. However, these bounds only imply that for any given algorithm, there is some worst-case parity function that will be hard to learn. Thus, they do not explain why fixed parities - say, the full parity function over all coordinates - are difficult to learn in practice, at least with standard predictors and gradient-based methods [Abbe and Boix-Adsera, 2022]. In this paper, we address this open problem, by showing that for any fixed parity of some minimal size, using it as a target function to train one-hidden-layer ReLU networks with perturbed gradient descent will fail to produce anything meaningful. To establish this, we prove a new result about the decay of the Fourier coefficients of linear threshold (or weighted majority) functions, which may be of independent interest.

arXiv:2501.00967v1 Announce Type: cross Abstract: Bayesian optimization (BO) is an effective paradigm for the optimization of expensive-to-sample systems. Standard BO learns the performance of a system $f(x)$ by using a Gaussian Process (GP) model; this treats the system as a black-box and limits its ability to exploit available structural knowledge (e.g., physics and sparse interconnections in a complex system). Grey-box modeling, wherein the performance function is treated as a composition of known and unknown intermediate functions $f(x, y(x))$ (where $y(x)$ is a GP model) offers a solution to this limitation; however, generating an analytical probability density for $f$ from the Gaussian density of $y(x)$ is often an intractable problem (e.g., when $f$ is nonlinear). Previous work has handled this issue by using sampling techniques or by solving an auxiliary problem over an augmented space where the values of $y(x)$ are constrained by confidence intervals derived from the GP models; such solutions are computationally intensive. In this work, we provide a detailed implementation of a recently proposed grey-box BO paradigm, BOIS, that uses adaptive linearizations of $f$ to obtain analytical expressions for the statistical moments of the composite function. We show that the BOIS approach enables the exploitation of structural knowledge, such as that arising in interconnected systems as well as systems that embed multiple GP models and combinations of physics and GP models. We benchmark the effectiveness of BOIS against standard BO and existing grey-box BO algorithms using a pair of case studies focused on chemical process optimization and design. Our results indicate that BOIS performs as well as or better than existing grey-box methods, while also being less computationally intensive.