AISTATS 2025 论文列表

In this paper, we explore the theoretical properties of subspace recovery using Winsorized Principal Component Analysis (WPCA), utilizing a common data transformation technique that caps extreme values to mitigate the impact of outliers. Despite the widespread use of winsorization in various tasks of multivariate analysis, its theoretical properties, particularly for subspace recovery, have received limited attention. We provide a detailed analysis of the accuracy of WPCA, showing that increasing the number of samples while decreasing the proportion of outliers guarantees the consistency of the sample subspaces from WPCA with respect to the true population subspace. Furthermore, we establish perturbation bounds that ensure the WPCA subspace obtained from contaminated data remains close to the subspace recovered from pure data. Additionally, we extend the classical notion of breakdown points to subspace-valued statistics and derive lower bounds for the breakdown points of WPCA. Our analysis demonstrates that WPCA exhibits strong robustness to outliers while maintaining consistency under mild assumptions. A toy example is provided to numerically illustrate the behavior of the upper bounds for perturbation bounds and breakdown points, emphasizing winsorization's utility in subspace recovery.

We present two Policy Gradient-based algorithms with general parametrization in the context of infinite-horizon average reward Markov Decision Process (MDP). The first one employs Implicit Gradient Transport for variance reduction, ensuring an expected regret of the order $\tilde{\mathcal{O}}(T^{2/3})$. The second approach, rooted in Hessian-based techniques, ensures an expected regret of the order $\tilde{\mathcal{O}}(\sqrt{T})$. These results significantly improve the state-of-the-art $\tilde{\mathcal{O}}(T^{3/4})$ regret and achieve the theoretical lower bound. We also show that the average-reward function is approximately $L$-smooth, a result that was previously assumed in earlier works.

Instrumental variables (IVs) are widely used to estimate causal effects in the presence of unobserved confounding between an exposure $X$ and outcome $Y$. An IV must affect $Y$ exclusively through $X$ and be unconfounded with $Y$. We present a framework for relaxing these assumptions with tuneable and interpretable "budget constraints". Our algorithm returns a feasible set of causal effects that can be identified exactly given perfect knowledge of observable covariance statistics. This feasible set might contain disconnected sets of possible solutions for the causal effect. We discuss conditions under which this set is sharp, i.e., contains all and only effects consistent with the background assumptions and the joint distribution of observable variables. Our method applies to a wide class of semiparametric models, and we demonstrate how its ability to select specific subsets of instruments confers an advantage over convex relaxations in both linear and nonlinear settings. We adapt our algorithm to form confidence sets that are asymptotically valid under a common statistical assumption from the Mendelian randomization literature. An accompanying R package, budgetIVr, is available from CRAN.

Current machine learning systems are brittle in the face of distribution shifts (DS), where the target distribution that the system is tested on differs from the source distribution used to train the system. This problem of robustness to DS has been studied extensively in the field of domain adaptation. For deep neural networks, popular methods for unsupervised domain adaptation (UDA) are domain matching methods that try to align the marginal distributions in the feature or output space. The current theoretical understanding of these methods, however, are limited and existing theoretical frameworks are not precise enough to characterize their performance in practice. To this end, we derive new bounds based on optimal transport that analyze the UDA problem. Our new bound includes a term which we dub as entanglement, consisting of an expectation of Wasserstein distance between conditionals with respect to changing data distributions. Analysis of the entanglement term provides a novel perspective on the unoptimizable aspects of UDA. In various experiments with multiple models across several DS scenarios, we show that this term can be used to explain the varying performance of UDA algorithms.

This paper addresses differential inference in time-varying parametric probabilistic models, like graphical models with changing structures. Instead of estimating a high-dimensional model at each time and estimating changes later, we directly learn the differential parameter, i.e., the time derivative of the parameter. The main idea is treating the time score function of an exponential family model as a linear model of the differential parameter for direct estimation. We use time score matching to estimate parameter derivatives. We prove the consistency of a regularized score matching objective and demonstrate the finite-sample normality of a debiased estimator in high-dimensional settings. Our methodology effectively infers differential structures in high-dimensional graphical models, verified on simulated and real-world datasets. The code reproducing our experiments can be found at: \url{https://github.com/Leyangw/tsm}.

In this paper, we present a novel analysis of $\texttt{FedAvg}$ with constant step size, relying on the Markov property of the underlying process. We demonstrate that the global iterates of the algorithm converge to a stationary distribution and analyze its resulting bias and variance relative to the problem's solution. We provide a first-order bias expansion in both homogeneous and heterogeneous settings. Interestingly, this bias decomposes into two distinct components: one that depends solely on stochastic gradient noise and another on client heterogeneity. Finally, we introduce a new algorithm based on the Richardson-Romberg extrapolation technique to mitigate this bias.

We introduce a new approach to processing complex-valued data using DNNs consisting of parallel real-valued subnetworks with coupled outputs. Our proposed class of architectures, referred to as Steinmetz Neural Networks, incorporates multi-view learning to construct more interpretable representations in the latent space. Moreover, we present the Analytic Neural Network, which incorporates a consistency penalty that encourages analytic signal representations in the latent space of the Steinmetz neural network. This penalty enforces a deterministic and orthogonal relationship between the real and imaginary components. Using an information-theoretic construction, we demonstrate that the generalization gap upper bound posited by the analytic neural network is lower than that of the general class of Steinmetz neural networks. Our numerical experiments depict the improved performance and robustness to additive noise, afforded by our proposed networks on benchmark datasets and synthetic examples.

Covariance matrix estimation is a fundamental problem in multivariate data analysis, which becomes particularly challenging in high-dimensional settings due to the curse of dimensionality. To enhance estimation accuracy, structural regularization is often imposed on the precision matrix (the inverse covariance matrix) for covariance selection. In this paper, we study covariance selection in a distributed setting, where data is spread across a network of agents. We formulate the problem as a Gaussian maximum likelihood estimation problem with structural penalties and propose a novel algorithmic framework called NetGGM. Unlike existing methods that rely on a central coordinator, NetGGM operates in a fully decentralized manner with low computational complexity. We provide theoretical guarantees showing that NetGGM converges linearly to the global optimum while ensuring consensus among agents. Numerical experiments validate its convergence properties and demonstrate that it outperforms state-of-the-art methods in precision matrix estimation.

We study the convex-concave bilinear saddle-point problem $\min_x \max_y f(x) + y^\top Ax - g(y)$, where both, only one, or none of the functions $f$ and $g$ are strongly convex, and suitable rank conditions on the matrix $A$ hold. The solution of this problem is at the core of many machine learning tasks. By employing tools from monotone operator theory, we systematically prove the contractivity (in turn, the linear convergence) of several first-order primal-dual algorithms, including the Chambolle–Pock method. Our approach results in concise proofs, and it yields new convergence guarantees and tighter bounds compared to known results.

Multimodal AI models are increasingly used in fields like healthcare, finance, and autonomous driving, where information is drawn from multiple sources or modalities such as images, texts, audios, videos. However, effectively managing uncertainty—arising from noise, insufficient evidence, or conflicts between modalities—is crucial for reliable decision-making. Current uncertainty-aware machine learning methods leveraging, for example, evidence averaging, or evidence accumulation underestimate uncertainties in high-conflict scenarios. Moreover, the state-of-the-art evidence averaging strategy is not order invariant and fails to scale to multiple modalities. To address these challenges, we propose a novel multimodal learning method with order-invariant evidence fusion and introduce a conflict-based discounting mechanism that reallocates uncertain mass when unreliable modalities are detected. We provide both theoretical analysis and experimental validation, demonstrating that unlike the previous work, the proposed approach effectively distinguishes between conflicting and non-conflicting samples based on the provided uncertainty estimates, and outperforms the previous models in uncertainty-based conflict detection.

We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. In contrast to the ubiquitous Empirical Risk Minimization (ERM) framework, which optimizes for average performance, FL demands satisfactory performance *on every individual data point*. Since any model that meets the prescribed performance threshold is a valid FL solution, the choice of optimization algorithm and its dynamics play a crucial role in shaping the properties of the resulting solutions. In particular, we study a primal-dual approach which dynamically re-weights the importance of each sample during training. To address the challenge of setting a meaningful threshold in practice, we introduce a relaxation of FL that incorporates slack variables of minimal norm. Our empirical analysis, spanning image classification, age regression, and preference optimization in large language models, demonstrates that models trained via FL can learn from data while displaying improved tail behavior compared to ERM, with only a marginal impact on average performance.

Diffusion models (DMs) as generative priors have recently shown great potential for denoising tasks but lack theoretical understanding with respect to their mean square error (MSE) optimality. This paper proposes a novel denoising strategy inspired by the structure of the MSE-optimal conditional mean estimator (CME). The resulting DM-based denoiser can be conveniently employed using a pre-trained DM, being particularly fast by truncating reverse diffusion steps and not requiring stochastic re-sampling. We present a comprehensive (non-)asymptotic optimality analysis of the proposed diffusion-based denoiser, demonstrating polynomial-time convergence to the CME under mild conditions. Our analysis also derives a novel Lipschitz constant that depends solely on the DM’s hyperparameters. Further, we offer a new perspective on DMs, showing that they inherently combine an asymptotically optimal denoiser with a powerful generator, modifiable by switching re-sampling in the reverse process on or off. The theoretical findings are thoroughly validated with experiments based on various benchmark datasets.

Estimating causal effects in social network data presents unique challenges due to the presence of spillover effects and network-induced confounding. While much of the existing literature addresses causal inference in social networks, many methods rely on strong assumptions about the form of network-induced confounding. These assumptions often fail to hold in high-dimensional networks, limiting the applicability of such approaches. To address this, we propose a novel methodology that integrates graph machine learning techniques with the double machine learning framework, facilitating accurate and efficient estimation of both direct and peer effects in a single observational social network. Our estimator achieves semiparametric efficiency under mild regularity conditions, enabling consistent uncertainty quantification. Through extensive simulations, we demonstrate the accuracy, robustness, and scalability of our method. Finally, we apply the proposed approach to examine the impact of Self-Help Group participation on financial risk tolerance, highlighting its practical relevance.

We propose reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals, recovering the copula density in the process. We derive equivalences between well-known copula classes and classification problems naturally arising in our interpretation. Furthermore, we show our estimator achieves theoretical guarantees akin to maximum likelihood estimation. By identifying a connection with density ratio estimation, we benefit from the rich literature and models available for such problems. Empirically, we demonstrate the applicability of our approach by estimating copulas of real and high-dimensional datasets, outperforming competing copula estimators in density evaluation as well as sampling.

Previous work has demonstrated that attention mechanisms are Turing complete. More recently, it has been shown that a looped 9-layer Transformer can function as a universal programmable computer. In contrast, the multi-layer perceptrons with $\mathsf{ReLU}$ activation ($\mathsf{ReLU}$-$\mathsf{MLP}$), one of the most fundamental components of neural networks, is known to be expressive; specifically, a two-layer neural network is a universal approximator given an exponentially large number of hidden neurons. However, it remains unclear whether a $\mathsf{ReLU}$-$\mathsf{MLP}$ can be made into a universal programmable computer using a practical number of weights. In this work, we provide an affirmative answer that a looped 23-layer $\mathsf{ReLU}$-$\mathsf{MLP}$ is capable of performing the basic necessary operations, more efficiently and effectively functioning as a programmable computer than a looped Transformer. This indicates simple modules have stronger expressive power than previously expected and have not been fully explored. Our work provides insights into the mechanisms of neural networks and demonstrates that complex tasks, such as functioning as a programmable computer, do not necessarily require advanced architectures like Transformers.

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over SOTA in single-cell population-level trajectory inference.

Randomization as a mean to improve the adversarial robustness of machine learning models has recently attracted significant attention. Unfortunately, much of the theoretical analysis so far has focused on binary classification, providing only limited insights into the more complex multiclass setting. In this paper, we take a step toward closing this gap by drawing inspiration from the field of graph theory. Our analysis focuses on discrete data distributions, allowing us to cast the adversarial risk minimization problems within the well-established framework of set packing problems. By doing so, we are able to identify three structural conditions on the support of the data distribution that are necessary for randomization to improve robustness. Furthermore, we are able to construct several data distributions where (contrarily to binary classification) switching from a deterministic to a randomized solution significantly reduces the optimal adversarial risk. These findings highlight the crucial role randomization can play in enhancing robustness to adversarial attacks in multiclass classification.

The problem of identifying the best answer among a collection of items having real-valued distribution is well-understood. Despite its practical relevance for many applications, fewer works have studied its extension when multiple and potentially conflicting metrics are available to assess an item's quality. Pareto set identification (PSI) aims to identify the set of answers whose means are not uniformly worse than another. This paper studies PSI in the transductive linear setting with potentially correlated objectives. Building on posterior sampling in both the stopping and the sampling rules, we propose the \hyperlink{PSIPS}{PSIPS} algorithm that deals simultaneously with structure and correlation without paying the computational cost of existing oracle-based algorithms. Both from a frequentist and Bayesian perspective, \hyperlink{PSIPS}{PSIPS} is asymptotically optimal. We demonstrate its good empirical performance in real-world and synthetic instances.

We consider the problem of causal effect estimation with an unobserved confounder, where we observe a single proxy variable that is associated with the confounder. Although it has been shown that the recovery of an average causal effect is impossible in general from a single proxy variable, we show that causal recovery is possible if the outcome is generated deterministically. This generalizes existing work on causal methods with a single proxy variable to the continuous treatment setting. We propose two kernel-based methods for this setting: the first based on the two-stage regression approach, and the second based on a maximum moment restriction approach. We prove that both approaches can consistently estimate the causal effect, and we empirically demonstrate that we can successfully recover the causal effect on challenging synthetic benchmarks.