机器学习

Properties of Fisher information matrices of 2-layer neural ReLU networks with random hidden weights are studied. For these networks, it is known that the eigenvalue distribution highly concentrates on several eigenspaces approximately. In…

We study offline constrained reinforcement learning with general function approximation in discounted constrained Markov decision processes. Prior methods either require full data coverage for evaluating intermediate policies, lack oracle…

Quantifying differences between probability distributions is fundamental to statistics and machine learning, primarily for comparing statistical uncertainty. In contrast, epistemic uncertainty -- due to incomplete knowledge -- requires…

Binary classification from positive-only samples is a variant of PAC learning where the learner receives i.i.d. positive samples and aims to learn a classifier with low error. Previous work by Natarajan, Gereb-Graus, and Shvaytser…

Surrogate models are often used as computationally efficient approximations to complex simulation models, enabling tasks such as solving inverse problems, sensitivity analysis, and probabilistic forward predictions, which would otherwise be…

Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…

In this paper we develop a Multilevel Orthogonal Subspace (MOS) Karhunen-Loeve feature theory based on stochastic tensor spaces, for the construction of robust machine learning features. Training data are treated as instances of a random…

The lasso model has been widely used for model selection in data mining, machine learning, and high-dimensional statistical analysis. However, with the ultrahigh-dimensional, large-scale data sets now collected in many real-world…

Large language models demonstrate remarkable ability in factual recall, yet the fundamental limits of storing and retrieving input--output associations with neural networks remain unclear. We study these limits in a minimal setting: a…

We study sparse recovery when observations come from mixed-quality sources: a small collection of high-quality measurements with small noise variance and a larger collection of lower-quality measurements with higher variance. For this…

Causal sensitivity analysis aims to provide bounds for causal effect estimates in the presence of unobserved confounding. However, existing methods for causal sensitivity analysis are per-instance procedures, meaning that changes to the…

Probabilistic linear solvers (PLSs) return probability distributions that quantify uncertainty due to limited computation in the solution of linear systems. The literature has traditionally distinguished between Bayesian PLSs, which…

Guided-diffusion black-box optimization (BO) has shown strong empirical performance on structured design problems such as molecules and crystals, but its regret behavior remains poorly understood. Existing BO regret analyses typically rely…

Solving nonlinear partial differential equations (PDEs) using kernel methods offers a compelling alternative to traditional numerical solvers. However, the performance of these methods strongly depends on the choice of kernel. In this work,…

Reliable uncertainty quantification is essential for the use of machine learning in physics, where scientific discoveries depend on validated probabilistic statements. We provide a structured overview of uncertainty quantification in ML for…

We propose a novel adaptive Mixture-of-Experts (MoE) framework for time series forecasting that enhances expert specialization by incorporating expert-specific loss information directly into the training process. Notably, the overall…

This paper aims at analyzing the regularization effect that data augmentation induces on supervised regression methods in the proportional regime, where the number of covariates grows proportionally to the number of samples. We provide a…

We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…

Recent work on causal abstraction, in particular graphical approaches focusing on causal structure between clusters of variables, aims to summarize a high-dimensional causal structure in terms of a low-dimensional one. Existing methods for…

Thompson sampling is a widely used strategy for contextual bandits: at each round, it samples a reward function from a Bayesian posterior and acts greedily under that sample. Prior-data fitted networks (PFNs), such as TabPFN v2+ and TabICL…