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Graphical models are a rich language for describing high-dimensional distributions in terms of their dependence structure. While there are algorithms with provable guarantees for learning undirected graphical models in a variety of…

Accurate and early diagnosis of malignant melanoma is critical for improving patient outcomes. While convolutional neural networks (CNNs) have shown promise in dermoscopic image analysis, they often neglect clinical metadata and require…

In this paper we provide a convergence analysis of some variational methods alternative to the classical Tikhonov regularization, namely Ivanov regularization (also called method of quasi solutions) with some versions of the discrepancy…

The growing prevalence of large language models (LLMs) and vision-language models (VLMs) has heightened the need for reliable techniques to determine whether a model has been fine-tuned from or is even identical to another. Existing…

Models like LASSO and ridge regression are extensively used in practice due to their interpretability, ease of use, and strong theoretical guarantees. Cross-validation (CV) is widely used for hyperparameter tuning in these models, but do…

Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) can be used to solve convex optimization problems that consist of a sum of two functions. Convergence rate estimates for these algorithms have received…

Symbolic regression is a fundamental tool for discovering interpretable mathematical expressions from data, with broad applications across scientific and engineering domains. Recently, large language models (LLMs) have demonstrated strong…

We introduce the Reduced-Rank Hidden Markov Model (RR-HMM), a generalization of HMMs that can model smooth state evolution as in Linear Dynamical Systems (LDSs) as well as non-log-concave predictive distributions as in…

Constrained partially observable Markov decision processes (CPOMDPs) have been used to model various real-world phenomena. However, they are notoriously difficult to solve to optimality, and there exist only a few approximation methods for…

Identifying important features linked to a response variable is a fundamental task in various scientific domains. This article explores statistical inference for simulated Markov random fields in high-dimensional settings. We introduce a…

In this paper, we present new optimization models for Support Vector Machine (SVM), with the aim of separating data points in two or more classes. The classification task is handled by means of nonlinear classifiers induced by kernel…

Large Language Models (LLMs) and their multimodal variants (LVLMs) hold immense promise for scientific and engineering applications, particularly in processing visual information like scientific diagrams. However, their practical deployment…

The soft-margin support vector machine (SVM) is a ubiquitous tool for prediction of binary-response data. However, the SVM is characterized entirely via a numerical optimization problem, rather than a probability model, and thus does not…

We develop a convex analytic approach to analyze finite width two-layer ReLU networks. We first prove that an optimal solution to the regularized training problem can be characterized as extreme points of a convex set, where simple…

Careful tuning of a regularization parameter is indispensable in many machine learning tasks because it has a significant impact on generalization performances. Nevertheless, current practice of regularization parameter tuning is more of an…

Nonlinear Markov Chains (nMC) are regarded as the original (linear) Markov Chains with nonlinear small perturbations. It fits real-world data better, but its associated properties are difficult to describe. A new approach is proposed to…

Recent advances highlight Reinforcement Learning with Verifiable Rewards (RLVR) as a promising method for enhancing LLMs' capabilities. However, it remains unclear whether the current practice of RLVR truly expands a model's reasoning…

Robust statistical inference often faces a severe computational-statistical gap when dealing with complex parameter spaces. We investigate minimax signal detection in the Gaussian sequence model under strong $\epsilon$-contamination, where…

Large Language Models (LLMs) have shown a high capability in answering questions on a diverse range of topics. However, these models sometimes produce biased, ideologized or incorrect responses, limiting their applications if there is no…

Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…