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We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…

Support Vector Machine (SVM) stands out as a prominent machine learning technique widely applied in practical pattern recognition tasks. It achieves binary classification by maximizing the "margin", which represents the minimum distance…

There remains an open question about the usefulness and the interpretation of Machine learning (MLE) approaches for discrimination of spatial patterns of brain images between samples or activation states. In the last few decades, these…

Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…

The linear Markov Decision Process (MDP) framework offers a principled foundation for reinforcement learning (RL) with strong theoretical guarantees and sample efficiency. However, its restrictive assumption-that both transition dynamics…

Markov decision processes (MDPs) with large number of states are of high practical interest. However, conventional algorithms to solve MDP are computationally infeasible in this scenario. Approximate dynamic programming (ADP) methods tackle…

Random feature latent variable models (RFLVMs) represent the state-of-the-art in latent variable models, capable of handling non-Gaussian likelihoods and effectively uncovering patterns in high-dimensional data. However, their heavy…

Retrieval Augmented Language Models (RALMs) have gained significant attention for their ability to generate accurate answer and improve efficiency. However, RALMs are inherently vulnerable to imperfect information due to their reliance on…

Studies on generalization performance of machine learning algorithms under the scope of information theory suggest that compressed representations can guarantee good generalization, inspiring many compression-based regularization methods.…

Mathematical reasoning is a central challenge for large language models (LLMs), requiring not only correct answers but also faithful reasoning processes. Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising…

The mathematical theory of reproducing kernel Hilbert spaces (RKHS) provides powerful tools for minimum variance estimation (MVE) problems. Here, we extend the classical RKHS based analysis of MVE in several directions. We develop a…

We study the generalization behavior of Markov Logic Networks (MLNs) across relational structures of different sizes. Multiple works have noticed that MLNs learned on a given domain generalize poorly across domains of different sizes. This…

Maximum Likelihood Estimation (MLE) and Likelihood Ratio Test (LRT) are widely used methods for estimating the transition probability matrix in Markov chains and identifying significant relationships between transitions, such as equality.…

We propose a boundary neuron method with random features (BNM-RF) for solving partial differential equations. The method approximates the unknown boundary function by a shallow network within the boundary integral formulation. With randomly…

We study linear regressions in a context where the outcome of interest and some of the covariates are observed in two different datasets that cannot be matched. Traditional approaches obtain point identification by relying, often…

Variance reduction (VR) methods employ stochastic gradients with decreasing variance, and they have been widely applied to solve large-scale optimization problems in machine learning because of their efficiency. Existing theoretical studies…

Logistic regression is a ubiquitous method for probabilistic classification. However, the effectiveness of logistic regression depends upon careful and relatively computationally expensive tuning, especially for the regularisation…

To overcome the curses of dimensionality and modeling of Dynamic Programming (DP) methods to solve Markov Decision Process (MDP) problems, Reinforcement Learning (RL) methods are adopted in practice. Contrary to traditional RL algorithms…

Sparse regularized regression methods are now widely used in genome-wide association studies (GWAS) to address the multiple testing burden that limits discovery of potentially important predictors. Linear mixed models (LMMs) have become an…

Due to the ease of modern data collection, applied statisticians often have access to a large set of covariates that they wish to relate to some observed outcome. Generalized linear models (GLMs) offer a particularly interpretable framework…