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This paper presents a novel algorithm that leverages Stochastic Gradient Descent strategies in conjunction with Random Features to augment the scalability of Conic Particle Gradient Descent (CPGD) specifically tailored for solving sparse…

The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…

We study offline reinforcement learning in average-reward MDPs, which presents increased challenges from the perspectives of distribution shift and non-uniform coverage, and has been relatively underexamined from a theoretical perspective.…

We consider PAC-learning a good item from $k$-subsetwise feedback information sampled from a Plackett-Luce probability model, with instance-dependent sample complexity performance. In the setting where subsets of a fixed size can be tested…

Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…

In real life, we frequently come across data sets that involve some independent explanatory variable(s) generating a set of ordinal responses. These ordinal responses may correspond to an underlying continuous latent variable, which is…

Inference-time scaling methods rely on Process Reward Models (PRMs), which are often poorly calibrated and overestimate success probabilities. We propose, to our knowledge, the first use of conditional optimal transport for calibrating…

In this study, we derive Probably Approximately Correct (PAC) bounds on the asymptotic sample-complexity for RL within the infinite-horizon Markov Decision Process (MDP) setting that are sharper than those in existing literature. The…

Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…

We consider variable selection in high-dimensional linear models where the number of covariates greatly exceeds the sample size. We introduce the new concept of partial faithfulness and use it to infer associations between the covariates…

Measuring how quickly iterative methods converge is essential in computational mathematics, but current approaches have significant limitations. Q-order analysis requires strict smoothness conditions, while R-order analysis lacks precision…

We consider a change-point detection problem for a simple class of Piecewise Deterministic Markov Processes (PDMPs). A continuous-time PDMP is observed in discrete time and through noise, and the aim is to propose a numerical method to…

Machine learning (ML) systems are increasingly deployed in high-stakes domains where reliability is paramount. This thesis investigates how uncertainty estimation can enhance the safety and trustworthiness of ML, focusing on selective…

A general approach to provide approximate parameterizations of the "small" scales by the "large" ones, is developed for stochastic partial differential equations driven by linear multiplicative noise. This is accomplished via the concept of…

The problem of detection and possible estimation of a signal generated by a dynamic system when a variable number of noisy measurements can be taken is here considered. Assuming a Markov evolution of the system (in particular, the pair…

We consider a partially observable Markov decision problem (POMDP) that models a class of sequencing problems. Although POMDPs are typically intractable, our formulation admits tractable solution. Instead of maintaining a value function…

This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…

Conformal prediction is a powerful tool to generate uncertainty sets with guaranteed coverage using any predictive model, under the assumption that the training and test data are i.i.d.. Recently, it has been shown that adversarial examples…

Partially observable Markov decision processes (POMDPs) provide a flexible representation for real-world decision and control problems. However, POMDPs are notoriously difficult to solve, especially when the state and observation spaces are…

This paper develops a predictive switching control algorithm for stochastic gene regulatory networks described by a Partial Integro-Differential Equation (PIDE) model, which enables direct shape control of the probability density function.…