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Large language models (LLMs) have shown promise in performing complex multi-step reasoning, yet they continue to struggle with mathematical reasoning, often making systematic errors. A promising solution is reinforcement learning (RL)…

Mixup generates augmented samples by linearly interpolating inputs and labels with a controllable ratio. However, since it operates in the latent embedding level, the resulting samples are not human-interpretable. In contrast, LLM-based…

Large-scale multiple testing is a fundamental problem in high dimensional statistical inference. It is increasingly common that various types of auxiliary information, reflecting the structural relationship among the hypotheses, are…

In this paper, a novel pattern classification approach is proposed by regularizing the classifier learning to maximize mutual information between the classification response and the true class label. We argue that, with the learned…

Data augmentation has been widely applied as an effective methodology to improve generalization in particular when training deep neural networks. Recently, researchers proposed a few intensive data augmentation techniques, which indeed…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

This paper presents computationally feasible rank-one relaxation algorithms for the efficient simulation of a time-incremental damage model with nonconvex incremental stress potentials in multiple spatial dimensions. While the standard…

$\ell_1$-penalized quantile regression is widely used for analyzing high-dimensional data with heterogeneity. It is now recognized that the $\ell_1$-penalty introduces non-negligible estimation bias, while a proper use of concave…

Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined…

We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems…

A new nonparametric estimator of a convex regression function in any dimension is proposed and its convergence properties are studied. We start by using any estimator of the regression function and we \emph{convexify} it by taking the…

One of the major limitations for the employment of model-based planning and scheduling in practical applications is the need of costly re-planning when an incongruence between the observed reality and the formal model is encountered during…

A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added…

The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in…

We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving empirical risk minimization (ERM) problems with a nonsmooth regularization term. Our algorithm is applicable…

We propose a doubly robust estimator for the average treatment effect in high dimensional low sample size observational studies, where contamination and model misspecification pose serious inferential challenges. The estimator combines…

In this paper, we develop a simulation-based framework for regularized logistic regression, exploiting two novel results for scale mixtures of normals. By carefully choosing a hierarchical model for the likelihood by one type of mixture,…

The optimality and sensitivity of the empirical risk minimization problem with relative entropy regularization (ERM-RER) are investigated for the case in which the reference is a sigma-finite measure instead of a probability measure. This…

This paper proposes an algorithm for computing regularized solutions to linear rational expectations models. The algorithm allows for regularization cross-sectionally as well as across frequencies. A variety of numerical examples illustrate…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…