Related papers: On Constructing Confidence Region for Model Parame…

We developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a…

Boosting methods are widely used in statistical learning to deal with high-dimensional data due to their variable selection feature. However, those methods lack straightforward ways to construct estimators for the precision of the…

We consider linear two-time-scale stochastic approximation algorithms driven by martingale noise. Recent applications in machine learning motivate the need to understand finite-time error rates, but conventional stochastic approximation…

We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…

We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic models. Especially, we propose a specific algorithm, termed STRME, in which the trust-region radius depends linearly on the…

Sketching and stochastic gradient methods are arguably the most common techniques to derive efficient large scale learning algorithms. In this paper, we investigate their application in the context of nonparametric statistical learning.…

Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known (or estimable from replicate data). A generalized method of moments approach can be used to estimate model…

This paper addresses the computational challenges in reliability-based topology optimization (RBTO) of structures associated with the estimation of statistics of the objective and constraints using standard sampling methods, and overcomes…

We study high-dimensional linear models with error-in-variables. Such models are motivated by various applications in econometrics, finance and genetics. These models are challenging because of the need to account for measurement errors to…

Stochastic gradient descent (SGD) and its variants have established themselves as the go-to algorithms for large-scale machine learning problems with independent samples due to their generalization performance and intrinsic computational…

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…

In recent years, methods of approximate parameter estimation have attracted considerable interest in complex problems where exact likelihoods are hard to obtain. In their most basic form, Bayesian methods such as Approximate Bayesian…

We propose a method to efficiently determine the optimal coarse-grained force field in mesoscopic stochastic simulations of Newtonian fluid and polymer melt systems modeled by dissipative particle dynamics (DPD) and energy conserving…

We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or…

Classical trust region methods were designed to solve problems in which function and gradient information are exact. This paper considers the case when there are bounded errors (or noise) in the above computations and proposes a simple…

Low-rank matrix regression refers to the instances of recovering a low-rank matrix based on specially designed measurements and the corresponding noisy outcomes. In the last decade, numerous statistical methodologies have been developed for…

Regression modeling is the workhorse of statistics and there is a vast literature on estimation of the regression function. It is realized in recent years that in regression analysis the ultimate aim may be the estimation of a level set of…

Low-rank matrix estimation plays a central role in various applications across science and engineering. Recently, nonconvex formulations based on matrix factorization are provably solved by simple gradient descent algorithms with strong…

The simplest, and most common, stochastic model for population processes, including those from biochemistry and cell biology, are continuous time Markov chains. Simulation of such models is often relatively straightforward as there are…

A general approach to selective inference is considered for hypothesis testing of the null hypothesis represented as an arbitrary shaped region in the parameter space of multivariate normal model. This approach is useful for hierarchical…