Related papers: An Optimal Convergence Rate for the Gaussian Regul…

In this paper we study a family of variance reduction methods with randomized batch size---at each step, the algorithm first randomly chooses the batch size and then selects a batch of samples to conduct a variance-reduced stochastic…

This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…

Small regularizers can preserve linear programming solutions exactly. This paper provides the first average-case analysis of exact regularization: with a standard Gaussian cost vector and fixed constraint set, bounds are established for the…

This work focuses on developing and motivating a stochastic version of a wellknown inverse problem methodology. Specifically, we consider the iteratively regularized Gauss-Newton method, originally proposed by Bakushinskii for…

In high-dimensional statistical inference, sparsity regularizations have shown advantages in consistency and convergence rates for coefficient estimation. We consider a generalized version of Sparse-Group Lasso which captures both…

This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…

Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…

Modeled along the truncated approach in Panigrahi (2016), selection-adjusted inference in a Bayesian regime is based on a selective posterior. Such a posterior is determined together by a generative model imposed on data and the selection…

A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate…

The cubic regularized Newton method of Nesterov and Polyak has become increasingly popular for non-convex optimization because of its capability of finding an approximate local solution with second-order guarantee. Several recent works…

This report mainly focused on the basic concepts and the recovery methods for the random sampling. The recovery methods involve the orthogonal matching pursuit algorithm and the gradient-based total variation strategy. In particular, a fast…

Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting. However, the uniform sampling model is unrealistic for a…

Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in…

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…

Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…

Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…

An energy efficient use of large scale sensor networks necessitates activating a subset of possible sensors for estimation at a fusion center. The problem is inherently combinatorial; to this end, a set of iterative, randomized algorithms…

This paper deals with the minimization of large sum of convex functions by Inexact Newton (IN) methods employing subsampled functions, gradients and Hessian approximations. The Conjugate Gradient method is used to compute the inexact Newton…

We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as…