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Stochastic optimization is an important task in many optimization problems where the tasks are not expressible as convex optimization problems. In the case of non-convex optimization problems, various different stochastic algorithms like…
We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, $X(t)$, and a scalar…
In this paper, we study a nonconvex, nonsmooth, and non-Lipschitz generalized symmetric matrix factorization model that unifies a broad class of matrix factorization formulations arising in machine learning, image science, engineering, and…
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. Unlike binary matrix factorization based on standard arithmetic, BMF employs the Boolean OR and AND operations for the…
In the non-negative matrix factorization (NMF) problem, the input is an $m\times n$ matrix $M$ with non-negative entries and the goal is to factorize it as $M\approx AW$. The $m\times k$ matrix $A$ and the $k\times n$ matrix $W$ are both…
This paper provides a theoretical analysis of a new learning problem for recommender systems where users provide feedback by comparing pairs of items instead of rating them individually. We assume that comparisons stem from latent user and…
Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…
We study inverse optimization (IO), where the goal is to use a parametric optimization program as the hypothesis class to infer relationships between input-decision pairs. Most of the literature focuses on learning only the objective…
We propose a new class of nonconvex penalty functions, based on data depth functions, for multitask sparse penalized regression. These penalties quantify the relative position of rows of the coefficient matrix from a fixed distribution…
Nonnegative matrix factorization (NMF) is a relatively new unsupervised learning algorithm that decomposes a nonnegative data matrix into a parts-based, lower dimensional, linear representation of the data. NMF has applications in image…
In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…
In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve a class of nonconvex optimization problems involving low-rank matrix variables. As opposed to the standard GN method, our algorithm allows one to handle…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…
Penalized estimation can conduct variable selection and parameter estimation simultaneously. The general framework is to minimize a loss function subject to a penalty designed to generate sparse variable selection. The…
We consider projection algorithms for solving (nonconvex) feasibility problems in Euclidean spaces. Of special interest are the Method of Alternating Projections (MAP) and the Douglas-Rachford or Averaged Alternating Reflection Algorithm…
In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. However, existing first-order methods for solving such problems either are too…
In this paper we consider the Nonnegative Matrix Factorization (NMF) problem: given an (elementwise) nonnegative matrix $V \in \R_+^{m\times n}$ find, for assigned $k$, nonnegative matrices $W\in\R_+^{m\times k}$ and $H\in\R_+^{k\times n}$…
Matrix factorization (MF) is a versatile learning method that has found wide applications in various data-driven disciplines. Still, many MF algorithms do not adequately scale with the size of available datasets and/or lack…
An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…
This paper investigates solving convex composite optimization on an undirected network, where each node, privately endowed with a smooth component function and a nonsmooth one, is required to minimize the sum of all the component functions…