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We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…
In contrast to the many continuous global optimization methods that assume the objective function and constraints are factorable, we study how to find globally maximal solutions to problems that are not factorable, focusing on a particular…
We address the minimization of a smooth objective function under an $\ell_0$-constraint and simple convex constraints. When the problem has no constraints except the $\ell_0$-constraint, some efficient algorithms are available; for example,…
Value functions are central to Dynamic Programming and Reinforcement Learning but their exact estimation suffers from the curse of dimensionality, challenging the development of practical value-function (VF) estimation algorithms. Several…
We study a general factor analysis framework where the $n$-by-$p$ data matrix is assumed to follow a general exponential family distribution entry-wise. While this model framework has been proposed before, we here further relax its…
The Conditional Gradient Method is generalized to a class of non-smooth non-convex optimization problems with many applications in machine learning. The proposed algorithm iterates by minimizing so-called model functions over the constraint…
Panel vector auto-regressive (VAR) models are widely used to capture the dynamics of multivariate time series across different subpopulations, where each subpopulation shares a common set of variables. In this work, we propose a panel VAR…
Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The…
In this paper we revisit under-determined linear systems of equations with sparse solutions. As is well known, these systems are among core mathematical problems of a very popular compressed sensing field. The popularity of the field as…
Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…
The convergence analysis of optimization algorithms using continuous-time dynamical systems has received much attention in recent years. In this paper, we investigate applications of these systems to analyze the convergence of linearized…
Tensor decomposition is a powerful tool for extracting physically meaningful latent factors from multi-dimensional nonnegative data, and has been an increasing interest in a variety of fields such as image processing, machine learning, and…
$\ell_1$ optimization is a well known heuristic often employed for solving various forms of sparse linear problems. In this paper we look at its a variant that we refer to as the \emph{partial} $\ell_1$ and discuss its mathematical…
We introduce the Stochastic Asynchronous Proximal Alternating Linearized Minimization (SAPALM) method, a block coordinate stochastic proximal-gradient method for solving nonconvex, nonsmooth optimization problems. SAPALM is the first…
Nonnegative matrix factorization (NMF), which is the approximation of a data matrix as the product of two nonnegative matrices, is a key issue in machine learning and data analysis. One approach to NMF is to formulate the problem as a…
We study the factor model problem, which aims to uncover low-dimensional structures in high-dimensional datasets. Adopting a robust data-driven approach, we formulate the problem as a saddle-point optimization. Our primary contribution is a…
This paper considers an approximate dynamic matrix factor model that accounts for the time series nature of the data by explicitly modelling the time evolution of the factors. We study estimation of the model parameters based on the…
As the Internet developed rapidly, it is important to choose suitable web services from a wide range of candidates. Quality of service (QoS) describes the performance of a web service dynamically with respect to the service requested by the…
The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undesirable phenomenon: the condition number, classically…
Anderson acceleration (AA) has a long history of use and a strong recent interest due to its potential ability to dramatically improve the linear convergence of the fixed-point iteration. Most authors are simply using and analyzing the…