Related papers: Factor Analysis and Alternating Minimization
Given a positive definite covariance matrix $\widehat \Sigma$, we strive to construct an optimal \emph{approximate} factor analysis model $HH^\top +D$, with $H$ having a prescribed number of columns and $D>0$ diagonal. The optimality…
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 $H\in\R_+^{k\times n}$…
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 $H\in\R_+^{k\times n}$…
The modal factor model represents a new factor model for dimension reduction in high dimensional panel data. Unlike the approximate factor model that targets for the mean factors, it captures factors that influence the conditional mode of…
The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…
We pose the approximation problem for scalar nonnegative input-output systems via impulse response convolutions of finite order, i.e. finite order moving averages, based on repeated observations of input/output signal pairs. The problem is…
Factor analysis is a classical data reduction technique that seeks a potentially lower number of unobserved variables that can account for the correlations among the observed variables. This paper presents an extension of the factor…
We face the factor analysis problem using a particular class of auto-regressive processes. We propose an approximate moment matching approach to estimate the number of factors as well as the parameters of the model. This algorithm…
The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application to many…
Factor Analysis is about finding a low-rank plus sparse additive decomposition from a noisy estimate of the signal covariance matrix. In order to get such a decomposition, we formulate an optimization problem using the nuclear norm for the…
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…
The alternating minimization (AM) method is a fundamental method for minimizing convex functions whose variable consists of two blocks. How to efficiently solve each subproblems when applying the AM method is the most concerned task. In…
We pose the deterministic, nonparametric, approximation problem for scalar nonnegative input/output systems via finite impulse response convolutions, based on repeated observations of input/output signal pairs. The problem is converted into…
Factor analysis aims to describe high dimensional random vectors by means of a small number of unknown common factors. In mathematical terms, it is required to decompose the covariance matrix $\Sigma$ of the random vector as the sum of a…
Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problem. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basic matrix and a nonnegative…
Due to the COVID-19 pandemic, there is an increasing demand for portable CT machines worldwide in order to diagnose patients in a variety of settings. This has led to a need for CT image reconstruction algorithms that can produce high…
We propose a multivariate probability distribution that models a linear correlation between binary and continuous variables. The proposed distribution is a natural extension of the previously developed multivariate binary distribution. As…
We present theoretical guarantees for an alternating minimization algorithm for the dictionary learning/sparse coding problem. The dictionary learning problem is to factorize vector samples $y^{1},y^{2},\ldots, y^{n}$ into an appropriate…
Structured prediction can be considered as a generalization of many standard supervised learning tasks, and is usually thought as a simultaneous prediction of multiple labels. One standard approach is to maximize a score function on the…
The paper considers an extension of factor analysis to moving average processes. The problem is formulated as a rank minimization of a suitable spectral density. It is shown that it can be adequately approximated via a trace norm convex…