Related papers: Factor Analysis of Moving Average Processes
We propose a combined model, which integrates the latent factor model and the logistic regression model, for the citation network. It is noticed that neither a latent factor model nor a logistic regression model alone is sufficient to…
Affine matrix rank minimization problem is a fundamental problem with a lot of important applications in many fields. It is well known that this problem is combinatorial and NP-hard in general. In this paper, a continuous promoting low rank…
We study the problem of learning a tensor from a set of linear measurements. A prominent methodology for this problem is based on a generalization of trace norm regularization, which has been used extensively for learning low rank matrices,…
Consider a set of N agents seeking to solve distributively the minimization problem $\inf_{x} \sum_{n = 1}^N f_n(x)$ where the convex functions $f_n$ are local to the agents. The popular Alternating Direction Method of Multipliers has the…
We present theoretical results on the convergence of \emph{non-convex} accelerated gradient descent in matrix factorization models with $\ell_2$-norm loss. The purpose of this work is to study the effects of acceleration in non-convex…
It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…
Procrustes problems are matrix approximation problems searching for a~transformation of the given dataset to fit another dataset. They find applications in numerous areas, such as factor and multivariate analysis, computer vision,…
We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…
This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise which are observed at high frequency. Our method generalizes the pre-averaging approach (see [Bernoulli 15 (2009) 634--658,…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate…
We present a novel factor analysis method that can be applied to the discovery of common factors shared among trajectories in multivariate time series data. These factors satisfy a precedence-ordering property: certain factors are recruited…
In this work, we consider non-collocated sensors and actuators, and we address the problem of minimizing the number of sensor-to-actuator transmissions while ensuring that the L2 gain of the system remains under a threshold. By using causal…
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…
This article focuses on covariance estimation for multi-study data. Popular approaches employ factor-analytic terms with shared and study-specific loadings that decompose the variance into (i) a shared low-rank component, (ii)…
The problem of low-rank approximation with convex constraints, which appears in data analysis, system identification, model order reduction, low-order controller design and low-complexity modelling is considered. Given a matrix, the…
We study the generalized trace regression with a near low-rank regression coefficient matrix, which extends notion of sparsity for regression coefficient vectors. Specifically, given a matrix covariate $X$, the probability density function…
The minimality of the penalization function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and…
Matrix rank minimization problems are gaining a plenty of recent attention in both mathematical and engineering fields. This class of problems, arising in various and across-discipline applications, is known to be NP-hard in general. In…
For the problem of reconstructing a low-rank matrix from a few linear measurements, two classes of algorithms have been widely studied in the literature: convex approaches based on nuclear norm minimization, and non-convex approaches that…