Related papers: Multi-reference factor analysis: low-rank covarian…
In this paper, we consider the Group Lasso estimator of the covariance matrix of a stochastic process corrupted by an additive noise. We propose to estimate the covariance matrix in a high-dimensional setting under the assumption that the…
We develop a fast algorithm for Kalman Filter applied to the random walk forecast model. The key idea is an efficient representation of the estimate covariance matrix at each time-step as a weighted sum of two contributions - the process…
Multivariate time series can often have a large number of dimensions, whether it is due to the vast amount of collected features or due to how the data sources are processed. Frequently, the main structure of the high-dimensional time…
In this paper we study covariance estimation with missing data. We consider missing data mechanisms that can be independent of the data, or have a time varying dependency. Additionally, observed variables may have arbitrary (non uniform)…
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…
In biomedical studies, testing for differences in covariance offers scientific insights beyond mean differences, especially when differences are driven by complex joint behavior between features. However, when differences in joint behavior…
This paper studies the problem of recovering a signal vector and the corrupted noise vector from a collection of corrupted linear measurements through the solution of a l1 minimization, where the sensing matrix is a partial Fourier matrix…
Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to…
Low-rank tensor approximation error bounds are proposed for the case of noisy input data that depend on low-rank representation type, rank and the dimensionality of the tensor. The bounds show that high-dimensional low-rank structured…
In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…
Pseudospectral analysis is fundamental for quantifying the sensitivity and transient behavior of nonnormal matrices, yet its computational cost scales cubically with dimension, rendering it prohibitive for large-scale systems. While…
We consider the problem of estimating the uncertainty in statistical inverse problems using Bayesian inference. When the probability density of the noise and the prior are Gaussian, the solution of such a statistical inverse problem is also…
Adaptive algorithms based on sample matrix inversion belong to an important class of algorithms used in radar target detection to overcome prior uncertainty of interference covariance. Sample matrix inversion problem is generally ill…
This paper considers blind methods for centrality estimation from graph signals. We model graph signals as the outcome of an unknown low-pass graph filter excited with influences governed by a sparse sub-graph. This model is compatible with…
We study the rank of the instantaneous or spot covariance matrix $\Sigma_X(t)$ of a multidimensional continuous semi-martingale $X(t)$. Given high-frequency observations $X(i/n)$, $i=0,\ldots,n$, we test the null hypothesis…
To recover a low rank structure from a noisy matrix, truncated singular value decomposition has been extensively used and studied. Recent studies suggested that the signal can be better estimated by shrinking the singular values. We pursue…
Low-rank regularization is an effective technique for addressing ill-posed inverse problems when the unknown variable exhibits low-rank characteristics. However, global low-rank assumptions do not always hold for seismic wavefields; in many…
A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…
We study the low-rank phase retrieval problem, where we try to recover a $d_1\times d_2$ low-rank matrix from a series of phaseless linear measurements. This is a fourth-order inverse problem, as we are trying to recover factors of matrix…
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…