Related papers: On the Computation and Applications of Large Dense…

Graphical modelling techniques based on sparse selection have been applied to infer complex networks in many fields, including biology and medicine, engineering, finance, and social sciences. One structural feature of some of the networks…

In-network distributed estimation of sparse parameter vectors via diffusion LMS strategies has been studied and investigated in recent years. In all the existing works, some convex regularization approach has been used at each node of the…

Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…

This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…

Machine Learning (ML) methods and tools have gained great success in many data, signal, image and video processing tasks, such as classification, clustering, object detection, semantic segmentation, language processing, Human-Machine…

Bilateral filters have wide spread use due to their edge-preserving properties. The common use case is to manually choose a parametric filter type, usually a Gaussian filter. In this paper, we will generalize the parametrization and in…

Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…

We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks…

Conventional compressed sensing theory assumes signals have sparse representations in a known, finite dictionary. Nevertheless, in many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the…

Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…

Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…

We propose a second-order accurate method to estimate the eigenvectors of extremely large matrices thereby addressing a problem of relevance to statisticians working in the analysis of very large datasets. More specifically, we show that…

Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many…

Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. Its solution is of central importance in covariance estimation, particularly in the recent…

Deep neural networks (DNNs) have emerged as key enablers of machine learning. Applying larger DNNs to more diverse applications is an important challenge. The computations performed during DNN training and inference are dominated by…

Random matrix theory has played an important role in recent work on statistical network analysis. In this paper, we review recent results on regimes of concentration of random graphs around their expectation, showing that dense graphs…

Despite the large research effort devoted to learning dependencies between time series, the state of the art still faces a major limitation: existing methods learn partial correlations but fail to discriminate across distinct frequency…

Graphical Gaussian models are popular tools for the estimation of (undirected) gene association networks from microarray data. A key issue when the number of variables greatly exceeds the number of samples is the estimation of the matrix of…