Related papers: High-dimensional Sparse Inverse Covariance Estimat…
We propose maximum likelihood estimation for learning Gaussian graphical models with a Gaussian (ell_2^2) prior on the parameters. This is in contrast to the commonly used Laplace (ell_1) prior for encouraging sparseness. We show that our…
Precision matrix estimation is an important problem in statistical data analysis. This paper introduces a fast sparse precision matrix estimation algorithm, namely GISS$^{{\rho}}$, which is originally introduced for compressive sensing. The…
Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic…
Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
Partial differential equation parameter estimation is a mathematical and computational process used to estimate the unknown parameters in a partial differential equation model from observational data. This paper employs a greedy sampling…
The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…
Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…
We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…
Inverse imaging problems rely on limited and indirect measurements, making reconstruction highly dependent on both regularization and sample locations. We introduce a novel greedy framework for the optimal selection of indirect measurements…
We consider multichannel sparse recovery problem where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known…
In this paper, we propose two new algorithms for maximum-likelihood estimation (MLE) of high dimensional sparse covariance matrices. Unlike most of the state of-the-art methods, which either use regularization techniques or penalize the…
For a tall $n\times d$ matrix $A$ and a random $m\times n$ sketching matrix $S$, the sketched estimate of the inverse covariance matrix $(A^\top A)^{-1}$ is typically biased: $E[(\tilde A^\top\tilde A)^{-1}]\ne(A^\top A)^{-1}$, where…
In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…
This paper is devoted to the problem of sampling Gaussian fields in high dimension. Solutions exist for two specific structures of inverse covariance : sparse and circulant. The proposed approach is valid in a more general case and…
Iterative methods for fitting a Gaussian Random Field (GRF) model via maximum likelihood (ML) estimation requires solving a nonconvex optimization problem. The problem is aggravated for anisotropic GRFs where the number of covariance…
Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained…
We propose a class of greedy algorithms for weighted sparse recovery by considering new loss function-based generalizations of Orthogonal Matching Pursuit (OMP). Given a (regularized) loss function, the proposed algorithms alternate the…
In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements…
Gaussian graphical models (GGM) have been widely used in many high-dimensional applications ranging from biological and financial data to recommender systems. Sparsity in GGM plays a central role both statistically and computationally.…