arXiv research

Method estimates sparse inverse covariance and partial correlation matrices efficiently.

The graphical lasso (glasso) is a widely-used fast algorithm for estimating sparse inverse covariance matrices. The glasso solves an L1 penalized maximum likelihood problem and is available as an R library on CRAN. The output from the glasso, a regularized covariance matrix estimate a sparse inverse covariance matrix e…

We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span a low dimensional linear subspace in the space of symmetric matrices, our aim i…

Efficiently estimates sparse inverse covariance matrices in distributed systems.

A new method for estimating sparse inverse covariance matrices.

New method optimizes sparse inverse covariance estimation with guaranteed optimality.

EiGLasso speeds up sparse Kronecker-sum covariance estimation.

Proposes a convex method for high-dimensional sparse sliced inverse regression.

Recently, there has been focus on penalized log-likelihood covariance estimation for sparse inverse covariance (precision) matrices. The penalty is responsible for inducing sparsity, and a very common choice is the convex $l_1$ norm. However, the best estimator performance is not always achieved with this penalty. The …

New methods improve portfolio risk minimization by estimating covariance matrix more accurately.

New estimator improves covariance matrix estimation under distributional uncertainty.

We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is numerically very challenging. We address this challenge by developing a new adaptive…

A multilevel framework speeds up sparse optimization for inverse covariance estimation and logistic regression.

HP-CONCORD optimizes sparse covariance estimation for large datasets.

We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional indepe…

A new method reduces the bias in estimating inverse covariance matrices from sketches.

The paper proposes AIS for Bayesian inversion of multioutput signals with covariance estimation.

Study shows sample complexity for logistic regression with normal covariates.

Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple regression approach with ideas of thresholding and refitting: first we infer a sparse u…

Several methods have been recently proposed for estimating sparse Gaussian graphical models using $\ell_{1}$ regularization on the inverse covariance matrix. Despite recent advances, contemporary applications require methods that are even faster in order to handle ill-conditioned high dimensional modern day datasets. I…

New bounds improve minimax estimation of banded precision matrices.

Study on Matérn covariance approximations on grids, finding issues with high-frequency aliasing.

Efficiently solves large-scale sparse covariance estimation problems.

In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying graph structure of a sparse Gaussian Markov Random Field (GMRF). We present two no…

Method estimates mean and covariance of unreplicated matrix-variate data.

New method balances covariates for stable causal survival effect estimation.

Efficiently models financial data with parsimonious sparse structures.

A-BLINK speeds up Gaussian process covariance estimation.

We consider the problem of estimating the inverse covariance matrix by maximizing the likelihood function with a penalty added to encourage the sparsity of the resulting matrix. We propose a new approach based on the split Bregman method to solve the regularized maximum likelihood estimation problem. We show that our m…

Efficiently learns RBMs using covariance estimates and adaptive learning rates.

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 the structure of the graph by estimating a sparse inverse covariance matrix from…

The L1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In this paper, a proximal gradient method (G-ISTA) for performing L1-regularized co…

Paper presents a new framework for covariance matrix estimation with geometric insights.

Given $n$ i.i.d. observations of a random vector $(X,Z)$, where $X$ is a high-dimensional vector and $Z$ is a low-dimensional index variable, we study the problem of estimating the conditional inverse covariance matrix $Ω(z) = (E[(X-E[X \mid Z])(X-E[X \mid Z])^T \mid Z=z])^{-1}$ under the assumption that the set of non…

Novel approach to robustly estimate inverse covariance matrix for multivariate data.

A method for converting NIW parameters for better estimation.

In a Gaussian graphical model, the conditional independence between two variables are characterized by the corresponding zero entries in the inverse covariance matrix. Maximum likelihood method using the smoothly clipped absolute deviation (SCAD) penalty (Fan and Li, 2001) and the adaptive LASSO penalty (Zou, 2006) hav…

The paper explores how multiway data from PDEs can be accurately tracked using EnKF with specific covariance and precision estimators.

Optimal data splitting improves covariance matrix estimation in large datasets.

New algorithm estimates Gaussian random fields without Cholesky factorization.

In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables $p\rightarrow\infty$ and the sample size $n\rightarrow\infty$ so that $p/n\rightarrow c\in (0, +\infty)$. The precision matrix is estimated directly, wit…

Paper analyzes ensemble Kalman updates for effective dimension and localization.

R-Learning uses inverse-variance weights to estimate treatment effects more accurately.

Meta-learning improves predictions with generalized ridge regression in high-dimensional settings.

In this paper, we obtain a property of the expectation of the inverse of compound Wishart matrices which results from their orthogonal invariance. Using this property as well as results from random matrix theory (RMT), we derive the asymptotic effect of the noise induced by estimating the covariance matrix on computing…

We establish a new framework for statistical estimation of directed acyclic graphs (DAGs) when data are generated from a linear, possibly non-Gaussian structural equation model. Our framework consists of two parts: (1) inferring the moralized graph from the support of the inverse covariance matrix; and (2) selecting th…

New method reduces memory usage for Bayesian inverse problems on large grids.

We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.