arXiv research

Efficiently estimates sparse inverse covariance matrices in distributed systems.

Method estimates sparse inverse covariance and partial correlation matrices efficiently.

Estimates joint inverse covariances with shared structure across groups.

New bounds improve minimax estimation of banded precision matrices.

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

Estimates multiple covariance matrices from high-dimensional data classes.

The paper develops scalable Bayesian models for dynamic covariance matrices using Gaussian processes.

A new method for estimating sparse inverse covariance matrices.

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

New method optimizes sparse inverse covariance estimation with guaranteed optimality.

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…

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…

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

Paper solves a key problem in learning from high-dimensional covariance matrices.

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 …

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…

Extended wMEM approach for MEG inverse problem using wavelet and spatial filters.

Undirected graphs can be used to describe matrix variate distributions. In this paper, we develop new methods for estimating the graphical structures and underlying parameters, namely, the row and column covariance and inverse covariance matrices from the matrix variate data. Under sparsity conditions, we show that one…

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

Predict covariance from features using convex optimization.

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

Framework estimates precision matrices for heterogeneous populations.

We propose a method to clean covariance matrices of nonstationary systems by using time-independent eigenvalues.

ENN uses covariance matrices for gradient-free optimization in neural networks.

Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable, meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mea…

Paper analyzes ensemble Kalman updates for effective dimension and localization.

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…

WS diffusion models handle anisotropic Gaussian noise better than conventional methods.

New method computes dense partial correlations with applications in graph theory and uncertainty quantification.

New algorithm speeds up cluster-based compressive sensing tasks.

Simplified optimization for structured matrices in deep learning.

A new data-adaptive prior stabilizes kernel learning in operators.

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

A new covariance estimator reduces dimensionality in high-dimensional undersized samples.

Optimal data splitting improves covariance matrix estimation in large datasets.

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…

Method regularizes Cholesky factors to detect nonstationarity in longitudinal data.

Paper proposes a deep learning method for better covariance matrix forecasting.

We calculate eigenvector overlaps between intersecting time periods of covariance matrices.

Paper explores geometry of covariance matrices using associated bundles.

Dual PC algorithm improves structure learning of Bayesian networks.

Simple bounds for covariance and Gram matrices across various settings.

Formula for conditional covariance matrices simplified for elliptical distributions.

Estimates covariance matrices with correlations between samples.

Efficiently computes matrix square roots and their inverses for large matrices.

Diagonal transformations preserve independence structures in non-Gaussian distributions.

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

Study extends bounds on sample covariance matrices with general dependence.