Related papers: Covariance Matrix Estimation from Linearly-Correla…

Spatial processes observed in various fields, such as climate and environmental science, often occur on a large scale and demonstrate spatial nonstationarity. Fitting a Gaussian process with a nonstationary Mat\'ern covariance is…

We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…

We study the minimal sample size N=N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, with an arbitrary fixed accuracy. We establish the optimal bound…

We study parameter estimation in linear Gaussian covariance models, which are $p$-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex…

Canonical correlation analysis investigates linear relationships between two sets of variables, but often works poorly on modern data sets due to high-dimensionality and mixed data types such as continuous, binary and zero-inflated. To…

An accurate covariance matrix is essential for obtaining reliable cosmological results when using a Gaussian likelihood. In this paper we study the covariance of pseudo-$C_\ell$ estimates of tomographic cosmic shear power spectra. Using two…

Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often…

For a multivariate normal distribution, the sparsity of the covariance and precision matrices encodes complete information about independence and conditional independence properties. For general distributions, the covariance and precision…

We study the problem of high-dimensional covariance estimation under the constraint that the partial correlations are nonnegative. The sign constraints dramatically simplify estimation: the Gaussian maximum likelihood estimator is well…

We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…

We evaluate the covariance matrix of the matter power spectrum using perturbation theory up to dominant terms at 1-loop order and compare it to numerical simulations. We decompose the covariance matrix into the disconnected (Gaussian) part,…

This paper deals with the time-varying high dimensional covariance matrix estimation. We propose two covariance matrix estimators corresponding with a time-varying approximate factor model and a time-varying approximate characteristic-based…

We consider the problem of estimating the covariance structure of a random vector $Y\in \mathbb R^d$ from a sample $Y_1,\ldots,Y_n$. We are interested in the situation when $d$ is large compared to $n$ but the covariance matrix $\Sigma$ of…

Statistical modeling of spatiotemporal phenomena often requires selecting a covariance matrix from a covariance class. Yet standard parametric covariance families can be insufficiently flexible for practical applications, while…

We consider the problem of learning error covariance matrices for robotic state estimation. The convergence of a state estimator to the correct belief over the robot state is dependent on the proper tuning of noise models. During inference,…

Gaussian copula has been employed to evaluate the outage performance of Fluid Antenna Systems (FAS), with the covariance matrix reflecting the dependence among multivariate normal random variables (RVs). While prior studies approximate this…

Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical…

We study the covariance of the cross-power spectrum of different tracers for the large-scale structure. We develop the counts-in-cells framework for the multi-tracer approach, and use this to derive expressions for the full non-Gaussian…

A separable covariance model for a random matrix provides a parsimonious description of the covariances among the rows and among the columns of the matrix, and permits likelihood-based inference with a very small sample size. However, in…

In the context of the Oppenheim-Horodecki paradigm of nonclassical correlation, a bipartite quantum state is (properly) classically correlated if and only if it is represented by a density matrix having a product eigenbasis. On the basis of…