Related papers: Estimation When Both Covariance And Precision Matr…
The estimation of the covariance matrix is an initial step in many multivariate statistical methods such as principal components analysis and factor analysis, but in many practical applications the dimensionality of the sample space is…
Many data-analysis problems involve large dense matrices that describe the covariance of stationary noise processes; the computational cost of inverting these matrices, or equivalently of solving linear systems that contain them, is often a…
We introduce a technique for estimating a structured covariance matrix from observations of a random vector which have been sketched. Each observed random vector $\boldsymbol{x}_t$ is reduced to a single number by taking its inner product…
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…
Covariance matrices are important tools for obtaining reliable parameter constraints. Advancements in cosmological surveys lead to larger data vectors and, consequently, increasingly complex covariance matrices, whose number of elements…
Estimating covariance parameters for multivariate spatial Gaussian random fields is computationally challenging, as the number of parameters grows rapidly with the number of variables, and likelihood evaluation requires operations of order…
Gradient-based solvers risk convergence to local optima, leading to incorrect researcher inference. Heuristic-based algorithms are able to ``break free" of these local optima to eventually converge to the true global optimum. However, given…
This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…
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…
We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…
We consider Gaussian mixture models in high dimensions and concentrate on the twin tasks of detection and feature selection. Under sparsity assumptions on the difference in means, we derive information bounds and establish the performance…
Supervised learning methods with missing data have been extensively studied not just due to the techniques related to low-rank matrix completion. Also in unsupervised learning one often relies on imputation methods. As a matter of fact,…
The maximum absolute correlation between regressors, which is called mutual coherence, plays an essential role in sparse estimation. A regressor matrix whose columns are highly correlated may result from optimal input design, since there is…
The sparse signal processing literature often uses random sensing matrices to obtain performance guarantees. Unfortunately, in the real world, sensing matrices do not always come from random processes. It is therefore desirable to evaluate…
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…
Consider a regression model with fixed design and Gaussian noise where the regression function can potentially be well approximated by a function that admits a sparse representation in a given dictionary. This paper resorts to exponential…
We address a problem of covariance selection, where we seek a trade-off between a high likelihood against the number of non-zero elements in the inverse covariance matrix. We solve a maximum likelihood problem with a penalty term given by…
Estimation of covariance matrices or their inverses plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. In this paper we present an…
Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where…
The accurate computation of the covariance matrix of fitted model parameters is a somewhat neglected task in Statistics. Algorithms are given for computing accurate covariance matrices derived from computing the Hessian matrix by numerical…