相关论文: Automatic Methods for Handling Nearly Singular Cov…

In many applications, it is of interest to assess the dependence structure in multivariate longitudinal data. Discovering such dependence is challenging due to the dimensionality involved. By concatenating the random effects from component…

Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…

We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…

A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…

We propose a general nonparametric Bayesian framework for binary regression, which is built from modeling for the joint response-covariate distribution. The observed binary responses are assumed to arise from underlying continuous random…

If a tensor with various symmetries is properly unfolded, then the resulting matrix inherits those symmetries. As tensor computations become increasingly important it is imperative that we develop efficient structure preserving methods for…

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization…

Cosmological covariance matrices are fundamental for parameter inference, since they are responsible for propagating uncertainties from the data down to the model parameters. However, when data vectors are large, in order to estimate…

Interior-point methods for linear programming problems require the repeated solution of a linear system of equations. Solving these linear systems is non-trivial due to the severe ill-conditioning of the matrices towards convergence. This…

In this paper, we present a novel framework incorporating a combination of sparse models in different domains. We posit the observed data as generated from a linear combination of a sparse Gaussian Markov model (with a sparse precision…

We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the…

Linear structural equation models, which relate random variables via linear interdependencies and Gaussian noise, are a popular tool for modeling multivariate joint distributions. These models correspond to mixed graphs that include both…

It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated…

The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…

Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a…

Numerical nonlinear algebra is applied to maximum likelihood estimation for Gaussian models defined by linear constraints on the covariance matrix. We examine the generic case as well as special models (e.g. Toeplitz, sparse, trees) that…

Randomly pivoted Cholesky (RPCholesky) is an algorithm for constructing a low-rank approximation of a positive-semidefinite matrix using a small number of columns. This paper develops an accelerated version of RPCholesky that employs block…

Kernel methods represent some of the most popular machine learning tools for data analysis. Since exact kernel methods can be prohibitively expensive for large problems, reliable low-rank matrix approximations and high-performance…

This paper addresses the statistical estimation of Gaussian Mixture Models (GMMs) with unknown diagonal covariances from independent and identically distributed samples. We employ the Beurling-LASSO (BLASSO), a convex optimization framework…