Related papers: Parameter inference with estimated covariance matr…

It is difficult to use subsampling with variational inference in hierarchical models since the number of local latent variables scales with the dataset. Thus, inference in hierarchical models remains a challenge at large scale. It is…

We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…

Covariance estimation for high-dimensional datasets is a fundamental problem in modern day statistics with numerous applications. In these high dimensional datasets, the number of variables p is typically larger than the sample size n. A…

Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…

The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important…

The sparse Cholesky parametrization of the inverse covariance matrix can be interpreted as a Gaussian Bayesian network; however its counterpart, the covariance Cholesky factor, has received, with few notable exceptions, little attention so…

This paper considers estimating a covariance matrix of $p$ variables from $n$ observations by either banding or tapering the sample covariance matrix, or estimating a banded version of the inverse of the covariance. We show that these…

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…

Many statistical problems in causal inference involve a probability distribution other than the one from which data are actually observed; as an additional complication, the object of interest is often a marginal quantity of this other…

This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…

We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several…

The missing data issue often complicates the task of estimating generalized linear models (GLMs). We describe why the pseudo-marginal Metropolis-Hastings algorithm, used in this setting, is an effective strategy for parameter estimation.…

An inference procedure is proposed to provide consistent estimators of parameters in a modal regression model with a covariate prone to measurement error. A score-based diagnostic tool exploiting parametric bootstrap is developed to assess…

Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…

This paper studies the problem of estimating a covariance matrix from correlated sub-Gaussian samples. We consider using the correlated sample covariance matrix estimator to approximate the true covariance matrix. We establish…

An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…

We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…

Profile likelihoods are rarely used in geostatistical models due to the computational burden imposed by repeated decompositions of large variance matrices. Accounting for uncertainty in covariance parameters can be highly consequential in…

Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…

Covariance estimation becomes challenging in the regime where the number p of variables outstrips the number n of samples available to construct the estimate. One way to circumvent this problem is to assume that the covariance matrix is…