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Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is sub-optimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings…
A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…
Early approaches to multiple-output Gaussian processes (MOGPs) relied on linear combinations of independent, latent, single-output Gaussian processes (GPs). This resulted in cross-covariance functions with limited parametric interpretation,…
Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables…
The Pearson-Matthews correlation coefficient (usually abbreviated MCC) is considered to be one of the most useful metrics for the performance of a binary classification or hypothesis testing method (for the sake of conciseness we will use…
Gaussian process (GP) covariance function is proposed as a matching tool in GPMatch within a full Bayesian framework under relatively weaker causal assumptions. The matching is accomplished by utilizing GP prior covariance function to…
We propose a new model selection criterion for mixed effects regression models that is computable when the model is fitted with a two-step method, even when the structure and the distribution of the random effects are unknown. The criterion…
It is known that the estimating equations for quantile regression (QR) can be solved using an EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent…
Finite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily…
Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…
This paper proposes computationally efficient methods that can be used for instrumental variable quantile regressions (IVQR) and related methods with statistical guarantees. This is much needed when we investigate heterogenous treatment…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
Accurately modeling the correlation structure of errors is critical for reliable uncertainty quantification in probabilistic time series forecasting. While recent deep learning models for multivariate time series have developed efficient…
We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse…
This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking…
Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
We investigate the complexity of covariance matrix estimation for Gibbs distributions based on dependent samples from a Markov chain. We show that when $\pi$ satisfies a Poincar\'e inequality and the chain possesses a spectral gap, we can…
Researchers are often interested in understanding the relationship between a set of covariates and a set of response variables. To achieve this goal, the use of regression analysis, either linear or generalized linear models, is largely…
We propose a novel approach for modeling multivariate longitudinal data in the presence of unobserved heterogeneity for the analysis of the Health and Retirement Study (HRS) data. Our proposal can be cast within the framework of linear…