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Generalized Advantage Estimation (GAE) has been used to mitigate the computational complexity of reinforcement learning (RL) by employing an exponentially weighted estimation of the advantage function to reduce the variance in policy…

This paper presents a simulation study comparing the performance of generalized joint regression models (GJRM) with generalized linear mixed models (GLMM) and generalized estimating equations (GEE) for regression of longitudinal data with…

This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean…

In an increasing number of neuroimaging studies, brain images, which are in the form of multidimensional arrays (tensors), have been collected on multiple subjects at multiple time points. Of scientific interest is to analyze such massive…

Interactions between genes and environmental factors may play a key role in the etiology of many common disorders. Several regularized generalized linear models (GLMs) have been proposed for hierarchical selection of gene by environment…

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…

Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on…

Extending generalized estimating equations (GEE) to ordinal response data requires a conversion of the ordinal response to a vector of binary category indicators. That leads to a rather complicated association structure, and the…

Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable…

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…

Mutual information is a measure of the dependence between random variables that has been used successfully in myriad applications in many fields. Generalized mutual information measures that go beyond classical Shannon mutual information…

We present a new and general method of weighted least square univariate regression where the dependent variable is expanded as a series of suitably chosen functions of the independent variables. Each term of the series is obtained by an…

Longitudinal data are common in clinical trials and observational studies, where missing outcomes due to dropouts are always encountered. Under such context with the assumption of missing at random, the weighted generalized estimating…

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

Regression classes modeling more than the mean of the response have found a lot of attention in the last years. Expectile regression is a special and computationally convenient case of this family of models. Expectiles offer a quantile-like…

This article revisits the fundamental problem of parameter selection for Gaussian process interpolation. By choosing the mean and the covariance functions of a Gaussian process within parametric families, the user obtains a family of…

We propose generalized resubstitution error estimators for regression, a broad family of estimators, each corresponding to a choice of empirical probability measures and loss function. The usual sum of squares criterion is a special case…

Analysts often use data-driven approaches to supplement their substantive knowledge when selecting covariates for causal effect estimation. Multiple variable selection procedures tailored for causal effect estimation have been devised in…

Gaussian process regression is a powerful method for predicting states based on given data. It has been successfully applied for probabilistic predictions of structural systems to quantify, for example, the crack growth in mechanical…

A hierarchical Bayesian approach that permits simultaneous inference for the regression coefficient matrix and the error precision (inverse covariance) matrix in the multivariate linear model is proposed. Assuming a natural ordering of the…