Related papers: A data driven equivariant approach to constrained …

This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…

In the mixture modeling frame, this paper presents the polynomial Gaussian cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate data, in a twofold way. Firstly, it allows for possible nonlinear dependencies in the…

This paper proposes a flexible Bayesian approach to multiple imputation using conditional Gaussian mixtures. We introduce novel shrinkage priors for covariate-dependent mixing proportions in the mixture models to automatically select the…

Recent literature provides many computational and modeling approaches for covariance matrices estimation in a penalized Gaussian graphical models but relatively little study has been carried out on the choice of the tuning parameter. This…

We study the problem of learning mixtures of Gaussians with censored data. Statistical learning with censored data is a classical problem, with numerous practical applications, however, finite-sample guarantees for even simple latent…

Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference…

Gaussian process regression (GPR) has been a well-known machine learning method for various applications such as uncertainty quantifications (UQ). However, GPR is inherently a data-driven method, which requires sufficiently large dataset.…

This paper deals with Bayesian inference of a mixture of Gaussian distributions. A novel formulation of the mixture model is introduced, which includes the prior constraint that each Gaussian component is always assigned a minimal number of…

We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…

In the high-dimensional data setting, the sample covariance matrix is singular. In order to get a numerically stable and positive definite modification of the sample covariance matrix in the high-dimensional data setting, in this paper we…

Gaussian processes provide probabilistic surrogates for various applications including classification, uncertainty quantification, and optimization. Using a gradient-enhanced covariance matrix can be beneficial since it provides a more…

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…

Recent work on overfitting Bayesian mixtures of distributions offers a powerful framework for clustering multivariate data using a latent Gaussian model which resembles the factor analysis model. The flexibility provided by overfitting…

Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments,…

Optimal transport has found widespread applications in signal processing and machine learning. Among its many equivalent formulations, optimal transport seeks to reconstruct a random variable/vector with a prescribed distribution at the…

Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…

We propose to learn latent graphical models when data have mixed variables and missing values. This model could be used for further data analysis, including regression, classification, ranking etc. It also could be used for imputing missing…

This report presents an Expectation-Maximization (EM) algorithm for estimation of the maximum-likelihood parameter values of constrained multivariate autoregressive Gaussian state-space (MARSS) models. The MARSS model can be written:…

We present a data-driven approach for distributionally robust chance constrained optimization problems (DRCCPs). We consider the case where the decision maker has access to a finite number of samples or realizations of the uncertainty. The…

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…