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Gaussian graphical models can capture complex dependency structures among variables. For such models, Bayesian inference is attractive as it provides principled ways to incorporate prior information and to quantify uncertainty through the…
Computer simulations often involve both qualitative and numerical inputs. Existing Gaussian process (GP) methods for handling this mainly assume a different response surface for each combination of levels of the qualitative factors and…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
The Gaussian process (GP) is a popular way to specify dependencies between random variables in a probabilistic model. In the Bayesian framework the covariance structure can be specified using unknown hyperparameters. Integrating over these…
Gaussian processes (GPs), or distributions over arbitrary functions in a continuous domain, can be generalized to the multi-output case: a linear model of coregionalization (LMC) is one approach. LMCs estimate and exploit correlations…
We present a Gaussian Process - Latent Class Choice Model (GP-LCCM) to integrate a non-parametric class of probabilistic machine learning within discrete choice models (DCMs). Gaussian Processes (GPs) are kernel-based algorithms that…
In this paper, we investigate a class of approximate Gaussian processes (GP) obtained by taking a linear combination of compactly supported basis functions with the basis coefficients endowed with a dependent Gaussian prior distribution.…
This paper presents a new approach to a robust Gaussian process (GP) regression. Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution, such as the…
Gaussian processes (GPs) play an essential role in biostatistics, scientific machine learning, and Bayesian optimization for their ability to provide probabilistic predictions and model uncertainty. However, GP inference struggles to scale…
We introduce constrained Gaussian process (CGP), a Gaussian process model for random functions that allows easy placement of mathematical constrains (e.g., non-negativity, monotonicity, etc) on its sample functions. CGP comes with…
This paper considers the Laplace method to derive approximate inference for the Gaussian process (GP) regression in the location and scale parameters of the Student-t probabilistic model. This allows both mean and variance of the data to…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…
We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank…
This paper presents a new approach for Gaussian process (GP) regression for large datasets. The approach involves partitioning the regression input domain into multiple local regions with a different local GP model fitted in each region.…
We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that…
Inverse problems are prevalent in both scientific research and engineering applications. In the context of Bayesian inverse problems, sampling from the posterior distribution can be particularly challenging when the forward models are…
Latent Gaussian models (LGMs) are widely used in statistics and machine learning. Bayesian inference in non-conjugate LGMs is difficult due to intractable integrals involving the Gaussian prior and non-conjugate likelihoods. Algorithms…
Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…
Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. For most covariance functions, however, exact GP prediction with $n$ points scales as $\mathcal{O}(n^3)$, making it prohibitively…
Gaussian covariance graph model is a popular model in revealing underlying dependency structures among random variables. A Bayesian approach to the estimation of covariance structures uses priors that force zeros on some off-diagonal…