Related papers: Scalable computation of predictive probabilities i…
It has become increasingly common to collect high-dimensional binary response data; for example, with the emergence of new sampling techniques in ecology. In smaller dimensions, multivariate probit (MVP) models are routinely used for…
Gaussian process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient…
We present two data-driven methods for estimating reachable sets with probabilistic guarantees. Both methods make use of a probabilistic formulation allowing for a formal definition of a data-driven reachable set approximation that is…
We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…
In applications of Gaussian processes where quantification of uncertainty is of primary interest, it is necessary to accurately characterize the posterior distribution over covariance parameters. This paper proposes an adaptation of the…
Recently, Fasano, Rebaudo, Durante and Petrone (2019) provided closed-form expressions for the filtering, predictive and smoothing distributions of multivariate dynamic probit models, leveraging on unified skew-normal distribution…
While Gaussian processes are a mainstay for various engineering and scientific applications, the uncertainty estimates don't satisfy frequentist guarantees and can be miscalibrated in practice. State-of-the-art approaches for designing…
Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…
Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to…
Generalized linear mixed models (GLMMs) are often used for analyzing correlated non-Gaussian data. The likelihood function in a GLMM is available only as a high dimensional integral, and thus closed-form inference and prediction are not…
Spatial generalized linear mixed-effects models are popularly used to analyze spatially indexed univariate responses. However, with modern technology, it is common to observe vector-valued mixed-type responses, e.g., a combination of…
We study probit regression from a Bayesian perspective and give an alternative form for the posterior distribution when the prior distribution for the regression parameters is the uniform distribution. This new form allows simple Monte…
We consider probabilistic multinomial probit classification using Gaussian process (GP) priors. The challenges with the multiclass GP classification are the integration over the non-Gaussian posterior distribution, and the increase of the…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…
The need for regression models to predict circular values arises in many scientific fields. In this work we explore a family of expressive and interpretable distributions over circle-valued random functions related to Gaussian processes…
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…
Gaussian processes are powerful non-parametric probabilistic models for stochastic functions. However, the direct implementation entails a complexity that is computationally intractable when the number of observations is large, especially…
Gaussian Process Networks (GPNs) are a class of directed graphical models which employ Gaussian processes as priors for the conditional expectation of each variable given its parents in the network. The model allows the description of…
This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…