Deep Gaussian Processes for Uncertainty Quantification in Large-Data Classification Settings

3272 

Contributed Abstract 

Poster 

Andrew Cooper (1), Annie Booth (2), Robert Gramacy (1)

(1) Virginia Tech, Blacksburg, Virginia, (2) NC State University, Raleigh, North Carolina

Annie Booth  
NC State University

Robert Gramacy  
Virginia Tech

Andrew Cooper  
Virginia Tech

Andrew Cooper  
N/A

Many applications of experimental design produce categorical response data. Gaussian Processes (GPs) are stochastic models that provide flexible fitting of response surfaces, but must be modified to handle non-Gaussian likelihoods. Performing fully Bayesian estimation of a GP classifier requires directly sampling from a latent layer, which involves the inversion of covariance matrices; this can be computationally infeasible in large-data regimes. The Vecchia approximation can reduce the cost of inverting covariance matrices by inducing sparse Cholesky decompositions. By combining this with the Elliptical Slice Sampling (ESS) algorithm for generating valid posterior samples from a latent layer, we obtain a tractable, fully Bayesian approach to fitting and predicting from a global GP classification model in large-data settings. We apply our methods to a Binary Black Hole (BBH) simulator example, which contains both binary and real-valued components in its response. Our method of combining fully Bayesian classification and regression provides us full Uncertainty Quantification (UQ) estimation of BBH formation and chirp mass.

Computer Experiments|Categorical Data|Vecchia Approximation|Black Hole Simulation|Elliptical Slice Sampling|

Uncertainty Quantification in Complex Systems Interest Group

Miscellaneous