Scalable Learning for Censored Gaussian Processes based on Conditional Independence Approximations

A variety of quantities are collected by spatially distributed sensors with known levels of detection (LOD), beyond which the response variable cannot be measured. When the (transformation of) underlying responses are modelled by a Gaussian process (GP), the measurements follow a (partially) censored GP, posing significant computational challenges for estimation and inference using existing methods. We propose scalable methods for estimating multivariate normal (MVN) probabilities and sampling truncated MVN (TMVN) distributions through tactically constructing conditional independence structures that address the likelihood estimation and posterior inference of censored GPs, respectively. The proposed methods are based on the minimax exponential tilting (MET) method and a comparison with the state-of-the-arts is provided.

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