A New Monte Carlo Based Algorithm for the Gaussian Process Classification Problem
This work addresses a computational bottleneck in Gaussian process classification for researchers and practitioners, though it appears incremental as it builds on existing Monte Carlo techniques.
The authors tackled the Gaussian process classification problem by developing a new Monte Carlo algorithm that transforms it into evaluating multivariate Gaussian orthant integrals, resulting in a simpler, more reliable, and faster approach compared to existing Markov Chain Monte Carlo methods.
Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the classification problem, because we encounter intractable integrals. In this paper we develop a new derivation that transforms the problem into that of evaluating the ratio of multivariate Gaussian orthant integrals. Moreover, we develop a new Monte Carlo procedure that evaluates these integrals. It is based on some aspects of bootstrap sampling and acceptancerejection. The proposed approach has beneficial properties compared to the existing Markov Chain Monte Carlo approach, such as simplicity, reliability, and speed.