Likelihood-Free Gaussian Process for Regression

Gaussian process regression can flexibly represent the posterior distribution of an interest parameter providing that information on the likelihood is sufficient. However, in some cases, we have little knowledge regarding the probability model. For example, when investing in a financial instrument, the probability model of cash flow is generally unknown. In this paper, we propose a novel framework called the likelihood-free Gaussian process (LFGP), which allows representation of the posterior distributions of interest parameters for scalable problems without directly setting their likelihood functions. The LFGP establishes clusters in which the probability distributions of the targets can be considered identical, and it approximates the likelihood of the interest parameter in each cluster to a Gaussian using the asymptotic normality of the maximum likelihood estimator. We expect that the proposed framework will contribute significantly to likelihood-free modeling, especially from the perspective of fewer assumptions for the probability model and low computational costs for scalable problems.