Likelihood-Free Gaussian Process for Regression

Gaussian process regression can flexibly represent the posterior distribution of an interest parameter given sufficient information on the likelihood. 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 value of the interest parameter can be considered approximately 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, particularly by reducing the assumptions for the probability model and the computational costs for scalable problems.