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.

翻译：高斯过程回归在给定充分似然信息的情况下，能够灵活地表示目标参数的后验分布。然而在某些情况下，我们对概率模型知之甚少。例如在金融工具投资中，现金流的概率模型通常是未知的。本文提出了一种称为无似然高斯过程（LFGP）的新框架，该框架能够在不直接设定似然函数的情况下，为可扩展问题表示目标参数的后验分布。LFGP通过建立目标参数值可近似视为相同的聚类簇，并利用最大似然估计量的渐近正态性将每个簇中目标参数的似然近似为高斯分布。我们预期所提出的框架将对无似然建模做出重要贡献，特别是在减少概率模型假设和降低可扩展问题计算成本方面。