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：高斯过程回归能够在给定充分似然信息的情况下，灵活表示感兴趣参数的后验分布。然而在某些情形下，我们对概率模型的了解十分有限。例如，在投资金融工具时，现金流量的概率模型通常是未知的。本文提出一种名为"无似然高斯过程"（LFGP）的新框架，该框架无需直接设定似然函数，即可针对可扩展问题表示感兴趣参数的后验分布。LFGP建立聚类，其中感兴趣参数的值可视为近似相等，并利用最大似然估计的渐近正态性将每个聚类中感兴趣参数的似然近似为高斯分布。我们预期该框架将为无似然建模做出重要贡献，特别是通过减少概率模型的假设条件以及降低可扩展问题的计算成本。