🤖 AI Summary
For regression tasks with unknown likelihood functions—such as financial cash flow modeling—this paper proposes a Gaussian process regression framework that does not require explicit likelihood specification. Methodologically, it partitions the input space into local regions via data-driven clustering and constructs a local Gaussian likelihood approximation within each cluster, leveraging the asymptotic normality of maximum likelihood estimators—thereby circumventing global probabilistic modeling assumptions. This work introduces the first “likelihood-agnostic” Gaussian process posterior inference scheme, combining theoretical rigor with computational scalability. Empirically, the method significantly reduces dependence on prior structural assumptions under likelihood misspecification or intractability, enhances posterior robustness, and lowers computational overhead compared to standard approaches.
📝 Abstract
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.