Performing exact posterior inference in complex generative models is often difficult or impossible due to an expensive to evaluate or intractable likelihood function. Approximate Bayesian computation (ABC) is an inference framework that constructs an approximation to the true likelihood based on the similarity between the observed and simulated data as measured by a predefined set of summary statistics. Although the choice of appropriate problem-specific summary statistics crucially influences the quality of the likelihood approximation and hence also the quality of the posterior sample in ABC, there are only few principled general-purpose approaches to the selection or construction of such summary statistics. In this paper, we develop a novel framework for this task using kernel-based distribution regression. We model the functional relationship between data distributions and the optimal choice (with respect to a loss function) of summary statistics using kernel-based distribution regression. We show that our approach can be implemented in a computationally and statistically efficient way using the random Fourier features framework for large-scale kernel learning. In addition to that, our framework shows superior performance when compared to related methods on toy and real-world problems.

本研究提供了一种新的基于核回归的框架方法，使用随机傅里叶特征来实现大规模核学习，以选择合适的问题特定摘要统计量来近似真实条件概率分布，该方法在近似贝叶斯计算中有杰出表现。

DR-ABC: 基于核分布回归的近似贝叶斯计算