Approximate Bayesian Computation with Deep Learning and Conformal prediction
提出一种无需汇总统计量、距离和容差阈值的ABC方法，结合神经网络和共形理论给出后验均值估计及其置信区间，在多维参数估计中表现高效。
Approximate Bayesian Computation (ABC) methods are commonly used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Classical ABC methods are based on nearest neighbor type algorithms and rely on the choice of so-called summary statistics, distances between datasets and a tolerance threshold. Recently, methods combining ABC with more complex machine learning algorithms have been proposed to mitigate the impact of these “user-choices”. In this paper, we propose the first, to our knowledge, ABC method completely free of summary statistics, distance, and tolerance threshold. Moreover, in contrast with usual generalizations of the ABC method, it associates a confidence interval (having a proper frequentist marginal coverage) with the posterior mean estimation (or other moment-type estimates).Our method, named ABCD-Conformal, uses a neural network with Monte Carlo Dropout to provide an estimation of the posterior mean (or other moment type functionals), and conformal theory to obtain associated confidence sets. Efficient for estimating multidimensional parameters and amortized, we test this new method on four different applications and compare it with other ABC methods in the literature. Supplementary materials are available online (appendix, source codes, notebooks, datasets).