Predictive Approximate Bayesian Computation via Saddle Points

Approximate Bayesian Computation (ABC) has been an important methodology for Bayesian inference when the likelihood function is intractable. Traditional sampling-based ABC algorithms such as ABC rejection and K2-ABC are inefficient performance-wise, while the regression-based algorithms such as K-ABC and DR-ABC are hard to scale. In this paper, we introduce an optimization-based framework for ABC that addresses these deficiencies. Leveraging a generative model for posterior and joint distribution matching, we show that ABC can be framed into saddle point problems, whose objectives can be accessed directly with samples. We present \emph{the predictive ABC algorithm (P-ABC)}, and provide a PAC bound guaranteeing its learning consistency. Numerical experiment shows that, when compared to K2-ABC and DR-ABC, the proposed P-ABC outperforms both with large margins.