Predictive Approximate Bayesian Computation Via Saddle Points

Authors:
Yingxiang Yang University of Illinois at Urbana Champaign
Bo Dai Google Brain
Negar Kiyavash Georgia Tech
Niao He UIUC

Introduction:

Approximate Bayesian computation (ABC) is an important methodology for Bayesian inference when the likelihood function is intractable.In this paper, the authors introduce an optimization-based ABC framework that addresses these deficiencies.

Abstract:

Approximate Bayesian computation (ABC) is an important methodology for Bayesian inference when the likelihood function is intractable. Sampling-based ABC algorithms such as rejection- and K2-ABC are inefficient when the parameters have high dimensions, while the regression-based algorithms such as K- and DR-ABC are hard to scale. In this paper, we introduce an optimization-based ABC framework that addresses these deficiencies. Leveraging a generative model for posterior and joint distribution matching, we show that ABC can be framed as saddle point problems, whose objectives can be accessed directly with samples. We present the predictive ABC algorithm (P-ABC), and provide a probabilistically approximately correct (PAC) bound that guarantees its learning consistency. Numerical experiment shows that P-ABC outperforms both K2- and DR-ABC significantly.

You may want to know: