Posterior-Aided Regularization for Likelihood-Free Inference

The recent development of likelihood-free inference aims training a flexible density estimator for the target posterior with a set of input-output pairs from simulation. Given the diversity of simulation structures, it is difficult to find a single unified inference method for each simulation model. This paper proposes a universally applicable regularization technique, called Posterior-Aided Regularization (PAR), which is applicable to learning the density estimator, regardless of the model structure. Particularly, PAR solves the mode collapse problem that arises as the output dimension of the simulation increases. PAR resolves this posterior mode degeneracy through a mixture of 1) the reverse KL divergence with the mode seeking property; and 2) the mutual information for the high quality representation on likelihood. Because of the estimation intractability of PAR, we provide a unified estimation method of PAR to estimate both reverse KL term and mutual information term with a single neural network. Afterwards, we theoretically prove the asymptotic convergence of the regularized optimal solution to the unregularized optimal solution as the regularization magnitude converges to zero. Additionally, we empirically show that past sequential neural likelihood inferences in conjunction with PAR present the statistically significant gains on diverse simulation tasks.