Reviews: Wasserstein Variational Inference

The authors describe a new framework for approximate inference called Wasserstain variational inference. This framework is based on the minimization of an entropic regularized version of the optimal transport cost through the Sinkhorn iterations. The result is a likelihood free training method which can be applied to implicit models. The proposed method is empirically evaluated on autoencoder models where it improves over two baselines: standard variational autoencoders and autoencoders trained with aversarially learned inference. Quality: The proposed method is theoretically well justified.