NeurIPS 2020
### Probabilistic Circuits for Variational Inference in Discrete Graphical Models

### Meta Review

The work develops a variational approximation for the log partition function of binary-variable graphical models using selective Sum-Product networks. The theoretical foundations rest heavily on Lowd and Domingos (2010) but the application (using S-SPN's as variational aproximants) is novel and the practical results look very promising.
The work received mixed reviews but the overall consensus was positive. The reviewers agree that the method is novel and that the ability to produce a bound on the partition function (albeit a lower one) is useful. The main weakness is the lack of an experimental comparison with competing post-mean-field-and-loopy-BP methods such as Tree-Reweighted BP, neural variational inference and the Wiseman reference. At a minimum the final paper needs to discuss these references and include the TRWBP experiments from the rebuttal and (non-GPU if necessary) SMF results in table 1.