The presented ideas are based on a recent paper [Halpern & Sontag, 2013], extending to a more general class of networks. The performance of the proposed algorithm is illustrated on synthetic examples. The exposition of paper is generally logical but the writing needs a lot of improvement. The paper contains potentially interesting algorithms but it is at times hard to tell which ideas are new and which ones are borrowed. A summary of the main contributions and their significance would be useful.

We give a polynomial-time algorithm for provably learning the structure and parameters of bipartite noisy-or Bayesian networks of binary variables where the top layer is completely hidden. Unsupervised learning of these models is a form of discrete factor analysis, enabling the discovery of hidden variables and their causal relationships with observed data. We obtain an efficient learning algorithm for a family of Bayesian networks that we call quartet-learnable. For each latent variable, the existence of a singly-coupled quartet allows us to uniquely identify and learn all parameters involving that latent variable. We give a proof of the polynomial sample complexity of our learning algorithm, and experimentally compare it to variational EM.