Discovering Hidden Variables in Noisy-Or Networks using Quartet Tests


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.

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@inproceedings{Jernite2013DiscoveringHV, title={Discovering Hidden Variables in Noisy-Or Networks using Quartet Tests}, author={Yacine Jernite and Yonatan Halpern and David A Sontag}, booktitle={NIPS}, year={2013} }