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, meaning that every latent variable has four children that do not have any other parents in common. We show that the existence of such a quartet allows us to uniquely identify each latent variable and to learn all parameters involving that latent variable. Underlying our algorithm are two new techniques for structure learning: a quartet test to determine whether a set of binary variables are singly coupled, and a conditional mutual information test that we use to learn parameters. We also show how to subtract already learned latent variables from the model to create new singly-coupled quartets, which substantially expands the class of structures that we can learn. Finally, we give a proof of the polynomial sample complexity of our learning algorithm, and experimentally compare it to variational EM.

A serious problem in learning probabilistic models is the presence of hid(cid:173) den variables. These variables are not observed, yet interact with several of the observed variables. As such, they induce seemingly complex de(cid:173) pendencies among the latter. In recent years, much attention has been devoted to the development of algorithms for learning parameters, and in some cases structure, in the presence of hidden variables. In this pa(cid:173) per, we address the related problem of detecting hidden variables that interact with the observed variables.

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, meaning that every latent variable has four children that do not have any other parents in common. We show that the existence of such a quartet allows us to uniquely identify each latent variable and to learn all parameters involving that latent variable. Underlying our algorithm are two new techniques for structure learning: a quartet test to determine whether a set of binary variables are singly coupled, and a conditional mutual information test that we use to learn parameters.

A serious problem in learning probabilistic models is the presence of hidden variables. These variables are not observed, yet interact with several of the observed variables. As such, they induce seemingly complex dependencies among the latter. In recent years, much attention has been devoted to the development of algorithms for learning parameters, and in some cases structure, in the presence of hidden variables. In this paper, we address the related problem of detecting hidden variables that interact with the observed variables.

A serious problem in learning probabilistic models is the presence of hidden variables. These variables are not observed, yet interact with several of the observed variables. As such, they induce seemingly complex dependencies among the latter. In recent years, much attention has been devoted to the development of algorithms for learning parameters, and in some cases structure, in the presence of hidden variables. In this paper, we address the related problem of detecting hidden variables that interact with the observed variables.

A serious problem in learning probabilistic models is the presence of hidden variables.These variables are not observed, yet interact with several of the observed variables. As such, they induce seemingly complex dependencies amongthe latter. In recent years, much attention has been devoted to the development of algorithms for learning parameters, and in some cases structure, in the presence of hidden variables. In this paper, weaddress the related problem of detecting hidden variables that interact with the observed variables. This problem is of interest both for improving our understanding of the domain and as a preliminary step that guides the learning procedure towards promising models.