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Title: Identifiability of discrete Bayesian network with a latent source Authors:  Hisayuki Hara - Doshisha University (Japan)
Hiroaki Naito - Doshisha University (Japan) [presenting]
Abstract: Identifiability of discrete graphical models defined by directed acyclic graphs with a latent source is discussed. In this case, identifiability of parameters is not trivial. The problem reduces to whether the parametrization map is generically finite-to-one or not. It is well known in algebra that there exist computational algebraic algorithms to detect if the parametrization map is finite-to-one or not. However, the computational cost of these algorithms is quite high even for moderate-sized models. As a preceding study, for Gaussian graphical models with a latent source, some useful sufficient conditions have been derived. On the other hand, for discrete graphical models with a latent source, the identifiability of all models with up to four observable variables has been investigated. We apply the results for the Gaussian model and derive some sufficient condition for binary Bayesian network models to be identifiable even for larger models with more than five observable variables. We also provide a useful algorithm to detect the identifiability of a given model within polynomial time.