Conditional Independence in Testing Bayesian Networks

Testing Bayesian Networks (TBNs) were introduced recently to represent a set of distributions, one of which is selected based on the given evidence and used for reasoning. TBNs are more expressive than classical Bayesian Networks (BNs): Marginal queries correspond to multi-linear functions in BNs and to piecewise multi-linear functions in TBNs. Moreover, TBN queries are universal approximators, like neural networks. In this paper, we study conditional independence in TBNs, showing that it can be inferred from d-separation as in BNs. We also study the role of TBN expressiveness and independence in dealing with the problem of learning with incomplete models (i. e. , ones that miss nodes or edges from the data-generating model). Finally, we illustrate our results on a number of concrete examples, including a case study on Hidden Markov Models.

Authors

• Yujia Shen
• Haiying Huang 0002
• Arthur Choi
• Adnan Darwiche

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