
Asymptotic Model Selection for Directed Networks with Hidden Variables
We extend the Bayesian Information Criterion (BIC), an asymptotic approx...
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Asymptotic Model Selection for Naive Bayesian Networks
We develop a closed form asymptotic formula to compute the marginal like...
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Efficient Approximations for the Marginal Likelihood of Incomplete Data Given a Bayesian Network
We discuss Bayesian methods for learning Bayesian networks when data set...
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Learning networks determined by the ratio of prior and data
Recent reports have described that the equivalent sample size (ESS) in a...
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On the overestimation of widely applicable Bayesian information criterion
A widely applicable Bayesian information criterion (Watanabe, 2013) is a...
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Factorized Asymptotic Bayesian Inference for Factorial Hidden Markov Models
Factorial hidden Markov models (FHMMs) are powerful tools of modeling se...
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On the Relative Expressiveness of Bayesian and Neural Networks
A neural network computes a function. A central property of neural netwo...
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Automated Analytic Asymptotic Evaluation of the Marginal Likelihood for Latent Models
We present and implement two algorithms for analytic asymptotic evaluation of the marginal likelihood of data given a Bayesian network with hidden nodes. As shown by previous work, this evaluation is particularly hard for latent Bayesian network models, namely networks that include hidden variables, where asymptotic approximation deviates from the standard BIC score. Our algorithms solve two central difficulties in asymptotic evaluation of marginal likelihood integrals, namely, evaluation of regular dimensionality drop for latent Bayesian network models and computation of nonstandard approximation formulas for singular statistics for these models. The presented algorithms are implemented in Matlab and Maple and their usage is demonstrated for marginal likelihood approximations for Bayesian networks with hidden variables.
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