Learning the Bayesian Network Structure: Dirichlet Prior versus Data

In the Bayesian approach to structure learning of graphical models, the equivalent sample size (ESS) in the Dirichlet prior over the model parameters was recently shown to have an important effect on the maximum-a-posteriori estimate of the Bayesian network structure. In our first contribution, we theoretically analyze the case of large ESS-values, which complements previous work: among other results, we find that the presence of an edge in a Bayesian network is favoured over its absence even if both the Dirichlet prior and the data imply independence, as long as the conditional empirical distribution is notably different from uniform. In our second contribution, we focus on realistic ESS-values, and provide an analytical approximation to the "optimal" ESS-value in a predictive sense (its accuracy is also validated experimentally): this approximation provides an understanding as to which properties of the data have the main effect determining the "optimal" ESS-value.

• Publication year

  2008

• Venue

  Conference on Uncertainty in Artificial Intelligence

• Publication date

  2008-07-09

• Fields of study

  Mathematics, Computer Science

• Identifiers
  arXiv 1206.3287
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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