Constrained Adjusted Maximum a Posteriori Estimation of Bayesian Network Parameters

Area of Science:

• Machine Learning
• Artificial Intelligence
• Statistical Modeling

Background:

• Maximum a posteriori (MAP) estimation with Dirichlet prior enhances Bayesian network parameter learning, especially with insufficient data.
• Uniform priors are standard for regularization but perform poorly with non-uniform or skewed parameter distributions.
• Domain expertise can refine priors and select equivalent sample size (ESS) for better model performance.

Purpose of the Study:

• To propose a novel Constrained adjusted Maximum a Posteriori (CaMAP) estimation method for Bayesian networks.
• To leverage domain knowledge for constructing informative priors and determining optimal ESS.
• To address limitations of uniform priors in scenarios with non-uniform parameter distributions.

Main Methods:

• Developed a novel sampling method to construct informative prior distributions from domain knowledge constraints.
• Derived constraints on ESS from parameter constraints to optimize prior strength.
• Utilized cross-validation for optimal ESS selection.

Main Results:

• The proposed CaMAP method effectively refines informative priors and selects optimal ESS.
• Numerical experiments demonstrate the superiority of CaMAP over existing Bayesian network learning algorithms.
• CaMAP shows improved parameter learning accuracy, particularly when domain knowledge is available.

Conclusions:

• CaMAP offers a robust approach to Bayesian network parameter learning by incorporating domain knowledge.
• The method enhances model performance in data-scarce or non-uniformly distributed parameter scenarios.
• CaMAP provides a flexible framework for utilizing expert knowledge in probabilistic graphical models.