A Comparison of Algorithms for Learning Hidden Variables in Bayesian Factor Graphs in Reduced Normal Form.

Area of Science:

• Machine Learning
• Graph Theory
• Statistical Inference

Background:

• Bayesian-directed acyclic graphs (BDAGs) are complex structures.
• Existing adaptation algorithms for BDAGs are often specialized.
• A unified framework is needed for efficient adaptation and deployment.

Purpose of the Study:

• To reduce BDAGs to a simplified normal form.
• To develop a single adaptation algorithm applicable to all parametric blocks.
• To compare different learning algorithms for parameter adaptation.

Main Methods:

• BDAGs are transformed into a normal form comprising replicator, source, and single-input/single-output units.
• Adaptation rules are derived using constrained maximum likelihood and minimum Kullback-Leibler divergence criteria with Karush-Kuhn-Tucker conditions.
• Learning algorithms are compared against localized decision and variational approximation methods.

Main Results:

• A simplified normal form for BDAGs is established.
• A unified adaptation algorithm is shown to be applicable across parametric blocks.
• Empirical validation on synthetic data demonstrates the performance of various algorithms.

Conclusions:

• The reduced normal form of factor graphs offers an efficient framework for BDAGs.
• This approach facilitates rapid deployment of Bayesian-directed graphs in practical applications.
• The unified adaptation strategy simplifies model training and enhances applicability.