Learning in Probabilistic Boolean Networks via Structural Policy Gradients

Area of Science:

• Computational Intelligence
• Machine Learning
• Artificial Intelligence

Background:

• Probabilistic Boolean Networks (PBNs) are powerful tools for modeling complex systems.
• A key limitation of PBNs is their non-differentiable structure, hindering direct gradient-based training.
• Artificial Neural Networks (ANNs) excel at function approximation but often lack interpretability.

Purpose of the Study:

• To develop a trainable PBN model that overcomes non-differentiability issues.
• To demonstrate the potential of PBNs as general-purpose function approximators.
• To maintain the inherent interpretability of PBNs while achieving competitive performance.

Main Methods:

• Casting the PBN structure as a stochastic policy optimized using REINFORCE gradients.
• Training continuous output heads with standard gradients.
• Formalizing the Learning Probabilistic Boolean Network (LPBN) and deriving unbiased structural gradients.
• Proving a universal approximation property for LPBNs over discretized inputs.

Main Results:

• LPBNs achieve performance comparable to ANNs in classification, regression, clustering, and reinforcement learning.
• LPBNs provide interpretable, rule-like internal units.
• Analysis shows the effect of binning resolution, operator sets, and unit counts on LPBN performance.
• Learned logic in LPBNs stabilizes during training.

Conclusions:

• Learning Probabilistic Boolean Networks are effective general-purpose learners.
• LPBNs offer a competitive alternative to ANNs in tabular and noisy data scenarios.
• LPBNs successfully combine high performance with model interpretability.