Scaling the Explanation of Multi-Class Bayesian Network Classifiers

2026-03-15

AI Summary

This work addresses the limited decision transparency of multiclass Bayesian network classifiers, which stems from the absence of efficient and interpretable logical representations. The paper proposes a novel algorithm that, for the first time, compiles multiclass Bayesian network classifiers into class formulas—logical expressions that precisely capture their input–output behavior. Moving beyond existing approaches restricted to binary classification, the method significantly improves compilation efficiency and produces negation normal form (NNF) circuits endowed with OR-decomposability, thereby offering a structured foundation for downstream logic-based explanations. Experimental results demonstrate that the proposed approach drastically reduces compilation time while yielding logical representations that are more amenable to interpretation.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

We propose a new algorithm for compiling Bayesian network classifier (BNC) into class formulas. Class formulas are logical formulas that represent a classifier's input-output behavior, and are crucial in the recent line of work that uses logical reasoning to explain the decisions made by classifiers. Compared to prior work on compiling class formulas of BNCs, our proposed algorithm is not restricted to binary classifiers, shows significant improvement in compilation time, and outputs class formulas as negation normal form (NNF) circuits that are OR-decomposable, which is an important property when computing explanations of classifiers.

Problem

• Bayesian network classifier
• multi-class classification
• class formulas
• explainable AI
• logical reasoning

Innovation

• Bayesian network classifier
• class formula
• negation normal form
• OR-decomposable
• multi-class explanation