Scaling the Explanation of Multi-Class Bayesian Network Classifiers

Bayesian Networks (BNs) are of interest from an explainable AI viewpoint, offering transparent probabilistic models for decision support. Baymex is a recently introduced multi-objective evolutionary algorithm for learning discretized BNs, enabling experts to trade-off different objectives of interest, such as likelihood, model complexity, and prior beliefs. While Baymex has been shown to outperform state-of-the-art BN learning approaches, Baymex still 1) requires a lot of computation time and 2) has only been evaluated on synthetic data. To improve scalability, we introduce a parallelization strategy as well as a mechanism that enables adaptively steering optimization toward networks that overfit less. We furthermore reconfigure Baymex to train a BN classifier through multi-objective optimization of cross-entropy loss and the BIC complexity term so as to evaluate its performance on real-world clinical classification tasks. Besides observing speedups up to over 54 times on a 16-core CPU, comparisons against clinically familiar baselines (decision trees, logistic regression, naive Bayes, and random forests) on two open-source (RADCURE and SUPPORT) and one in-house dataset, show that Baymex obtains statistically similar or better predictive performance while producing compact, clinically inspectable BNs. Importantly, Baymex finds multiple plausible BN classifiers that contain predictors consistent with established clinical factors.

The widespread adoption of artificial intelligence (AI) within real-world applications has raised a lot of concerns regarding their trustworthiness, especially in critical applications. The field of eXplainable AI (XAI) has emerged with the objective of providing explanations to the users about the decisions made by AI systems. Several explanations for boolean classifiers have been introduced in the literature, including abductive and contrastive explanations, each giving a different insight on the decision of the classifier. However, computing an explanation for a decision of a boolean classifier is a hard problem in general. One way to deal with this complexity is to rely on a compiled representation of the classifier for which each explanation can be computed efficiently. Unfortunately, we prove in this paper that several classes of abductive explanations, remain hard to compute even for Ordered Binary Decision Diagrams, one of the most tractable subsets of the knowledge compilation map. Included in such classes are shorter abductive explanations or abductive explanations that include the explainee's preferences. To recover the benefits of working with compiled representations, we show that a proper representation of the dual-rail encoding of the classifier can be used to compute efficiently these classes of explanations.

Traditional neural networks have an impressive classification performance, but what they learn cannot be inspected, verified or extracted. Neural Logic Networks on the other hand have an interpretable structure that enables them to learn a logical mechanism relating the inputs and outputs with AND and OR operations. We generalize these networks with NOT operations and biases that take into account unobserved data and develop a rigorous logical and probabilistic modeling in terms of concept combinations to motivate their use. We also propose a novel factorized IF-THEN rule structure for the model as well as a modified learning algorithm. Our method improves the state-of-the-art in Boolean networks discovery and is able to learn relevant, interpretable rules in tabular classification, notably on examples from the medical and industrial fields where interpretability has tangible value.