Random Fuzzy-Rule Foams for Explainable AI

Abstract

A random foam trains several fuzzy-rule-foam function approximators and then combines them into a single rule-based approximator. The foam systems train independently on bootstrapped random samples from a trained neural classifier. The foam systems convert the neural black box into an interpretable set of rules. The fuzzy rule-based systems have an underlying probability mixture structure that gives rise to an interpretable Bayesian posterior over the rules for each input. A rule foam also measures the uncertainty in its outputs through the conditional variance of the generalized probability mixture. A random foam combines the learned additive fuzzy systems by averaging their throughputs or rule structure. A random foam is also interpretable in terms of its rules, its posterior of its rules, and its conditional variance. Thirty 1000-rule foams trained on random subsets of the MNIST digit data set. Each such foam system had about 93.5% classification accuracy. The random foam that averaged throughputs achieved \(96.80\%\) accuracy while the random foam that averaged only their outputs achieved 96.06% accuracy. The throughput-averaged random foam also slightly outperformed a standard random forest that output-averaged 30 classification trees. Thirty 1000-rule foams also trained on a deep neural classifier that had 96.26% accuracy. The random foam that averaged these foam throughputs was itself 96.14% accurate. The random foam that averaged their outputs was just 95.6% accurate. The appendix proves a Gaussian combined-foam version of the uniform approximation theorem for additive fuzzy systems.