Bayesian Pruned Random Rule Foams for XAI

Abstract

A random rule foam grows and combines several independent fuzzy rule-based systems by randomly sampling input-output data from a trained deep neural classifier. The random rule foam defines an interpretable proxy system for the sampled black-box classifier. The random foam gives the complete Bayesian posterior probabilities over the foam subsystems that contribute to the proxy system's output for a given pattern input. It also gives the Bayesian posterior over the if-then fuzzy rules in each of these constituent foams. The random foam also computes a conditional variance that describes the uncertainty in its predicted output given the random foam's learned rule structure. The mixture structure leads to bootstrap confidence intervals around the output. Using the Bayesian posterior probabilities to prune or discard low-probability sub-foams improves the system's classification accuracy. Simulations used the MNIST image data set of 60,000 gray-scale images of ten hand-written digits. Dropping the lowest-probability foams per input pattern brought the pruned random foam's classification accuracy nearly to that of the neural classifier. Posterior pruning outperformed simple accuracy pruning of a random foam and outperformed a random forest trained on the same neural classifier.