How to Open a Black Box Classifier for Tabular Data

Author:

Walters Bradley1,Ortega-Martorell Sandra1ORCID,Olier Ivan1ORCID,Lisboa Paulo J. G.1

Affiliation:

1. School of Computer Science and Mathematics, Liverpool John Moores University, Liverpool L3 2AF, UK

Abstract

A lack of transparency in machine learning models can limit their application. We show that analysis of variance (ANOVA) methods extract interpretable predictive models from them. This is possible because ANOVA decompositions represent multivariate functions as sums of functions of fewer variables. Retaining the terms in the ANOVA summation involving functions of only one or two variables provides an efficient method to open black box classifiers. The proposed method builds generalised additive models (GAMs) by application of L1 regularised logistic regression to the component terms retained from the ANOVA decomposition of the logit function. The resulting GAMs are derived using two alternative measures, Dirac and Lebesgue. Both measures produce functions that are smooth and consistent. The term partial responses in structured models (PRiSM) describes the family of models that are derived from black box classifiers by application of ANOVA decompositions. We demonstrate their interpretability and performance for the multilayer perceptron, support vector machines and gradient-boosting machines applied to synthetic data and several real-world data sets, namely Pima Diabetes, German Credit Card, and Statlog Shuttle from the UCI repository. The GAMs are shown to be compliant with the basic principles of a formal framework for interpretability.

Funder

Liverpool John Moores University

Publisher

MDPI AG

Subject

Computational Mathematics,Computational Theory and Mathematics,Numerical Analysis,Theoretical Computer Science

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