Symbolic Metamodels for Interpreting Black-boxes Using Primitive Functions

TL;DR

This paper introduces a novel memetic algorithm that combines genetic programming and gradient descent to create interpretable symbolic metamodels for understanding black-box machine learning models, enhancing interpretability and analysis.

Contribution

It proposes a new method utilizing the Kolmogorov superposition theorem and a memetic algorithm for constructing interpretable symbolic metamodels, improving over existing approaches.

Findings

Outperforms recent metamodeling approaches in experiments

Effectively interprets black-box models through symbolic representations

Enhances understanding of feature interactions and model functions

Abstract

One approach for interpreting black-box machine learning models is to find a global approximation of the model using simple interpretable functions, which is called a metamodel (a model of the model). Approximating the black-box with a metamodel can be used to 1) estimate instance-wise feature importance; 2) understand the functional form of the model; 3) analyze feature interactions. In this work, we propose a new method for finding interpretable metamodels. Our approach utilizes Kolmogorov superposition theorem, which expresses multivariate functions as a composition of univariate functions (our primitive parameterized functions). This composition can be represented in the form of a tree. Inspired by symbolic regression, we use a modified form of genetic programming to search over different tree configurations. Gradient descent (GD) is used to optimize the parameters of a given configuration. Our method is a novel memetic algorithm that uses GD not only for training numerical constants but also for the training of building blocks. Using several experiments, we show that our method outperforms recent metamodeling approaches suggested for interpreting black-boxes.