Symbolic Metamodels for Interpreting Black-boxes Using Primitive Functions
This work addresses the need for better interpretability in machine learning, particularly for understanding complex models, though it appears incremental as it builds on existing metamodeling and symbolic regression techniques.
The authors tackled the problem of interpreting black-box machine learning models by proposing a new method for finding interpretable metamodels using Kolmogorov superposition theorem and a memetic algorithm, and they showed that it outperforms recent metamodeling approaches in experiments.
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.