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.

翻译：解释黑箱机器学习模型的一种方法是使用简单可解释函数对模型进行全局近似，这被称为元模型（模型的模型）。用元模型近似黑箱可用于：1）估计实例级特征重要性；2）理解模型的函数形式；3）分析特征交互。本文提出一种寻找可解释元模型的新方法。该方法利用Kolmogorov叠加定理，将多元函数表示为一元函数（即原始参数化函数）的复合形式，这种复合结构可以树的形式表达。受符号回归启发，我们采用改进的遗传编程方法搜索不同的树结构，并使用梯度下降（GD）优化给定结构的参数。本文方法是一种新颖的模因算法，不仅利用GD训练数值常量，还用于训练基本构建模块。通过多项实验表明，该方法优于近期提出的用于解释黑箱的元模型方法。