用原始函数解释黑盒的符号元模型
Symbolic Metamodels for Interpreting Black-boxes Using Primitive Functions
摘要：
解释黑盒机器学习模型的一种方法是使用简单的可解释函数找到模型的全局近似，这被称为元模型（模型的模型）。用元模型近似黑盒可以用于1）估计实例特征重要性; 2）理解模型的函数形式; 3）分析特征交互。在这项工作中，我们提出了一种新的方法来寻找可解释的元模型。我们的方法利用Kolmogorov叠加定理，它表示多元函数作为一个组成的单变量函数（我们的原始参数化函数）。这种组合可以用树的形式表示。受符号回归的启发，我们使用一种改进的遗传编程来搜索不同的树配置。梯度下降（GD）用于优化给定配置的参数。我们的方法是一种新的模因算法，使用GD不仅用于训练数值常数，而且用于训练积木。使用几个实验，我们表明，我们的方法优于最近的元建模方法建议解释黑盒。
英文摘要：
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.
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