Distilling data into compact and interpretable analytic equations is one of the goals of science. Instead, contemporary supervised machine learning methods mostly produce unstructured and dense maps from input to output. Particularly in deep learning, this property is owed to the generic nature of simple standard link functions. To learn equations rather than maps, standard non-linearities can be replaced with structured building blocks of atomic functions. However, without strong priors on sparsity and structure, representational complexity and numerical conditioning limit this direct approach. To scale to realistic settings in science and engineering, we propose an informed equation learning system. It provides a way to incorporate expert knowledge about what are permitted or prohibited equation components, as well as a domain-dependent structured sparsity prior. Our system then utilizes a robust method to learn equations with atomic functions exhibiting singularities, as e.g. logarithm and division. We demonstrate several artificial and real-world experiments from the engineering domain, in which our system learns interpretable models of high predictive power.
翻译:将数据蒸馏成紧凑和可解释的分析方程式是科学的目标之一。相反,当代受监督的机器学习方法大多产生从输入到输出的不结构的密集地图。特别是深层学习,这种属性是由于简单标准链接功能的通用性质。为了学习方程式而不是地图,标准非线性可以被结构化原子函数的构件所取代。然而,如果没有关于广度和结构的有力前科,代表性复杂性和数字调节限制了这种直接方法。为了在科学和工程的现实环境中推广,我们提议了一个知情的方程学习系统。它提供了一种将关于哪些是允许的或被禁止的方程式组件的专家知识纳入其中的方法,以及一个以域为基础的结构宽度之前的系统。我们的系统随后使用一种强有力的方法学习原子函数显示独一的方程式的方程式,例如对数和分法。我们从工程领域演示了几项人工和现实世界实验,我们从中学习了高预测力的可解释模型。