论文标题

学习一个可解释性的公式,以学习可解释的公式

Learning a Formula of Interpretability to Learn Interpretable Formulas

论文作者

Virgolin, Marco, De Lorenzo, Andrea, Medvet, Eric, Randone, Francesca

论文摘要

许多风险敏感的应用需要机器学习(ML)模型。尝试获得可解释模型的尝试通常依赖于调谐,通过试用,模型复杂性的超参数,这些参数仅与解释性松散相关。我们表明,可以采用元学习方法:可以从人类反馈中学到的非平凡代理(PHI)的ML模型,然后可以将该模型纳入ML训练过程中,以直接优化可解释性。我们将其显示为进化符号回归。我们首先设计并分发了一项调查,以查找数学公式的特征与两个已建立的PHI,可相似性和可分辨性之间的联系。接下来,我们使用结果数据集学习可解释性的ML模型。最后,我们询问该模型以估计双目标遗传编程中不断发展的解决方案的解释性。与传统使用解决方案尺寸最小化相比,我们对五个合成和八个现实世界符号回归问题进行实验。结果表明,我们的模型的使用会导致公式,这些公式在相同的准确性解干性权衡方面,要么明显更高或同样准确。此外,公式也可以说是更容易解释的。鉴于非常积极的结果,我们认为我们的方法代表了下一代可解释(进化)ML算法设计的重要垫脚石。

Many risk-sensitive applications require Machine Learning (ML) models to be interpretable. Attempts to obtain interpretable models typically rely on tuning, by trial-and-error, hyper-parameters of model complexity that are only loosely related to interpretability. We show that it is instead possible to take a meta-learning approach: an ML model of non-trivial Proxies of Human Interpretability (PHIs) can be learned from human feedback, then this model can be incorporated within an ML training process to directly optimize for interpretability. We show this for evolutionary symbolic regression. We first design and distribute a survey finalized at finding a link between features of mathematical formulas and two established PHIs, simulatability and decomposability. Next, we use the resulting dataset to learn an ML model of interpretability. Lastly, we query this model to estimate the interpretability of evolving solutions within bi-objective genetic programming. We perform experiments on five synthetic and eight real-world symbolic regression problems, comparing to the traditional use of solution size minimization. The results show that the use of our model leads to formulas that are, for a same level of accuracy-interpretability trade-off, either significantly more or equally accurate. Moreover, the formulas are also arguably more interpretable. Given the very positive results, we believe that our approach represents an important stepping stone for the design of next-generation interpretable (evolutionary) ML algorithms.

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