Algorithmic decision making has proliferated and now impacts our daily lives in both mundane and consequential ways. Machine learning practitioners make use of a myriad of algorithms for predictive models in applications as diverse as movie recommendations, medical diagnoses, and parole recommendations without delving into the reasons driving specific predictive decisions. Machine learning algorithms in such applications are often chosen for their superior performance, however popular choices such as random forest and deep neural networks fail to provide an interpretable understanding of the predictive model. In recent years, rule-based algorithms have been used to address this issue. Wang et al. (2017) presented an or-of-and (disjunctive normal form) based classification technique that allows for classification rule mining of a single class in a binary classification; this method is also shown to perform comparably to other modern algorithms. In this work, we extend this idea to provide classification rules for both classes simultaneously. That is, we provide a distinct set of rules for both positive and negative classes. In describing this approach, we also present a novel and complete taxonomy of classifications that clearly capture and quantify the inherent ambiguity in noisy binary classifications in the real world. We show that this approach leads to a more granular formulation of the likelihood model and a simulated-annealing based optimization achieves classification performance competitive with comparable techniques. We apply our method to synthetic as well as real world data sets to compare with other related methods that demonstrate the utility of our proposal.

翻译：算法决策已广泛渗透至日常生活的方方面面，从电影推荐、医疗诊断到假释建议，机器学习从业者运用多种算法构建预测模型，却鲜少深究具体预测决策背后的逻辑。在此类应用中，机器学习算法常因卓越性能而被选用，然而随机森林、深度神经网络等主流方案却无法提供对预测模型的可解释性理解。近年来，基于规则的算法被用于解决这一问题。Wang等人（2017）提出了一种基于“或-与”（析取范式）的分类技术，可在二分类任务中为单一类别挖掘分类规则；该方法的性能亦被证实可媲美其他现代算法。本研究将此思想拓展至同时为两个类别提供分类规则，即为正类和负类分别生成独立的规则集。在阐述该方法时，我们提出了一套新颖且完整的分类学框架，能够清晰捕捉并量化现实世界中噪声二分类任务固有的模糊性。研究表明，该方法能构建更具粒度的似然模型，且基于模拟退火的优化过程可实现与同类技术竞争的分类性能。我们将该方法应用于合成数据集与真实世界数据集，通过与相关方法的对比验证了其有效性。