基于超解析线性递归模型的医学评分系统优化
Supersparse Linear Integer Models for Optimized Medical Scoring Systems
摘要：
评分系统是线性分类模型，只需要用户添加，减去和乘以几个小数字，以作出预测。这些模型被医学界广泛使用，但很难从数据中学习，因为它们需要精确和稀疏，具有互质整数系数，并满足多个操作约束。我们提出了一种新的方法来创建数据驱动的评分系统，称为超解析线性模型（SLIM）。SLIM评分系统是通过求解一个整数规划来构建的，该整数规划直接对准确性（0-1损失）和稀疏性（$\ell_0$ -稀疏性）的度量进行编码，同时将系数限制为互质整数。SLIM可以无缝地结合与精度和稀疏性相关的广泛的操作约束，并且可以在没有参数调整的情况下生成高度定制的模型。我们提供了SLIM评分系统的测试和训练精度的界限，并提出了一种新的数据减少技术，可以通过事先消除一部分训练数据来提高可扩展性。我们的论文包括与马萨诸塞州总医院睡眠实验室合作的结果，其中SLIM用于创建高度定制的睡眠呼吸暂停筛查评分系统
英文摘要：
Scoring systems are linear classification models that only require users to add, subtract and multiply a few small numbers in order to make a prediction. These models are in widespread use by the medical community, but are difficult to learn from data because they need to be accurate and sparse, have coprime integer coefficients, and satisfy multiple operational constraints. We present a new method for creating data-driven scoring systems called a Supersparse Linear Integer Model (SLIM). SLIM scoring systems are built by solving an integer program that directly encodes measures of accuracy (the 0-1 loss) and sparsity (the $\ell_0$-seminorm) while restricting coefficients to coprime integers. SLIM can seamlessly incorporate a wide range of operational constraints related to accuracy and sparsity, and can produce highly tailored models without parameter tuning. We provide bounds on the testing and training accuracy of SLIM scoring systems, and present a new data reduction technique that can improve scalability by eliminating a portion of the training data beforehand. Our paper includes results from a collaboration with the Massachusetts General Hospital Sleep Laboratory, where SLIM was used to create a highly tailored scoring system for sleep apnea screening
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