简单机器学习模型的存在性
On the Existence of Simpler Machine Learning Models
摘要：
找到一个准确但复杂的模型几乎总是比找到一个准确但简单的模型更容易。寻找各种形式的最优、稀疏、精确的模型（整数系数线性模型、决策集、规则列表、决策树）通常是NP难的。我们常常不知道寻找一个更简单的模型是否值得，因此我们不去寻找一个。在这项工作中，我们提出了一个重要的实际问题：在明确搜索之前，准确而简单的模型是否可以被证明存在，或者可能存在？我们假设有一个重要的原因，即简单而准确的模型往往确实存在。这个假设是罗生门集合的大小通常很大，其中罗生门集合是来自函数类的几乎同样准确的模型的集合。如果罗生门集合很大，那么它包含许多精确的模型，也许其中至少有一个是我们想要的简单模型。在这项工作中，我们正式提出了罗生门比作为一个新的衡量简单的学习问题，取决于一个函数类和数据集。罗生门比率是一组精确模型的体积与假设空间的体积之比，它不同于统计学习理论的标准复杂性度量。通过研究罗生门比率获得的见解提供了一种简单的方法，可以在发现问题之前检查是否存在更简单的模型，即几种不同的机器学习方法是否在数据上实现了相似的性能。从这个意义上说，罗生门比率是一个强大的工具，可以用来理解为什么以及何时可能存在一个准确而简单的模型。如果，正如我们在这项工作中假设的那样，许多真实世界的数据集承认大罗生门集，其含义是巨大的：这意味着简单或可解释的模型通常可以用于高风险决策而不会失去准确性。
英文摘要：
It is almost always easier to find an accurate-but-complex model than an accurate-yet-simple model. Finding optimal, sparse, accurate models of various forms (linear models with integer coefficients, decision sets, rule lists, decision trees) is generally NP-hard. We often do not know whether the search for a simpler model will be worthwhile, and thus we do not go to the trouble of searching for one. In this work, we ask an important practical question: can accurate-yet-simple models be proven to exist, or shown likely to exist, before explicitly searching for them? We hypothesize that there is an important reason that simple-yet-accurate models often do exist. This hypothesis is that the size of the Rashomon set is often large, where the Rashomon set is the set of almost-equally-accurate models from a function class. If the Rashomon set is large, it contains numerous accurate models, and perhaps at least one of them is the simple model we desire. In this work, we formally present the Rashomon ratio as a new gauge of simplicity for a learning problem, depending on a function class and a data set. The Rashomon ratio is the ratio of the volume of the set of accurate models to the volume of the hypothesis space, and it is different from standard complexity measures from statistical learning theory. Insight from studying the Rashomon ratio provides an easy way to check whether a simpler model might exist for a problem before finding it, namely whether several different machine learning methods achieve similar performance on the data. In that sense, the Rashomon ratio is a powerful tool for understanding why and when an accurate-yet-simple model might exist. If, as we hypothesize in this work, many real-world data sets admit large Rashomon sets, the implications are vast: it means that simple or interpretable models may often be used for high-stakes decisions without losing accuracy.
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