Wallenius Bayes
Wallenius Bayes
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DOI：
10.1007/s10994-018-5699-z
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发表时间：
2018
期刊：
影响因子：
7.5
通讯作者：
Enric Junqué de Fortuny;David Martens;F. Provost
中科院分区：
文献类型：
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作者：
Enric Junqué de Fortuny;David Martens;F. Provost
本文介绍了一种新的事件模型，适用于分类（二进制）数据产生的“破坏性选择”的过程中，如某些人的行为。在这样的过程中，做出一个选择就可以将这个选择从未来的考虑中去除，但不会影响选择集中其他选择的相对概率。提出的Wallenius事件模型是基于Wallenius引入的一个有点被遗忘的非中心超几何分布（有偏抽样：非中心超几何概率分布。博士论文，斯坦福大学，1963年）。我们讨论了它与人类选择行为是如何产生的模型的关系，突出了一个关键的（简单的）数学属性。我们使用这个背景来具体描述为什么传统的多变量伯努利朴素贝叶斯和多项式朴素贝叶斯都是次优的，这样的数据。然后，我们提出了一种基于Wallenius事件模型的朴素贝叶斯的实现，并通过实验表明，对于我们期望通过破坏性选择行为生成的特征的数据，Wallenius贝叶斯确实优于传统版本的朴素贝叶斯，用于基于这些特征的预测。此外，我们还证明了它与非朴素方法（特别是支持向量机）具有竞争力。相比之下，我们还表明，Wallenius贝叶斯表现不佳时，数据生成过程是不是基于破坏性的选择。
This paper introduces a new event model appropriate for classifying (binary) data generated by a “destructive choice” process, such as certain human behavior. In such a process, making a choice removes that choice from future consideration yet does not influence the relative probability of other choices in the choice set. The proposed Wallenius event model is based on a somewhat forgotten non-central hypergeometric distribution introduced by Wallenius (Biased sampling: the non-central hypergeometric probability distribution. Ph.D. thesis, Stanford University, 1963). We discuss its relationship with models of how human choice behavior is generated, highlighting a key (simple) mathematical property. We use this background to describe specifically why traditional multivariate Bernoulli naive Bayes and multinomial naive Bayes each are suboptimal for such data. We then present an implementation of naive Bayes based on the Wallenius event model, and show experimentally that for data where we would expect the features to be generated via destructive choice behavior Wallenius Bayes indeed outperforms the traditional versions of naive Bayes for prediction based on these features. Furthermore, we also show that it is competitive with non-naive methods (in particular, support-vector machines). In contrast, we also show that Wallenius Bayes underperforms when the data generating process is not based on destructive choice.