论文标题
将天真的贝叶斯作为歧视分类器
Using the Naive Bayes as a discriminative classifier
论文作者
论文摘要
对于分类任务，概率模型可以分为两个不相交类别：生成或歧视性。给定观察$ y $，$ p（x | y）$的标签$ x $的后验概率计算。一方面，在使用贝叶斯规则计算$ p（x | y）$之前，就需要计算关节概率p（x，y）的生成分类器，例如幼稚的贝叶斯或隐藏的马尔可夫模型（hmm）。另一方面，歧视分类器直接计算$ p（x | y）$，无论观察法。它们如今被大量使用，模型为逻辑回归，有条件的随机场（CRF）和人工神经网络。但是，最近的熵前向后算法表明，被认为是生成模型的HMM也可以匹配歧视性人的定义。此示例导致质疑其他生成模型是否是这种情况。在本文中，我们表明，天真的贝叶斯分类器也可以匹配判别分类器的定义，因此可以以生成性或歧视性方式使用它。此外，该观察结果还讨论了生成歧视对的概念，例如链接，例如天真的贝叶斯和逻辑回归，或hmm and CRF。与这一点相关，我们表明逻辑回归可以被视为以歧视方式使用的天真贝叶斯的特定情况。
For classification tasks, probabilistic models can be categorized into two disjoint classes: generative or discriminative. It depends on the posterior probability computation of the label $x$ given the observation $y$, $p(x | y)$. On the one hand, generative classifiers, like the Naive Bayes or the Hidden Markov Model (HMM), need the computation of the joint probability p(x,y), before using the Bayes rule to compute $p(x | y)$. On the other hand, discriminative classifiers compute $p(x | y)$ directly, regardless of the observations' law. They are intensively used nowadays, with models as Logistic Regression, Conditional Random Fields (CRF), and Artificial Neural Networks. However, the recent Entropic Forward-Backward algorithm shows that the HMM, considered as a generative model, can also match the discriminative one's definition. This example leads to question if it is the case for other generative models. In this paper, we show that the Naive Bayes classifier can also match the discriminative classifier definition, so it can be used in either a generative or a discriminative way. Moreover, this observation also discusses the notion of Generative-Discriminative pairs, linking, for example, Naive Bayes and Logistic Regression, or HMM and CRF. Related to this point, we show that the Logistic Regression can be viewed as a particular case of the Naive Bayes used in a discriminative way.
