This paper investigates the consequences of encoding a $K$-valued categorical variable incorrectly as $K$ bits via one-hot encoding, when using a Na\"{\i}ve Bayes classifier. This gives rise to a product-of-Bernoullis (PoB) assumption, rather than the correct categorical Na\"{\i}ve Bayes classifier. The differences between the two classifiers are analysed mathematically and experimentally. In our experiments using probability vectors drawn from a Dirichlet distribution, the two classifiers are found to agree on the maximum a posteriori class label for most cases, although the posterior probabilities are usually greater for the PoB case.

翻译：本文研究了在使用朴素贝叶斯分类器时，将$K$值类别变量错误地通过独热编码编码为$K$个比特所产生的后果。这导致了伯努利乘积假设（PoB），而非正确的类别朴素贝叶斯分类器。本文通过数学分析和实验比较了这两种分类器之间的差异。在使用从狄利克雷分布中抽取的概率向量进行的实验中，发现两种分类器在大多数情况下对最大后验类别标签保持一致，尽管后验概率在PoB情况下通常更大。