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.

通过错误地将一个 $K$ 值分类变量编码为 $K$ 位二进制数，将其用于朴素贝叶斯分类器，本文研究了这种编码方式的后果，从而得出了一个伯努利乘积（PoB）假设，而不是正确的分类朴素贝叶斯分类器。通过数学和实验分析了两种分类器之间的差异。在从狄利克雷分布中抽取的概率向量实验中，大多数情况下，这两种分类器在最大后验类标签上达成一致，尽管 PoB 情况下的后验概率通常更大。