In this paper we derive an explicit formula for calculating the marginal likelihood of a given factorization of a categorical dataset. Since the marginal likelihood is proportional to the posterior probability of the factorization, these likelihoods can be used to order all possible factorizations and select the "best" way to factor the overall distribution from which the dataset is drawn. The best factorization can then be used to construct a Bayes classifier which benefits from factoring out mutually independent sets of variables.

中文翻译：

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分解多维数据以创建复杂的贝叶斯分类器

在本文中，我们导出了一个显式公式，用于计算分类数据集给定因子分解的边际可能性。由于边际可能性与因式分解的后验概率成正比，因此这些可能性可以用于对所有可能的因式分解进行排序，并选择“最佳”方式对从中提取数据集的总体分布进行因式分解。然后，可以使用最佳分解来构造贝叶斯分类器，该贝叶斯分类器得益于排除相互独立的变量集。