A finite sample analysis of the Naive Bayes classifier
A finite sample analysis of the Naive Bayes classifier
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DOI：
10.5555/2789272.2886797
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
D. Berend;A. Kontorovich
中科院分区：
文献类型：
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作者：
D. Berend;A. Kontorovich
我们重新审视，从统计学习的角度来看，加权专家投票的经典决策理论问题。特别是，我们研究的一致性（渐近和有限）的最佳朴素贝叶斯加权多数和相关规则。在已知专家能力水平的情况下，我们给出了最优规则的精确误差估计。我们得到我们的估计的最优性结果，也建立了一些结构特征。当能力水平未知时，必须根据经验进行估计。我们为这种情况提供了频率论和贝叶斯分析。我们的一些证明技术是非标准的，可能是独立的利益。提出了几个具有挑战性的开放问题，并提供了实验结果来说明理论。
We revisit, from a statistical learning perspective, the classical decision-theoretic problem of weighted expert voting. In particular, we examine the consistency (both asymptotic and finitary) of the optimal Naive Bayes weighted majority and related rules. In the case of known expert competence levels, we give sharp error estimates for the optimal rule. We derive optimality results for our estimates and also establish some structural characterizations. When the competence levels are unknown, they must be empirically estimated. We provide frequentist and Bayesian analyses for this situation. Some of our proof techniques are non-standard and may be of independent interest. Several challenging open problems are posed, and experimental results are provided to illustrate the theory.