We revisit the classic problem of aggregating binary advice from conditionally independent experts, also known as the Naive Bayes setting. Our quantity of interest is the error probability of the optimal decision rule. In the symmetric case (sensitivity = specificity), reasonably tight bounds on the optimal error probability are known. In the general asymmetric case, we are not aware of any nontrivial estimates on this quantity. Our contribution consists of sharp upper and lower bounds on the optimal error probability in the general case, which recover and sharpen the best known results in the symmetric special case. Since this amounts to estimating the total variation distance between two product distributions, our results also have bearing on this important and challenging problem.

翻译：本文重新审视了聚合条件独立专家的二元建议这一经典问题，即朴素贝叶斯设定。我们关注的核心量是最优决策规则的错误概率。在对称情形（敏感度=特异度）下，已有研究给出了最优错误概率的较紧界。而在一般非对称情形中，学界尚未发现对该量的非平凡估计。我们的贡献在于给出了一般情形下最优错误概率的尖锐上下界，这些结果不仅涵盖且强化了对称特例中已知的最佳结论。由于该问题等价于估计两个乘积分布之间的全变差距离，我们的研究结论对这一重要且具有挑战性的问题亦具有参考价值。