Sharp bounds on aggregate expert error
This work addresses a foundational problem in statistical decision theory and machine learning, with implications for expert aggregation and total variation distance estimation, though it appears incremental as it extends existing bounds to a more general setting.
The paper tackles the problem of aggregating binary advice from conditionally independent experts in the Naive Bayes setting, focusing on the error probability of the optimal decision rule, and provides sharp upper and lower bounds for the general asymmetric case, recovering and improving known results for the symmetric case.
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 case of symmetric errors (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 turns out to be equivalent to estimating the total variation distance between two product distributions, our results also have bearing on this important and challenging problem.