Sharp bounds on aggregate expert error

TL;DR

This paper derives precise bounds on the error probability when aggregating binary advice from experts, extending known results to asymmetric error cases and linking to the total variation distance problem.

Contribution

It provides sharp upper and lower bounds on the optimal error probability for asymmetric expert errors, improving upon previous symmetric case results.

Findings

Established tight bounds on error probability in asymmetric expert advice aggregation.

Connected the problem to estimating total variation distance between product distributions.

Sharpened existing bounds, enhancing understanding of expert decision aggregation.

Abstract

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.