# Sharp bounds on aggregate expert error

arXiv: https://arxiv.org/abs/2407.16642 · HTML: https://mlsanity.com/paper/2407.16642/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 18 references that are in the map.
- First posted on arXiv 23 Jul 2024.

## Builds on (most cited first, 10 of 10)

- [Spectral Methods meet EM: A Provably Optimal Algorithm for Crowdsourcing](https://mlsanity.com/paper/1406.3824/) (2014)
- [Ranking and combining multiple predictors without labeled data](https://mlsanity.com/paper/1303.3257/) (2013)
- [Unsupervised Ensemble Learning with Dependent Classifiers](https://mlsanity.com/paper/1510.05830/) (2015)
- [Estimating the Accuracies of Multiple Classifiers Without Labeled Data](https://mlsanity.com/paper/1407.7644/) (2014)
- [On Approximating Total Variation Distance](https://mlsanity.com/paper/2206.07209/) (2022)
- [A Deep Learning Approach to Unsupervised Ensemble Learning](https://mlsanity.com/paper/1602.02285/) (2016)
- [Exact Exponent in Optimal Rates for Crowdsourcing](https://mlsanity.com/paper/1605.07696/) (2016)
- [Exact Lower Bounds for the Agnostic Probably-Approximately-Correct (PAC) Machine Learning Model](https://mlsanity.com/paper/1606.08920/) (2016)
- [A simple polynomial-time approximation algorithm for the total variation distance between two product distributions](https://mlsanity.com/paper/2208.00740/) (2022)
- [On Deterministically Approximating Total Variation Distance](https://mlsanity.com/paper/2309.14696/) (2023)

## Built on by (most cited first, 2 of 2)

- [Approximating the total variation distance between spin systems](https://mlsanity.com/paper/2502.05437/) (2025)
- [On approximating the f-divergence between two Ising models](https://mlsanity.com/paper/2509.05016/) (2025)

## Abstract (arXiv)

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.