# Exact Exponent in Optimal Rates for Crowdsourcing

arXiv: https://arxiv.org/abs/1605.07696 · HTML: https://mlsanity.com/paper/1605.07696/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 May 2016.

## Built on by (most cited first, 10 of 10)

- [Learning From Crowdsourced Noisy Labels: A Signal Processing Perspective](https://mlsanity.com/paper/2407.06902/) (2024)
- [A Worker-Task Specialization Model for Crowdsourcing: Efficient Inference and Fundamental Limits](https://mlsanity.com/paper/2111.12550/) (2021)
- [Sharp bounds on aggregate expert error](https://mlsanity.com/paper/2407.16642/) (2024)
- [Dependence-Aware Label Aggregation for LLM-as-a-Judge via Ising Models](https://mlsanity.com/paper/2601.22336/) (2026)
- [Optimal Fair Aggregation of Crowdsourced Noisy Labels using Demographic Parity Constraints](https://mlsanity.com/paper/2601.23221/) (2026)
- [Stability of Weighted Majority Voting under Estimated Weights](https://mlsanity.com/paper/2207.06118/) (2022)
- [Multi-LLM Query Optimization](https://mlsanity.com/paper/2603.24617/) (2026)
- [A Symmetric Loss Perspective of Reliable Machine Learning](https://mlsanity.com/paper/2101.01366/) (2021)
- [Recovering Top-Two Answers and Confusion Probability in Multi-Choice Crowdsourcing](https://mlsanity.com/paper/2301.00006/) (2022)
- [Spectral Clustering for Crowdsourcing with Inherently Distinct Task Types](https://mlsanity.com/paper/2302.07393/) (2023)

## Abstract (arXiv)

In many machine learning applications, crowdsourcing has become the primary means for label collection. In this paper, we study the optimal error rate for aggregating labels provided by a set of non-expert workers. Under the classic Dawid-Skene model, we establish matching upper and lower bounds with an exact exponent mI(π) in which m is the number of workers and I(π) the average Chernoff information that characterizes the workers' collective ability. Such an exact characterization of the error exponent allows us to state a precise sample size requirement m>frac1I(π)logfrac1ε in order to achieve an ε misclassification error. In addition, our results imply the optimality of various EM algorithms for crowdsourcing initialized by consistent estimators.