# Sequential Mode Estimation with Oracle Queries

arXiv: https://arxiv.org/abs/1911.08197 · HTML: https://mlsanity.com/paper/1911.08197/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2019.

## Built on by (most cited first, 5 of 5)

- [Optimal Self-Consistency for Efficient Reasoning with Large Language Models](https://mlsanity.com/paper/2511.12309/) (2025)
- [Optimal Bayesian Stopping for Efficient Inference of Consistent LLM Answers](https://mlsanity.com/paper/2602.05395/) (2026)
- [PAC Mode Estimation using PPR Martingale Confidence Sequences](https://mlsanity.com/paper/2109.05047/) (2021)
- [Sequential Community Mode Estimation](https://mlsanity.com/paper/2111.08535/) (2021)
- [Adaptive Self-Consistency: From Black-Box Sampling to Distribution-Valued Feedback](https://mlsanity.com/paper/2609.38931/) (2026)

## Abstract (arXiv)

We consider the problem of adaptively PAC-learning a probability distribution P's mode by querying an oracle for information about a sequence of i.i.d. samples X1, X2, ldots generated from P. We consider two different query models: (a) each query is an index i for which the oracle reveals the value of the sample Xi, (b) each query is comprised of two indices i and j for which the oracle reveals if the samples Xi and Xj are the same or not. For these query models, we give sequential mode-estimation algorithms which, at each time t, either make a query to the corresponding oracle based on past observations, or decide to stop and output an estimate for the distribution's mode, required to be correct with a specified confidence. We analyze the query complexity of these algorithms for any underlying distribution P, and derive corresponding lower bounds on the optimal query complexity under the two querying models.