# Query Complexity of k-NN based Mode Estimation

arXiv: https://arxiv.org/abs/2010.13491 · HTML: https://mlsanity.com/paper/2010.13491/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2020.

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

- [Approximate Function Evaluation via Multi-Armed Bandits](https://mlsanity.com/paper/2203.10124/) (2022)
- [Adaptive Data Depth via Multi-Armed Bandits](https://mlsanity.com/paper/2211.03985/) (2022)

## Abstract (arXiv)

Motivated by the mode estimation problem of an unknown multivariate probability density function, we study the problem of identifying the point with the minimum k-th nearest neighbor distance for a given dataset of n points. We study the case where the pairwise distances are apriori unknown, but we have access to an oracle which we can query to get noisy information about the distance between any pair of points. For two natural oracle models, we design a sequential learning algorithm, based on the idea of confidence intervals, which adaptively decides which queries to send to the oracle and is able to correctly solve the problem with high probability. We derive instance-dependent upper bounds on the query complexity of our proposed scheme and also demonstrate significant improvement over the performance of other baselines via extensive numerical evaluations.