# Large sample analysis of the median heuristic

arXiv: https://arxiv.org/abs/1707.07269 · HTML: https://mlsanity.com/paper/1707.07269/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2017.

## Built on by (most cited first, 8 of 8)

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- [Data augmented bootstrap: Unifying confidence interval construction by approximate invariance](https://mlsanity.com/paper/2606.09049/) (2026)
- [Distributional Random Forests for Complex Survey Designs](https://mlsanity.com/paper/2512.08179/) (2025)
- [The Theory and Practice of Highly Scalable Gaussian Process Regression with Nearest Neighbours](https://mlsanity.com/paper/2604.07267/) (2026)
- [Identifiability and Estimation for Unlabeled Finite Mixtures under Marginal Independence](https://mlsanity.com/paper/2606.07914/) (2026)
- [Multi-kernel spectral clustering: Entrywise eigenvector perturbation bounds and exact recovery](https://mlsanity.com/paper/2608.08704/) (2026)
- [SCORE: Spectral Correlation Estimation for Multivariate Gaussians](https://mlsanity.com/paper/2610.12096/) (2026)

## Abstract (arXiv)

In kernel methods, the median heuristic has been widely used as a way of setting the bandwidth of RBF kernels. While its empirical performances make it a safe choice under many circumstances, there is little theoretical understanding of why this is the case. Our aim in this paper is to advance our understanding of the median heuristic by focusing on the setting of kernel two-sample test. We collect new findings that may be of interest for both theoreticians and practitioners. In theory, we provide a convergence analysis that shows the asymptotic normality of the bandwidth chosen by the median heuristic in the setting of kernel two-sample test. Systematic empirical investigations are also conducted in simple settings, comparing the performances based on the bandwidths chosen by the median heuristic and those by the maximization of test power.