# Variance-Aware Estimation of Kernel Mean Embedding

arXiv: https://arxiv.org/abs/2210.06672 · HTML: https://mlsanity.com/paper/2210.06672/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 58 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 11 of 11)

- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Training generative neural networks via Maximum Mean Discrepancy optimization](https://mlsanity.com/paper/1505.03906/) (2015)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Statistical Inference for Generative Models with Maximum Mean Discrepancy](https://mlsanity.com/paper/1906.05944/) (2019)
- [A Linear-Time Kernel Goodness-of-Fit Test](https://mlsanity.com/paper/1705.07673/) (2017)
- [Finite sample properties of parametric MMD estimation: robustness to misspecification and dependence](https://mlsanity.com/paper/1912.05737/) (2019)
- [Kernel Mean Shrinkage Estimators](https://mlsanity.com/paper/1405.5505/) (2014)
- [Kernel Mean Estimation and Stein's Effect](https://mlsanity.com/paper/1306.0842/) (2013)
- [Estimation of copulas via Maximum Mean Discrepancy](https://mlsanity.com/paper/2010.00408/) (2020)
- [Near-Optimal Confidence Sequences for Bounded Random Variables](https://mlsanity.com/paper/2006.05022/) (2020)

## Built on by (most cited first, 6 of 6)

- [A Dictionary of Closed-Form Kernel Mean Embeddings](https://mlsanity.com/paper/2504.18830/) (2025)
- [On the Robustness of Kernel Goodness-of-Fit Tests](https://mlsanity.com/paper/2408.05854/) (2024)
- [Domain Generalization by Functional Regression](https://mlsanity.com/paper/2302.04724/) (2023)
- [Nonparametric Kernel Clustering with Bandit Feedback](https://mlsanity.com/paper/2601.07535/) (2026)
- [Data Fusion with Distributional Equivalence Test-then-pool](https://mlsanity.com/paper/2603.11867/) (2026)
- [Markov Chain Convergence in Kernel-Induced Geometry](https://mlsanity.com/paper/2610.13916/) (2026)

## Abstract (arXiv)

An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness features of the kernel. We show how to speed-up convergence by leveraging variance information in the reproducing kernel Hilbert space. Furthermore, we show that even when such information is a priori unknown, we can efficiently estimate it from the data, recovering the desiderata of a distribution agnostic bound that enjoys acceleration in fortuitous settings. We further extend our results from independent data to stationary mixing sequences and illustrate our methods in the context of hypothesis testing and robust parametric estimation.