# Kernel Mean Estimation by Marginalized Corrupted Distributions

arXiv: https://arxiv.org/abs/2107.04855 · HTML: https://mlsanity.com/paper/2107.04855/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 49 references that are in the map.
- First posted on arXiv 10 Jul 2021.

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

- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [Kernel Mean Shrinkage Estimators](https://mlsanity.com/paper/1405.5505/) (2014)
- [Bayesian Learning of Kernel Embeddings](https://mlsanity.com/paper/1603.02160/) (2016)
- [One-Class Support Measure Machines for Group Anomaly Detection](https://mlsanity.com/paper/1303.0309/) (2013)
- [Kernel Mean Estimation and Stein's Effect](https://mlsanity.com/paper/1306.0842/) (2013)
- [Nonparametric Independence Testing for Small Sample Sizes](https://mlsanity.com/paper/1406.1922/) (2014)
- [Kernel Mean Estimation via Spectral Filtering](https://mlsanity.com/paper/1411.0900/) (2014)

## Abstract (arXiv)

Estimating the kernel mean in a reproducing kernel Hilbert space is a critical component in many kernel learning algorithms. Given a finite sample, the standard estimate of the target kernel mean is the empirical average. Previous works have shown that better estimators can be constructed by shrinkage methods. In this work, we propose to corrupt data examples with noise from known distributions and present a new kernel mean estimator, called the marginalized kernel mean estimator, which estimates kernel mean under the corrupted distribution. Theoretically, we show that the marginalized kernel mean estimator introduces implicit regularization in kernel mean estimation. Empirically, we show on a variety of datasets that the marginalized kernel mean estimator obtains much lower estimation error than the existing estimators.