# Kernel Mean Estimation and Stein's Effect

arXiv: https://arxiv.org/abs/1306.0842 · HTML: https://mlsanity.com/paper/1306.0842/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2013.

## Built on by (most cited first, 11 of 11)

- [Nystr"om Kernel Mean Embeddings](https://mlsanity.com/paper/2201.13055/) (2022)
- [Monotonicity and Double Descent in Uncertainty Estimation with Gaussian Processes](https://mlsanity.com/paper/2210.07612/) (2022)
- [Efficient Numerical Integration in Reproducing Kernel Hilbert Spaces via Leverage Scores Sampling](https://mlsanity.com/paper/2311.13548/) (2023)
- [Variance-Aware Estimation of Kernel Mean Embedding](https://mlsanity.com/paper/2210.06672/) (2022)
- [Kernel Relative-prototype Spectral Filtering for Few-shot Learning](https://mlsanity.com/paper/2207.11685/) (2022)
- [Cross-Space Adaptive Filter: Integrating Graph Topology and Node Attributes for Alleviating the Over-smoothing Problem](https://mlsanity.com/paper/2401.14876/) (2024)
- [Sequential Decision Making on Unmatched Data using Bayesian Kernel Embeddings](https://mlsanity.com/paper/2210.13692/) (2022)
- [Kernel Mean Estimation by Marginalized Corrupted Distributions](https://mlsanity.com/paper/2107.04855/) (2021)
- [SENet: A Spectral Filtering Approach to Represent Exemplars for Few-shot Learning](https://mlsanity.com/paper/2305.18970/) (2023)
- [Operator-Informed Score Matching for Markov Diffusion Models](https://mlsanity.com/paper/2406.09084/) (2024)
- [Adaptive Personalized Federated Learning via Multi-task Averaging of Kernel Mean Embeddings](https://mlsanity.com/paper/2603.02233/) (2026)

## Abstract (arXiv)

A mean function in reproducing kernel Hilbert space, or a kernel mean, is an important part of many applications ranging from kernel principal component analysis to Hilbert-space embedding of distributions. Given finite samples, an empirical average is the standard estimate for the true kernel mean. We show that this estimator can be improved via a well-known phenomenon in statistics called Stein's phenomenon. After consideration, our theoretical analysis reveals the existence of a wide class of estimators that are better than the standard. Focusing on a subset of this class, we propose efficient shrinkage estimators for the kernel mean. Empirical evaluations on several benchmark applications clearly demonstrate that the proposed estimators outperform the standard kernel mean estimator.