# Kernel Mean Estimation via Spectral Filtering

arXiv: https://arxiv.org/abs/1411.0900 · HTML: https://mlsanity.com/paper/1411.0900/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2014.

## Built on by (most cited first, 3 of 3)

- [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)
- [Kernel Mean Estimation by Marginalized Corrupted Distributions](https://mlsanity.com/paper/2107.04855/) (2021)

## Abstract (arXiv)

The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference step of modern kernel methods (e.g., kernel-based non-parametric tests) that rely on embedding probability distributions in RKHSs. Muandet et al. (2014) has shown that shrinkage can help in constructing "better" estimators of the kernel mean than the empirical estimator. The present paper studies the consistency and admissibility of the estimators in Muandet et al. (2014), and proposes a wider class of shrinkage estimators that improve upon the empirical estimator by considering appropriate basis functions. Using the kernel PCA basis, we show that some of these estimators can be constructed using spectral filtering algorithms which are shown to be consistent under some technical assumptions. Our theoretical analysis also reveals a fundamental connection to the kernel-based supervised learning framework. The proposed estimators are simple to implement and perform well in practice.