# Conditional mean embeddings and optimal feature selection via positive definite kernels

arXiv: https://arxiv.org/abs/2305.08100 · HTML: https://mlsanity.com/paper/2305.08100/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 28 references that are in the map.
- First posted on arXiv 14 May 2023.

## Builds on (most cited first, 7 of 7)

- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [A Rigorous Theory of Conditional Mean Embeddings](https://mlsanity.com/paper/1912.00671/) (2019)
- [Minimax Rate Optimal Adaptive Nearest Neighbor Classification and Regression](https://mlsanity.com/paper/1910.10513/) (2019)
- [COKE: Communication-Censored Decentralized Kernel Learning](https://mlsanity.com/paper/2001.10133/) (2020)
- [Multi-task Reinforcement Learning in Reproducing Kernel Hilbert Spaces via Cross-learning](https://mlsanity.com/paper/2008.11895/) (2020)
- [Kernel Smoothing, Mean Shift, and Their Learning Theory with Directional Data](https://mlsanity.com/paper/2010.13523/) (2020)
- [Conditional Deep Gaussian Processes: multi-fidelity kernel learning](https://mlsanity.com/paper/2002.02826/) (2020)

## Abstract (arXiv)

Motivated by applications, we consider here new operator theoretic approaches to Conditional mean embeddings (CME). Our present results combine a spectral analysis-based optimization scheme with the use of kernels, stochastic processes, and constructive learning algorithms. For initially given non-linear data, we consider optimization-based feature selections. This entails the use of convex sets of positive definite (p.d.) kernels in a construction of optimal feature selection via regression algorithms from learning models. Thus, with initial inputs of training data (for a suitable learning algorithm,) each choice of p.d. kernel K in turn yields a variety of Hilbert spaces and realizations of features. A novel idea here is that we shall allow an optimization over selected sets of kernels K from a convex set C of positive definite kernels K. Hence our textquotedblleft optimaltextquotedblright choices of feature representations will depend on a secondary optimization over p.d. kernels K within a specified convex set C.