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Conditional mean embedding and optimal feature selection via positive definite kernels
Journal article   Open access   Peer reviewed

Conditional mean embedding and optimal feature selection via positive definite kernels

Palle E.T. Jorgensen, Myung-Sin Song and James Tian
Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica, Vol.44(1), pp.79-103
2024
DOI: 10.7494/OpMath.2024.44.1.79
url
https://doi.org/10.7494/OpMath.2024.44.1.79View
Published (Version of record) Open Access

Abstract

Motivated by applications, we consider new operator-theoretic approaches to conditional mean embedding (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 kernels in a construction o foptimal feature selection via regression algorithms from learning models. Thus, with initial inputs of training data (for a suitable learning algorithm), each choice of a kernel \(K\) in turn yields a variety of Hilbert spaces and realizations of features. A novel aspect of our work is the inclusion of a secondary optimization process over a specified convex set of positive definite kernels, resulting in the determination of "optimal" feature representations.

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