Journal article
Conditional mean embedding and optimal feature selection via positive definite kernels
Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica, Vol.44(1), pp.79-103
2024
DOI: 10.7494/OpMath.2024.44.1.79
Appears in Diamond 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.
Details
- Title: Subtitle
- Conditional mean embedding and optimal feature selection via positive definite kernels
- Creators
- Palle E.T. JorgensenMyung-Sin SongJames Tian
- Resource Type
- Journal article
- Publication Details
- Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica, Vol.44(1), pp.79-103
- DOI
- 10.7494/OpMath.2024.44.1.79
- ISSN
- 1232-9274
- Language
- English
- Date published
- 2024
- Academic Unit
- Mathematics
- Record Identifier
- 9984487501602771
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