@Article{Jorgensen2024,
author = "Jorgensen, Palle E.T. and Song, Myung-Sin and Tian, James",
title = "Conditional mean embedding and optimal feature selection via positive definite kernels",
journal = "Opuscula Math.",
year = "2024",
volume = "44",
number = "1",
pages = "79--103",
doi = "https://doi.org/10.7494/OpMath.2024.44.1.79",
url = "https://doi.org/10.7494/OpMath.2024.44.1.79",
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.",
keywords = "positive-definite kernels, reproducing kernel Hilbert space, stochastic processes, frames, machine learning, embedding problems, optimization",
issn = "1232-9274"
}