TY  - JOUR
ID  - Jorgensen2024
LB  - Jorgensen2024
AU  - Jorgensen, Palle E.T.
AU  - Song, Myung-Sin
AU  - Tian, James
TI  - Conditional mean embedding and optimal feature selection via positive definite kernels
ST  - Conditional mean embedding and optimal feature selection via positive definite kernels
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2024
VL  - 44
IS  - 1
SP  - 79
EP  - 103
DO  - https://doi.org/10.7494/OpMath.2024.44.1.79
UR  - https://doi.org/10.7494/OpMath.2024.44.1.79
AB  - 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.
KW  - positive-definite kernels
KW  - reproducing kernel Hilbert space
KW  - stochastic processes
KW  - frames
KW  - machine learning
KW  - embedding problems
KW  - optimization
SN  - 1232-9274
ER  -