Preprint
Conditional mean embeddings and optimal feature selection via positive definite kernels
Arxiu (València. Internet)
05/14/2023
DOI: 10.48550/arxiv.2305.08100
Abstract
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
optimal\textquotedblright{} choices of feature representations will depend on a
secondary optimization over p.d. kernels $K$ within a specified convex set $C$.
Details
- Title: Subtitle
- Conditional mean embeddings and optimal feature selection via positive definite kernels
- Creators
- Palle E. T JorgensenMyung-Sin SongJames Tian
- Resource Type
- Preprint
- Publication Details
- Arxiu (València. Internet)
- DOI
- 10.48550/arxiv.2305.08100
- ISSN
- 2951-9810
- eISSN
- 2952-0460
- Language
- English
- Date posted
- 05/14/2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984418459902771
Metrics
3 Record Views