Conditional mean embedding and optimal feature selection via positive definite kernels

DOI10.7494/opmath.2024.44.1.79arXiv2305.08100MaRDI QIDQ6091085

James Tian, Palle E. T. Jorgensen, Myung-Sin Song

Publication date: 23 November 2023

Published in: Opuscula Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2305.08100

zbMATH Keywords

optimizationstochastic processesframesmachine learningembedding problemsreproducing kernel Hilbert spacepositive-definite kernels

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Ridge regression; shrinkage estimators (Lasso) (62J07) Artificial neural networks and deep learning (68T07) Quadratic programming (90C20) General harmonic expansions, frames (42C15) Positive definite functions in one variable harmonic analysis (42A82) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On multivariate discrete least squares
• Geometry on probability spaces
• Sampling with positive definite kernels and an associated dichotomy
• High-dimensional variable screening through kernel-based conditional mean dependence
• Testing independence of functional variables by angle covariance
• Model-based feature selection and clustering of RNA-seq data for unsupervised subtype discovery
• Reproducing kernels and choices of associated feature spaces, in the form of \(L^2\)-spaces
• Solving a class of feature selection problems via fractional 0--1 programming
• A kernel-based measure for conditional mean dependence
• Realizations and factorizations of positive definite kernels
• Online learning algorithms
• Reproducing kernels: harmonic analysis and some of their applications
• Error bounds for learning the kernel
• Non-commutative Analysis
• A Topological View of Unsupervised Learning from Noisy Data
• Infinite-Dimensional Analysis
• Minimax Rate Optimal Adaptive Nearest Neighbor Classification and Regression
• A Rigorous Theory of Conditional Mean Embeddings
• Decomposition of Gaussian processes, and factorization of positive definite kernels
• Theory of Reproducing Kernels

This page was built for publication: Conditional mean embedding and optimal feature selection via positive definite kernels