Infinite-dimensional stochastic transforms and reproducing kernel Hilbert space
DOI10.1007/s43670-023-00051-zarXiv2209.03801MaRDI QIDQ6049820
Palle E. T. Jorgensen, Myung-Sin Song, James Tian
Publication date: 18 September 2023
Published in: Sampling Theory, Signal Processing, and Data Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2209.03801
momentsgeometryinterpolationsamplingoptimizationalgorithmssplinesprincipal component analysisstochastic processesGaussian processdimension reductionFourier analysisprobabilitycovariance matrixframesinformation theoryfactorizationsmachine learningembedding problemsreproducing kernel Hilbert spacemathematical physicspositive-definite kernelsdigital image analysisKarhunen-LoèveKaczmarzsignal/image processingcomplex function-theory
Factor analysis and principal components; correspondence analysis (62H25) Gaussian processes (60G15) Artificial neural networks and deep learning (68T07) Quadratic programming (90C20) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) General harmonic expansions, frames (42C15) Positive definite functions in one variable harmonic analysis (42A82) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Spline approximation (41A15) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10) Sampling theory in information and communication theory (94A20) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)
Cites Work
- Regularized kernel PCA for the efficient parameterization of complex geological models
- Sampled forms of functional PCA in reproducing kernel Hilbert spaces
- Geometry on probability spaces
- Fast encoding of low-entropy sources
- Infinite-dimensional measure spaces and frame analysis
- On kernel methods for covariates that are rankings
- Dimension reduction analysis with mapping and direct integration algorithm
- Distributed regularized least squares with flexible Gaussian kernels
- The elliptic stochastic quantization of some two dimensional Euclidean QFTs
- Distributed kernel gradient descent algorithm for minimum error entropy principle
- Non-local Markovian symmetric forms on infinite dimensional spaces. I: The closability and quasi-regularity
- The generalized degrees of freedom of multilinear principal component analysis
- Realizations and factorizations of positive definite kernels
- Positive matrices in the Hardy space with prescribed boundary representations via the Kaczmarz algorithm
- Shannon sampling. II: Connections to learning theory
- Learning theory estimates via integral operators and their approximations
- Stochastic Processes Induced by Singular Operators
- Model-based machine learning
- Entropy encoding, Hilbert space, and Karhunen-Loève transforms
- Stable Positive Definite Functions
- Gaussian Hilbert Spaces
- Camera-Aware Multi-Resolution Analysis for Raw Image Sensor Data Compression
- Multiple description image compression based on multiwavelets
- Learning Theory
- A matrix characterization of boundary representations of positive matrices in the Hardy space
- Generalized dual Sudakov minoration via dimension-reduction—a program
- Mean-Field Limit for a Class of Stochastic Ergodic Control Problems
- Decomposition of Gaussian processes, and factorization of positive definite kernels
- Robust kernel-based distribution regression
- Gradient-Free Construction of Active Subspaces for Dimension Reduction in Complex Models with Applications to Neutronics
- Bayesian Model and Dimension Reduction for Uncertainty Propagation: Applications in Random Media
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Infinite-dimensional stochastic transforms and reproducing kernel Hilbert space
