The Completion of Covariance Kernels

07/15/2021
by   Kartik G. Waghmare, et al.
0

We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Ω of a domain I× I to a covariance kernel on the entire domain I× I. For a broad class of domains Ω called serrated domains, we are able to present a complete theory. Namely, we demonstrate that a canonical completion always exists and can be explicitly constructed. We characterise all possible completions as suitable perturbations of the canonical completion, and determine necessary and sufficient conditions for a unique completion to exist. We interpret the canonical completion via the graphical model structure it induces on the associated Gaussian process. Furthermore, we show how the estimation of the canonical completion reduces to the solution of a system of linear statistical inverse problems in the space of Hilbert-Schmidt operators, and derive rates of convergence under standard source conditions. We conclude by providing extensions of our theory to more general forms of domains.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 4

page 19

page 20

page 24

page 25

02/12/2021

Algebraic cocompleteness and finitary functors

A number of categories is presented that are algebraically complete and ...
05/09/2017

Influence Function and Robust Variant of Kernel Canonical Correlation Analysis

Many unsupervised kernel methods rely on the estimation of the kernel co...
02/17/2016

Robust Kernel (Cross-) Covariance Operators in Reproducing Kernel Hilbert Space toward Kernel Methods

To the best of our knowledge, there are no general well-founded robust m...
11/20/2014

Maximum Entropy Kernels for System Identification

A new nonparametric approach for system identification has been recently...
07/15/2021

Hida-Matérn Kernel

We present the class of Hida-Matérn kernels, which is the canonical fami...
10/08/2019

Canonical extensions of locally compact frames

Canonical extension of finitary ordered structures such as lattices, pos...
03/15/2020

Guaranteed convergence for a class of coupled-cluster methods based on Arponen's extended theory

A wide class of coupled-cluster methods is introduced, based on Arponen'...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.