Publications by Kartik Waghmare

Continuously indexed graphical models

Let X={Xu}u is an element of U be a real-valued Gaussian process indexed by a set U. We show that X can be viewed as a graphical model with an uncountably infinite graph, where each Xu is a vertex. This graph is characterized by the reproducing property of ...

OXFORD UNIV PRESS2025

THE POSITIVE-DEFINITE COMPLETION PROBLEM

Victor Panaretos, Kartik Waghmare

We study the positive-definite completion problem for kernels on a variety of domains and prove results concerning the existence, uniqueness, and characterization of solutions. In particular, we study a special solution called the canonical completion whic ...

2024

A Karhunen–Loève theorem for random flows in Hilbert spaces

Victor Panaretos, Kartik Waghmare

We develop a generalisation of Mercer’s theorem to operator-valued kernels in infinite dimensional Hilbert spaces. We then apply our result to prove a Karhunen-Loève theorem, valid for mean-square continuous random functions valued in a separable Hilbert s ...

2024

Positive Definite Completions and Continuous Graphical Models

Kartik Waghmare

This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...

EPFL2023

The Completion Of Covariance Kernels

Victor Panaretos, Kartik Waghmare

We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Omega of a rectangular domain I x I to a covariance kernel on the entire domain I x I. For a broad class of domains Omega call ...

INST MATHEMATICAL STATISTICS-IMS2022