1 citations · 1 across the 7 of their papers we have counts for
8 papers
Kernel Embeddings and the Separation of Measure Phenomenon
Leonardo V. Santoro, Kartik G. Waghmare, Victor M. Panaretos
We prove that kernel covariance embeddings lead to information-theoretically perfect separation of distinct continuous probability distributions. In statistical terms, we establish…
Proper scoring rules for estimation and forecast evaluation
Kartik Waghmare, Johanna Ziegel
Proper scoring rules have been a subject of growing interest in recent years, not only as tools for evaluation of probabilistic forecasts but also as methods for estimating probabi…
Extreme Points of Spectrahedra
Kartik G. Waghmare, Victor M. Panaretos
We consider the problem of characterizing extreme points of the convex set of positive linear operators on a possibly infinite-dimensional Hilbert space under linear constraints. W…
The Positive-Definite Completion Problem
Kartik G. Waghmare, Victor M. Panaretos
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…
The Functional Graphical Lasso
Kartik G. Waghmare, Tomas Masak, Victor M. Panaretos
We consider the problem of recovering conditional independence relationships between jointly distributed Hilbertian random elements given realizations thereof. We operate i…
A Karhunen-Loève Theorem for Random Flows in Hilbert spaces
Leonardo V. Santoro, Kartik G. Waghmare, Victor M. Panaretos
We develop a generalisation of Mercer's theorem to operator-valued kernels in infinite dimensional Hilbert spaces. We then apply our result to deduce a Karhunen-Loève theorem, vali…
Continuously Indexed Graphical Models
Kartik G. Waghmare, Victor M. Panaretos
Let be a real-valued Gaussian process indexed by a set . It can be thought of as an undirected graphical model with every random variable servi…
The Completion of Covariance Kernels
Kartik G. Waghmare, Victor M. Panaretos
We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain of a rectangular domain to a covar…