IACM Colloquium
Speaker: Victor Panaretos
Title: The Extrapolation of Correlation
Abstract:
We discuss the problem of positive-semidefinite extension: extending a
partially specified covariance kernel from a subdomain Ω of [0,1]2 to a
covariance kernel on the entire domain [0,1]2. For a broad class of
domains Ω called serrated domains, we can obtain a complete picture.
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
determination of the canonical completion reduces to the solution of a
system of linear inverse problems in the space of Hilbert-Schmidt
operators, and derive rates of convergence when the kernel is to be
empirically estimated. We conclude by providing extensions of our theory
to more general forms of domains, and by demonstrating how our results
can be used in statistical inverse problems associated with stochastic
processes. Based on joint work with in collaboration with K.G. Waghmare
(EPFL).
Short Bio:
Victor M. Panaretos is Full Professor and former Director at the
Mathematics Institute at the EPFL. He received his PhD in 2007 from UC
Berkeley, advised by David Brillinger. Upon graduation he was appointed
as Assistant Professor at the EPFL, where he rose the ranks to Full
Professor. He received the Erich Lehmann Award for an Outstanding PhD
(UC Berkeley, 2007), an ERC Starting Grant Award (2011) and was named
"One of 40 extraordinary scientists under 40" by the World Economic
Forum (2014). He is an Elected Member of the ISI (2008) and a Fellow of
the IMS (2019). He was the Bernoulli Society Forum Lecturer in 2019, and
and an IMS Medallion Lecturer on 2025. He is an Associate Editor for
Biometrika, and the Journal of the American Statistical Association
(Theory and Methods), and previously for the Annals of Statistics,
Annals of Applied Statistics, and Electronic Journal of Statistics. He
has served the discipline from various posts, most notably as incoming
President of the Bernoulli Society.
Time, Date & Location: 15:00, Thursday, 1st of June, 2023, Seminar Room 1
Host: Charalambos Makridakis