Universal coding under Gaussian noise and the Willis functional

The Working Group on Risk - CREAR, with the support of the IDS dpt, Institut des actuaires, LabEx MME-DII and the group BFA-SFdS, has the pleasure to invite you to the seminar by:

Jaouad Mourtada, CREST, ENSAE Paris, Assistant Professor in Statistics,

“Universal coding under Gaussian noise and the Willis functional”

Tuesday, February 14th 2023 12:30 pm to 1:30 pm (CET)

Dual format: ESSEC Paris La Défense (CNIT), Room 237, and via Zoom, please click here (Password/Code : WGRisk)

Topic: Sequential probability assignment is a classical prediction problem, wherein one aims to assign a large probability to a sequence of observations revealed one at a time. This problem is closely related to that of lossless data compression (also called universal coding) in information theory.
We study this problem in the case where the base model is a subset of the standard multivariate Gaussian model, with mean constrained to a general convex domain. We show that the hardness of the problem can be expressed in terms of certain quantities from convex geometry, namely the so-called intrinsic volumes of the constraint set. We then provide an alternative characterization of the optimal error in terms of different complexity measures of the domain, which also holds in the nonconvex case. We finally illustrate these results in some special domains, including ellipsoids.