Event
Communication, Control and Signal Processing Seminar
Tuesday, March 24, 2026
11:00 a.m.
Room 2168, A. V. Williams Building
CCSP Seminar with Mokshay Madiman
Time: Tuesday, March 24, 11 am ET
Venue: AVW 2168
Zoom link: https://umd.zoom.us/j/
Meeting ID: 435 787 6880
Passcode: yd5MH6
Title: Foundations of a theory of metric complexities
Speaker: Mokshay Madiman (University of Delaware)
Abstract:
The family of Rényi entropies, including the famous Shannon entropy, provide ways of measuring the “amount of randomness” of a probability distribution, whether on a countable set or on a finite-dimensional vector space. However, these entropies are not sensitive to the metric structure of the underlying set— for example, the entropy of the uniform distribution on a subset of the integers depends only on the cardinality of the support and not on how spread out the support is. We explore a metric-sensitive generalization of Rényi entropies called complexities. Leinster, Cobbold, Meckes, and Roff have recently developed a theory of these metric complexities for finite and compact metric spaces— we extend this theory to a broad class of locally compact metric spaces that includes Euclidean space. We also develop fundamental properties of these metric complexities, which are new even for finite metric spaces, and show connections to the Rényi information dimensions in the Euclidean setting. Finally we make some remarks on the relevance of metric complexities to problems of data compression.
