Fundamental Limits for Bayesian Signal Inference at Growing Rank

Date(s): Thursday 14th November 2024 (14:00-15:00)
Contact: Event Convenor Contact: William.Salkeld@nottingham.ac.uk
Description: Speaker's Name: Anas Rahan
Speaker's Affiliation: International Centre for Theoretical Physics
Speaker's Research Theme(s): Statistics and Probability,
Abstract:
We consider the classical problem of transmitting a signal through an additive Gaussian noise channel. Working in the Bayesian setting and using methods from spin glass theory, the community has thus far been able to express the optimal mutual information between input and output of various finite-rank matrix and tensor inference models in terms of a simple variational formula. In recent joint work with Jean Barbier and Justin Ko, we showed in the case of symmetric matrix factorisation with i.i.d. signals that said formula can be simplified further to demonstrate equivalence with the rank 1 setting. Moreover, we developed tools to extend our result to the regime where the signal rank grows (slowly) with system size. We expect our methodology to be applicable to a variety of signal inference models.

Venue: UP-CHEM-X2

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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