LJKProbability & Statistics Seminar

On Thursday May 4 2017 at 14h00 in Room 2  RDC IMAG Building

Seminary of Jonathan WEED (MIT, Department of Mathematics)

Optimal rates of estimation for the multireference alignment problem

Summary

How should one estimate a signal, given only access to noisy versions of the signal corrupted by unknown circular shifts? This simple problem has surprisingly broad applications, in fields from structural biology to aircraft radar imaging. We describe how this model can be viewed as a multivariate Gaussian mixture model whose centers belong to an orbit of a group of orthogonal transformations. This enables us to derive matching lower and upper bounds for the optimal rate of statistical estimation for the underlying signal. These bounds show a striking dependence on the signaltonoise ratio of the problem.
Joint work with Afonso Bandeira and Philippe Rigollet.
