PCA, likelihood ratios, and a transition to the Tracy-Widom law
Date: Thursday, 18 November 2021
Time: 10 am - 11 am
Speaker: Professor Iain Johnstone (Stanford University and ANU)
Abstract:
The Tracy-Widom distribution has found broad use in statistical theory and application. We review some of this, focusing first on Principal Components Analysis and the `spiked model'. When the spike signal is below the Baik-Ben Arous-Peche threshold, likelihood ratio tests for
presence of a spike are more efficient than the largest eigenvalue in many settings of multivariate statistics. In recent work with Egor Klochkov, Alexei Onatski and Damian Pavlyshyn, we study the likelihood ratio test in the transition zone around the BBP threshold, making use of a connection with the spherical Sherrington-Kirkpatrick model.
Zoom Link:
https://anu.zoom.us/j/86015752944?pwd=TEpvRjRrTDh0NWZMc0J3RDVNVndHQT09
Meeting ID:860 1575 2944
Password:069205
Please contact Yanrong Yang (yanrong.yang@anu.edu.au) if you have any questions about this seminar.