Machine Learning Seminar: Wormell -- A statistical indicator for eigenvalues of matrices approximated by least squares

The details about the machine learning seminar are as follows: 

Time: Mon 4 May (1:00 - 2:00pm): 

Location: SMRI Seminar Room (A12-03-301) A12 Macleay Building, Level 3, Room 301.  

Speaker: Caroline Wormell (USYD) 

Title: A statistical indicator for eigenvalues of matrices approximated by least squares 

Abstract: Eigenvalues and eigenvectors of operators are interesting to us in a very a
wide range of applications.  In many of these applications, we are tempted to estimate
these operators from a limited amount of observational data.  The issue with this is
that it is hard to know the effects of limited data on the accuracy of our eigenvalues
(and by extension, eigenvectors), especially when the matrices are non-normal.  

In this talk I will present a very general approach for studying spectral errors of
data-driven least-squares approximations of matrices.  Knowledge of the infinite-data
limit allows us to generate a pseudo-spectrum-like function on the complex plane that
allows us to predict where true eigenvalues are likely to go under the finite data
error.  In the other direction, by reprocessing our finite data sample, we can test
statistically for the location of the true eigenvalues.  This gives us a rigorous way to
assess whether the patterns we extract from finite data are likely to be signal or
noise.