Generalized Haar systems, with applications to machine learning

This talk will cover some recent results of Coifman and Gavish on the use of partition trees and their corresponding generalized Haar systems to problems in machine learning. Topics may include: the equivalence between a function’s regularity and the decay of its Haar coefficients; the use of the Haar basis for function extension (regression and classification problems); and Calderon-Zygmund-type decompositions and their applications to matrix compression and denoising. I assume no prior familiarity with the material and will develop all ideas from scratch. If time permits, I will also discuss methods for building partition trees on data.