IMS Medallion Award & Lecture V

A fundamental task in the analysis of data is to detect and estimate interesting "structures" hidden in it.
In this talk I'll focus on aspects of this problem under a high dimensional regime,
where each observed sample has many coordinates, and the number of samples is limited.
We will show how in such cases: (i) standard methods to detect structure in high dimensions
may not work well ; (ii) sparsity can come to the rescue,
albeit it brings with it significant statistical and computational challenges; and
(iii) some interesting phenomena may occur in semi-supervised learning settings where for few of the samples we are also given
their underlying labels.