Seeking Interpretable Models for High Dimensional Data

Bin Yu 
Department of Statistics
Department of Electrical Engineering & Computer Science
University of California at Berkeley
www.stat.berkeley.edu/~binyu

Abstract

Extracting useful information from high-dimensional data is the focus of today's 
statistical research and practice. After broad success of statistical machine 
learning on prediction through regularization, interpretability is gaining attention 
and sparsity has been used as its proxy.  With the virtues of both regularization 
and sparsity, L1 penalized minimization (e.g. Lasso) has been very popular recently.

In this talk, I would like to cover both theory and pratcice of L1 penalized minimization.  
First, I will give a brief overview of recent theoretical results on model selection consistency 
(when p>>n) of Lasso and graphical Lasso.  Second, I will present on-going collaborative 
research with the Gallant Lab at Berkeley on understanding visual pathway. In particular, 
sparse models (linear, non-linear, and graphical) have been built to relate natural images 
to fMRI responses in human primary visual cortex area V1. Issues of model validation 
will be discussed.