Prof. Haonan Wang,  CSU Statistics Dept.

Functional Sparsity and Its Application in Neuroscience

In this talk, we consider the problem of estimation and selection in
nonparametric regression.  The notion of functional sparsity is
introduced as a generalization of parameter sparsity in classical
parametric regression model.  In particular, two different types of
sparsity are of interest, including both global sparsity and local
sparsity.  The goal is to produce a sparse estimate which assigns zero
values over regions where the true underlying function is zero.  Most
classical smoothing techniques yield consistent estimates with no
sparsity.  Here, a penalized approach is proposed for simultaneous
functional estimation and model selection.  Asymptotic properties of
the procedure, including both consistency in estimation and
sparsistency in model selection, are established.  The proposed method
has been applied in neuron dynamic modeling.  Each input neuron and the
output neuron have a functional relationship.  Here, a dynamic
Multiple-Input, Single-Output model of neural information
communication is proposed.  The performance of the proposed method is
assessed using Monte Carlo simulation studies and real data analysis.