Speaker:
Prof.
Haonan Wang, CSU Statistics Dept.
Title:
Functional Sparsity and Its Application in Neuroscience
Abstract:
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.