[Ml-stat-talks] FW: IDeAS Seminar on Wed. 3/14/12

Amit Singer amits at math.Princeton.EDU
Tue Mar 13 11:46:26 EDT 2012



From: Valerie Marino [mailto:vmarino at math.princeton.edu] 
Sent: Tuesday, March 13, 2012 11:23 AM
To: PACM Grad Students
Cc: PACM etc.; Amit Singer; Peter Constantin; E Weinan; Phill Holmes
Subject: IDeAS Seminar on Wed. 3/14/12


Date: Wednesday March 14, 2012
Place: 214 Fine Hall

Time:  3:00 pm

Speaker:Hau-Tieng Wu, PACM, Princeton University.
Title: Manifold adaptive local linear regression and its application to
sleep depth estimation
We study nonparametric regression with high-dimensional massive dataset,
when the predictors lie on an unknown,
lower-dimensional geometric object. In particular, we focus on the sleep
depth estimation problem, where the dataset is generated by applying
Synchrosqueezing transform, a time frequency analysis technique, to the
sleep data.
When the geometric object is a smooth manifold, our approach to the
nonparametric regression is to reduce the dimensionality first and then
construct the local linear regression (LLR) directly on the tangent plane
approximation to the manifold. Under mild conditions, asymptotic expressions
for the conditional mean squared error of the proposed estimator are derived
for both the interior and the boundary cases. One implication of these
results is that the optimal convergence rate depends only on the intrinsic
dimension $d$ of the manifold,  but not on the ambient space dimension $p$.
Another implication is that the estimator is design adaptive and
automatically adapts to the boundary of the unknown manifold. The proposed
method has a strong connection with manifold learning and the second
implication leads to a new diffusion map framework.

Valerie Marino
Program Secretary
Program in Applied & Computational Mathematics
Tel: 609-258-3703
Fax: 609-258-1735
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