Department of Computational and Data Sciences
Department Seminar
Speaker : Prof. Sabyasachi Chatterjee, University of Illinois at Urbana Champaign.
Title : A New Locally Adaptive Nonparametric Regression Method.
Date & Time : August 12, 2024, 2:30 PM
Venue : # 102, CDS Seminar Hall
ABSTRACT
We propose and study a new locally adaptive nonparametric regression method. The method performs variable bandwidth local averaging/local polynomial regression. To certify its local adaptivity we show that it adapts near optimally to the local Holder smoothness exponent of the regression function at any point in the domain. Despite the vast literature on Nonparametric Regression, we only know one existing method which attains such local adaptivity proveably. This method is known as Lepski’s method. There are some drawbacks to Lepski’s method such as a) it is specifically tailored to a given class of functions such as Holder Smooth function class b) it is rather theoretical and impractical to implement with effectively many tuning parameters. Our proposed method seems to overcome these drawbacks. Firstly, our method is defined without any reference to any function class and secondly there is only one tuning parameter, which when set properly, adjusts all the bandwidths at all locations near optimally. Our method is practically implementable and appears to perform reasonably well in our numerical experiments.
BIO: Dr. Sabyasachi Chatterjee is currently working as an Associate Professor in the Department of Statistics at the University of Illinois at Urbana Champaign. He earned his PhD in Statistics at Yale University, USA. Then, he worked as a Postdoctoral Research Scholar and William Kruskal Instructor in the Department of Statistics at the University of Chicago, USA. His research interests lie in Mathematical Statistics and Machine Learning Theory, along with their connections with Information Theory, Probability, and Optimization. For more about his research, please see https://sabyasachi.web.illinois.edu/
Host Faculty: Dr. Ratikanta Behera
ALL ARE WELCOME
