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UID:2021042203311620210414T16000020210414T1650006080ee042035f@uic.edu
CATEGORIES:MEETING
STATUS:TENTATIVE
DTSTAMP:20210421T101821
DTSTART:20210414T160000
DTEND:20210414T165000
SUMMARY:Statistics and Data Science Seminar: Locally Weighted Nearest Neighbor Classifier and Its Theoretical Properties, by Guan Yu
DESCRIPTION:Guan Yu (University of Buffalo): Locally Weighted Nearest Neighbor Classifier and Its Theoretical Properties Weighted nearest neighbor (WNN) classifiers are fundamental non-parametric classifiers for classification. They have become the methods of choice in many applications where limited knowledge of the data generation process is available a priori. There exists a vast room of flexibility in the choice of weights for the neighbors in a WNN classifier. In this talk, I will introduce a new locally weighted nearest neighbor (LWNN) classifier, which adaptively assigns weights for different test data points. Given a training data set and a test data point x0, the weights for classifying x0 in LWNN is obtained by minimizing an upper bound of the conditional expected estimation error of the regression function at x0. The resultant weights have a neat closed-form expression, and therefore the computation of LWNN is more efficient than some existing adaptive WNN classifiers that require estimating the marginal feature density. Like most other WNN classifiers, LWNN assigns larger weights for closer neighbors. However, in addition to the ranks of neighbors' distances, the weights in LWNN also depend on the raw values of the distances. Our theoretical study shows that LWNN achieves the minimax rate of convergence of the excess risk, when the marginal feature density is bounded away from zero. In the general case with an additional tail assumption on the marginal feature density, the upper bound of the excess risk of LWNN matches the minimax lower bound up to a logarithmic term. Please click here to make changes to, or delete, this seminar announcement.
LOCATION:Zoom Chicago IL
CLASS:PRIVATE
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