Convergence of Nearest Neighbor Classification - Sanjoy Dasgupta

Explore the convergence of nearest neighbor classification in this 49-minute Members' Seminar presented by Sanjoy Dasgupta from the University of California, San Diego. Delve into the nonparametric estimator, statistical learning theory setup, and consistency results under continuity. Examine universal consistency in RPA and metric spaces, smoothness and margin conditions, and accurate rates of convergence. Investigate tradeoffs in choosing k, adaptive NN classifiers, and nonparametric notions of margin. Conclude with open problems in the field of nearest neighbor classification.

Intro
Nearest neighbor
A nonparametric estimator
The data space
Statistical learning theory setup
Questions of interest
Consistency results under continuity
Universal consistency in RP
A key geometric fact
Universal consistency in metric spaces
Smoothness and margin conditions
A better smoothness condition for NN
Accurate rates of convergence under smoothness
Under the hood
Tradeoffs in choosing k
An adaptive NN classifier
A nonparametric notion of margin
Open problems