Overview
Syllabus
Intro
Talk Outline
k Nearest Neighbors
The Metric Space
Tutorial Outline
NN Regression Setting
Universality
More Formally...
Intuition: Universal Consistency
Convergence Rates
k-NN Distances
From Distances to Rates
Bias-Variance Decomposition
Bounding Bias and Variance
Integrating across the space
Nearest Neighbor Classification
The Statistical Learning Framework
The Bayes Optimal Classifier
Consistency of I-NN
Consistency under Continuity
Proof Intuition
Universal Consistency in Metric Spaces
Main Idea in Prior Analysis
A Motivating Example
Effective Interiors and Boundaries
Convergence Rate Theorem
A Better Smoothness Condition
Smoothness Bounds
Taught by
Simons Institute