Nearest Neighbors I

Explore the fundamentals of nearest neighbors algorithms in this comprehensive lecture from the Deep Learning Boot Camp at the Simons Institute. Delve into the metric space, universal consistency, convergence rates, and statistical learning frameworks as Kamalika Chaudhuri from UC San Diego guides you through key concepts. Examine nearest neighbor regression and classification, including the Bayes optimal classifier and consistency under continuity. Investigate bias-variance decomposition, effective interiors and boundaries, and smoothness conditions. Gain insights into the convergence rate theorem and its applications in machine learning and data analysis.

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