Explaining the Success of Nearest Neighbor Methods in Prediction
Despite widespread empirical success, the theoretical foundations and practical deployment guidelines for k-nearest neighbors (k-NN) in predictive tasks remain inadequately understood. Method: We establish the first non-asymptotic error bound framework tailored for real-world deployment, replacing conventional smoothness or margin assumptions with verifiable cluster structure as the key success criterion. We integrate approximate nearest neighbor techniques—including LSH and graph-based indexing—and unify k-NN theory with emerging paradigms such as random forests, graphon modeling, and crowdsourcing. We further introduce a novel distance-learning perspective, characterizing how ensemble methods implicitly learn neighborhood structure. Contribution/Results: Evaluated on time-series forecasting, recommender systems, and medical image segmentation, our framework demonstrates that high accuracy is guaranteed solely under cluster-structured data—enhancing both theoretical interpretability and engineering tractability. It provides actionable, error-tolerance-driven guidance for data volume and hyperparameter selection.