# k*-Nearest Neighbors: From Global to Local

arXiv: https://arxiv.org/abs/1701.07266 · HTML: https://mlsanity.com/paper/1701.07266/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jan 2017.

## Built on by (most cited first, 4 of 4)

- [Efficient Policy Iteration for Robust Markov Decision Processes via Regularization](https://mlsanity.com/paper/2205.14327/) (2022)
- [Improving Forecasts for Heterogeneous Time Series by "Averaging", with Application to Food Demand Forecast](https://mlsanity.com/paper/2306.07119/) (2023)
- [Explaining the Success of Nearest Neighbor Methods in Prediction](https://mlsanity.com/paper/2502.15900/) (2025)
- [Data is missing again -- Reconstruction of power generation data using k-Nearest Neighbors and spectral graph theory](https://mlsanity.com/paper/2409.00300/) (2024)

## Abstract (arXiv)

The weighted k-nearest neighbors algorithm is one of the most fundamental non-parametric methods in pattern recognition and machine learning. The question of setting the optimal number of neighbors as well as the optimal weights has received much attention throughout the years, nevertheless this problem seems to have remained unsettled. In this paper we offer a simple approach to locally weighted regression/classification, where we make the bias-variance tradeoff explicit. Our formulation enables us to phrase a notion of optimal weights, and to efficiently find these weights as well as the optimal number of neighbors efficiently and adaptively, for each data point whose value we wish to estimate. The applicability of our approach is demonstrated on several datasets, showing superior performance over standard locally weighted methods.