  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.
