Generative Local Metric Learning for Nadaraya-Watson Kernel Estimation

• For Gaussian data, the regression needs to calculate kernel with only two-dimensional information regardless of the original dimensionality, and it always obtains mean square error (MSE) close to zero with finite samples. • Previously a well-known extension of the NW estimator, locally linear regression (LLR), is known to alleviate the asymptotic bias. The proposed metric acts differently from LLR to reduce the bias, and the proposed method highly outperforms LLR in the empirical experiments. • In order to reduce MSE, reducing variance with metric is not important. The asymptotic contribution of the variance shows little dependency on the metric once appropriate bandwidth is selected in a high dimensional space. • A simple and coarse generative model captures appropriate metric for nonparametric NW estimation.