This paper shows how metric learning can be used with Nadaraya-Watson (NW) kernel regression. Compared with standard approaches, such as bandwidth selection, we show how metric learning can significantly reduce the mean square error (MSE) in kernel regression, particularly for high-dimensional data. We propose a method for efficiently learning a good metric function based upon analyzing the performance of the NW estimator for Gaussian-distributed data. A key feature of our approach is that the NW estimator with a learned metric uses information from both the global and local structure of the training data. Theoretical and empirical results confirm that the learned metric can considerably reduce the bias and MSE for kernel regression even when the data are not confined to Gaussian.
|Number of pages||11|
|Journal||Advances in Neural Information Processing Systems|
|State||Published - 2017 Jan 1|
|Event||31st Annual Conference on Neural Information Processing Systems, NIPS 2017 - Long Beach, United States|
Duration: 2017 Dec 4 → 2017 Dec 9