Generative Local Metric Learning for Kernel Regression
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.
Code (0)
등록된 구현이 없습니다.
Tasks
Metric LearningregressionSimilar Papers 제목 키워드 기반
Adaptivity to Local Smoothness and Dimension in Kernel Regression
We present the first result for kernel regression where the procedure adapts locally at a point $x$ to both the unknown local dimension of the metric and the unknown H\{o}lder-continuity of the regression function at $x$…
regressionNonparametric regression using needlet kernels for spherical data
Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods ass…
regressionBayesian Kernel Shaping for Learning Control
In kernel-based regression learning, optimizing each kernel individually is useful when the data density, curvature of regression surfaces (or decision boundaries) or magnitude of output noise (i.e., heteroscedasticity) …
Gaussian ProcessesregressionReinforcement LearningLocal regression on path spaces with signature metrics
We study nonparametric regression and classification for path-valued data. We introduce a functional Nadaraya-Watson estimator that combines the signature transform from rough path theory with local kernel regression. Th…
Time Series ClassificationComputational EfficiencyMultiple Kernel Clustering via Local Regression Integration
Multiple kernel methods less consider the intrinsic manifold structure of multiple kernel data and estimate the consensus kernel matrix with quadratic number of variables, which makes it vulnerable to the noise and outli…
Clusteringregression