Abstract: Many current regression algorithms have unsatisfactory prediction accuracy with small samples. To solve this problem, a regression algorithm based on Nadaraya-Watson kernel regression (NWKR) is proposed. The proposed method advocates parameter selection directly from the standard deviation of training data, optimized with leave-one-out cross- validation (LOO-CV). Good generalization performance of the proposed parameter selection is demonstrated empirically using small sample regression problems with Gaussian noise. The results show that proposed parameter optimization method is more robust and accurate than other methods for different noise levels and different sample sizes, and indicate the importance of Vapnik’s e-insensitive loss for regression problems with small samples.
Keywords: small samples regression; Nadaraya-Watson kernel regression; parameter optimization; loss function; cross validation