A KNN Based Kalman Filter Gaussian Process Regression

The standard Gaussian process (GP) regression is often intractable when a data set is large or spatially nonstationary. In this paper, we address these challenging data properties by designing a novel K nearest neighbor based Kalman filter Gaussian process (KNN-KFGP) regression. Based on a state space model established by the KNN driven data grouping, our KNN-KFGP recursively filters out the latent function values in a computationally efficient and accurate Kalman filtering framework. Moreover, KNN allows each test point to find its strongly correlated local training subset, so our KNN-KFGP provides a suitable way to deal with spatial nonstationary problems. We evaluate the performance of our KNN-KFGP on several synthetic and real data sets to show its validity.