Incremental Local Gaussian Regression

Locally weighted regression (LWR) was created as a nonparametric method that can approximate a wide range of functions, is computationally efficient, and can learn continually from very large amounts of incrementally collected data. However, it does not provide a proper generative model for function values, and existing algorithms have a variety of manual tuning parameters that strongly influence bias, variance and learning speed of the results. Gaussian (process) regression, on the other hand, does provide a generative model with rather black-box automatic parameter tuning, but it has higher computational cost, especially for big data sets and if a non-stationary model is required. In this paper, we suggest a path from Gaussian (process) regression to locally weighted regression, where we retain the best of both approaches. Using a localizing function basis and approximate inference techniques, we build a Gaussian (process) regression algorithm of increasingly local nature and similar computational complexity to LWR.