Coresets for Kernel Regression

Kernel regression is an essential and ubiquitous tool for non-parametric data analysis, particularly popular among time series and spatial data. However, the central operation which is performed many times, evaluating a kernel on the data set, takes linear time. This is impractical for modern large data sets. In this paper we describe coresets for kernel regression: compressed data sets which can be used as proxy for the original data and have provably bounded worst case error. The size of the coresets are independent of the raw number of data points, rather they only depend on the error guarantee, and in some cases the size of domain and amount of smoothing. We evaluate our methods on very large time series and spatial data, and demonstrate that they incur negligible error, can be constructed extremely efficiently, and allow for great computational gains.