Coresets for Kernel Regression
This addresses the scalability problem for researchers and practitioners using kernel regression in fields like time series and spatial analysis, offering an incremental improvement over existing methods.
The paper tackles the computational inefficiency of kernel regression on large datasets by introducing coresets that compress data with provable error bounds, achieving negligible error and significant computational gains on large time series and spatial data.
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.