Adaptive Wavelet Density Estimators over Data Streams

A variety of scientific and commercial applications requires an immediate analysis of transient data streams. Many approaches for analyzing data share the property that an estimation of the underlying data distribution is used as a fundamental building block. To estimate the density of a continuous data distribution, wavelet density estimation, a technique from the area of nonparametric statistics, is very appealing as it is theoretically well-founded and practically approved. For that reason, its application to data streams is highly promising; it provides a convenient way to analyze the characteristics of a stream. However, the heavy computational cost of wavelet density estimators renders their direct application to the streaming scenario impossible. In this work, we tackle this problem and present a novel approach to adaptive wavelet density estimators over data streams. Not only do our estimators meet the rigid processing requirements for data streams, they also adapt to changing system resources in a well-defined manner. A thorough experimental evaluation demonstrates the efficacy of our wavelet density estimators and shows their superiority to competing kernel- and histogram-based estimators.