Independence is good: dependency-based histogram synopses for high-dimensional data

Approximating the joint data distribution of a multi-dimensional data set through a compact and accurate histogram synopsis is a fundamental problem arising in numerous practical scenarios, including query optimization and approximate query answering. Existing solutions either rely on simplistic independence assumptions or try to directly approximate the full joint data distribution over the complete set of attributes. Unfortunately, both approaches are doomed to fail for high-dimensional data sets with complex correlation patterns between attributes. In this paper, we propose a novel approach to histogram-based synopses that employs the solid foundation of statistical interaction models to explicitly identify and exploit the statistical characteristics of the data. Abstractly, our key idea is to break the synopsis into (1) a statistical interaction model that accurately captures significant correlation and independence patterns in data, and (2) a collection of histograms on low-dimensional marginals that, based on the model, can provide accurate approximations of the overall joint data distribution. Extensive experimental results with several real-life data sets verify the effectiveness of our approach. An important aspect of our general, model-based methodology is that it can be used to enhance the performance of other synopsis techniques that are based on data-space partitioning (e.g., wavelets) by providing an effective tool to deal with the “dimensionality curse”.