document: Efficient and effective explanation of change in hierarchical summaries Dimension attributes in data warehouses are typically hierarchical ( e.g. , geographic locations in sales data , URLs in Web traffic logs ) . OLAP tools are used to summarize the measure attributes ( e.g. , total sales ) along a dimension hierarchy , and to characterize changes ( e.g. , trends and anomalies ) in a hierarchical summary over time . When thenumber of changes identified is large ( e.g. , total sales in many stores differed from their expected values ) , a parsimonious explanation of the most significant changes is desirable . In this paper , we propose a natural model of parsimonious explanation , as a composition of node weights along the root-to-leaf paths in a dimension hierarchy , which permits changes to be aggregated with maximal generalization along the dimension hierarchy . We formalize this model of explaining changes in hierarchical summaries and investigate the problem of identifying optimally parsimonious explanations on arbitrary rooted one dimensional tree hierarchies . We show that such explanations can be computed efficiently in time essentially proportional to the number of leaves and the depth of the hierarchy . Further , our method can produce parsimonious explanations from the output of any statistical model that provides predictions and confidence intervals , making it widely applicable . Our experiments use real data sets to demonstrate the utility and robustness of our proposed model for explaining significant changes , as well as its superior parsimony compared to alternatives .
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