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 the number 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 t...