Parsimonious Representation of Random Variables in Data Cubes

• Activity Number: 429
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Phillip Yelland*+
• Companies: Google Inc
• Keywords: data cube ; multivariate statistics ; graphical models ; information entropy

Abstract

Data cubes, first developed in the context of on-line analytic processing (OLAP) applications for databases, have become increasingly widespread as a means of structuring data aggregations in other contexts. For example, increasing levels of aggregation in a data cube can be used to impose a hierarchical structure on sets of cross-categorized values, producing a summary description that takes advantage of commonalities within the cube categories. In this paper, we describe a novel technique for realizing such a hierarchical structure in a data cube containing discrete random variables. Using a generalization of an approach due to Chow and Liu, this technique produces a parsimonious approximation to the joint distribution of the variables in terms of the aggregation structure of the cube. The efficacy of the technique is illustrated using a real-life application that involves monitoring and reporting anomalies in Web traffic streams over time.