Quantifying and Visualizing Attribute Interactions

Abstract

Interactions are patterns between several attributes in data that cannot be inferred from any subset of these attributes. While mutual information is a well-established approach to evaluating the interactions between two attributes, we surveyed its generalizations as to quantify interactions between several attributes. We have chosen McGill's interaction information, which has been independently rediscovered a number of times under various names in various disciplines, because of its many intuitively appealing properties. We apply interaction information to visually present the most important interactions of the data. Visualization of interactions has provided insight into the structure of data on a number of domains, identifying redundant attributes and opportunities for constructing new features, discovering unexpected regularities in data, and have helped during construction of predictive models; we illustrate the methods on numerous examples. A machine learning method that disregards interactions may get caught in two traps: myopia is caused by learning algorithms assuming independence in spite of interactions, whereas fragmentation arises from assuming an interaction in spite of independence.

30 pages, 11 figures. Changes from v2: improved bibliography

References in corpus (2)

• The Role of Relative Entropy in Quantum Information Theory
• Entropic Bell Inequalities

Cited by in corpus (11)

• A Review of Feature Selection Methods Based on Mutual Information
• Multivariate dependence and genetic networks inference
• Measures of quantum correlations in infinite-dimensional systems
• The Partial Entropy Decomposition: Decomposing multivariate entropy and mutual information via pointwise common surprisal
• Feature construction using explanations of individual predictions
• Polyadic Entropy, Synergy and Redundancy among Statistically Independent Processes in Nonlinear Statistical Physics with Microphysical Codependence
• PredDiff: Explanations and Interactions from Conditional Expectations
• An Information-Theoretic Formalism for Multiscale Structure in Complex Systems
• Uniform continuity bounds for characteristics of multipartite quantum systems
• Summary of Information Theoretic Quantities
• On Information Links