Hierarchical Tensor Priors for Deep Interactions

• Activity Number: 587
• Type: Invited
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Alex Volfovsky*+ and Peter David Hoff
• Companies: University of Washington and University of Washington
• Keywords: ANOVA ; tensor ; Hierarchical

Abstract

Interaction terms are the primary means of describing heterogeneity in an outcome variable across levels of multiple factors. In a given model, the complete set of main effects and interaction terms can be viewed as a collection of tensors that share various index sets. For example, in an ANOVA decomposition with three factors, the main-effects, two- and three-way interactions can be viewed as three one-way tensors, three two-way tensors and one three-way tensor, respectively.

We introduce a class of hierarchical prior distributions for collections of interaction tensors, based on a type of array normal distribution with separable covariance structure. This prior is able to recognize potential similarities among the levels of a factor, and incorporate such information into the estimation of the effects in which the factor appears. In effect, this prior is able to borrow information from well-estimated main effects and low-order interactions to assist in the estimation of higher-order terms for which data information is limited.