3/11/2011, Peter Hoff, University of Washington, Mean and covariance models for tensor-valued data

Peter Hoff, Department of Statistics and Center for Statistics and the Social Sciences, University of Washington //.stat.washington.edu/people/people.php?id=67

Mean and covariance models for tensor-valued data

Abstract: Modern datasets are often in the form of matrices or arrays, potentially having correlations along each set of data indices. For example, researchers often gather relational data measured on pairs of units, where the population of units may consist of people, genes, websites or some other set of objects. Multivariate relational data include multiple relational measurements on the same set of units, possibly gathered under different conditions or at different time points. Such data can be represented as a multiway array, or tensor. In this talk I consider models of mean and covariance structure for such array-valued datasets. I will present a model for mean structure based upon the idea of reduced-rank array decompositions, in which the elements of an array are expressed as products of low-dimensional latent factors. The model-based version extends the scope of reduced rank methods to accommodate a variety of data types such as binary longitudinal network data. For modeling covariance structure I will discuss a class of array normal distributions, a generalization of the matrix normal class, and show how it is related to a popular version of a higher-order singular value decomposition for tensor-valued data.