ICERM: Connecting Higher-Order Statistics and Symmetric Tensors

ICERM, Providence, RI

This workshop focuses on connections between higher-order statistics and symmetric tensors, and their applications to machine learning, network science and other domains. Higher-order statistics refers to the study of correlations between three or more covariates. This is in contrast to the usual mean and covariance, which are based on one and two covariates.

Higher-order statistics are needed to characterize complex data distributions, such as mixture models. Symmetric tensors, meanwhile, are multi-dimensional arrays. They generalize covariance matrices and affinity matrices, and can be used to represent higher-order correlations. Tensor decompositions extend matrix factorizations from numerical linear algebra to multilinear algebra. Recently tensor-based approaches have been become more practical, due to the availability of bigger datasets and new algorithms.

The workshop brings together applied mathematicians, statisticians, probabilists, machine learning experts and computational algebraic geometers. Presentations will expose how symmetric tensors, with nonlinear algebra and nonconvex optimization, provide natural mathematical machinery for exploiting higher-order interactions. Topics include: moment tensor decompositions; spectral methods for hypergraphs; and related random matrix theory.

Organizing Committee:

  • Joe Kileel, University of Texas at Austin;
  • Tamara Kolda, Sandia National Labs;
  • Joao Morais Carreira Pereira, Instituto de Matematica Pura e Aplicada

Image credit: Henrik Schumacher