Duality of Graphical Models and Tensor Networks

• Activity Number: 392 - Big Tensor Data Analysis
• Type: Invited
• Date/Time: Wednesday, August 5, 2020 : 1:00 PM to 2:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Elina Robeva*
• Companies: University of British Columbia

Abstract

We show a simple duality correspondence between tensor networks and graphical models. We study tensor networks on hypergraphs which we call tensor hypernetworks. In this sense the information of a tensor hypernetwork corresponding to a given hypergraph is exactly the same as a discrete graphical model on the dual hypergraph. We translate various notions under duality. For example, marginalization in a graphical model is the same as contraction in the corresponding tensor network. Algorithms also translate under duality. This simple correspondence is a reminder that the fields of graphical models and tensor networks could benefit from interaction.