Numerical Analysis and Scientific Computing Seminar | Houman Owhadi, Computational Hypergraph Discovery, a Gaussian Process framework for connecting the dots

Zoom (Please contact ddelreyfernandez@uwaterloo.ca for meeting link) 

Speaker

Houman Owhadi, Professor, Department of Computing and Mathematical Sciences California Institute of Technology

Title

Computational Hypergraph Discovery, a Gaussian Process framework for connecting the dots

Abstract

Most scientific challenges can be framed into one of the following three levels of complexity of function approximation. 

• Type 1: Approximate an unknown function given input/output data. 
• Type 2: Consider a collection of variables and functions, some of which are unknown, indexed by the nodes and hyperedges of a hypergraph (a generalized graph where edges can connect more than two vertices). Given partial observations of the variables of the hypergraph (satisfying the functional dependencies imposed by its structure), approximate all the unobserved variables and unknown functions. 
• Type 3: Expanding on Type 2, if the hypergraph structure itself is unknown, use partial observations of the variables of the hypergraph to discover its structure and approximate its unknown functions. 

Although Gaussian Process (GP) methods are sometimes perceived as a well-founded but old technology limited to Type 1 curve fitting, we will show that they can be generalized to an interpretable framework for solving Type 2 and Type 3 problems, all while maintaining the simple and transparent theoretical and computational guarantees of kernel/optimal recovery methods.