Regionalized Optimization
Gr\'egoire Sergeant-Perthuis

TL;DR
This paper introduces a mathematical framework for reconstructing global loss functions from local ones using functors, enabling new message passing algorithms for complex optimization problems with multiple perspectives.
Contribution
It presents a novel theoretical framework for regionalized loss reconstruction and connects it to existing and new message passing algorithms for diverse optimization scenarios.
Findings
Framework unifies various message passing algorithms.
New algorithms for noisy channel networks.
Shows how to derive critical points of regionalized losses.
Abstract
We propose a theoretical framework for non redundant reconstruction of a global loss from a collection of local ones under constraints given by a functor; we call this loss the regionalized loss in honor to Yedidia, Freeman, Weiss' celebrated article `Constructing free-energy approximations and generalized belief propagation algorithms' where a first example of regionalized loss, for entropy and the marginal functor, is built. We show how one can associate to these regionalized losses message passing algorithms for finding their critical points. It is a natural mathematical framework for optimization problems where there are multiple points of views on a dataset and replaces message passing algorithms as canonical ways of finding the optima of these problems. We explain how Generalized Belief propagation algorithms fall into the framework we propose and propose novel message passing…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsTopological and Geometric Data Analysis · Neural Networks and Applications · Gene Regulatory Network Analysis
MethodsNetwork On Network · Principal Components Analysis
