Message Passing for Collective Graphical Models

• Main Authors: SUN, Tao, SHELDON, Daniel, KUMAR, Akshat
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2015
• Subjects: Artificial intelligence; Free energy; Functions; Graphic methods; Inference engines; Learning systems; Population statistics; Artificial Intelligence and Robotics; Computer Sciences; Numerical Analysis and Scientific Computing; Theory and Algorithms
• Online Access: https://ink.library.smu.edu.sg/sis_research/2914; https://ink.library.smu.edu.sg/context/sis_research/article/3914/viewcontent/MessagePassingCollectiveGraphicalModels_2015_ICML.pdf
• Institution: Singapore Management University

Collective graphical models (CGMs) are a formalism for inference and learning about a population of independent and identically distributed individuals when only noisy aggregate data are available. We highlight a close connection between approximate MAP inference in CGMs and marginal inference in standard graphical models. The connection leads us to derive a novel Belief Propagation (BP) style algorithm for collective graphical models. Mathematically, the algorithm is a strict generalization of BP—it can be viewed as an extension to minimize the Bethe free energy plus additional energy terms that are non-linear functions of the marginals. For CGMs, the algorithm is much more efficient than previous approaches to inference. We demonstrate its performance on two synthetic experiments concerning bird migration and collective human mobility.