Inference with Aggregate Data: An Optimal Transport Approach

Understand

We consider inference (filtering) problems over probabilistic graphical models with aggregate data generated by a large population of individuals.

• We propose a new efficient belief propagation type algorithm over tree-structured graphs with polynomial computational complexity as well as a global convergence guarantee.
• This is in contrast to previous methods that either exhibit prohibitive complexity as the population grows or do not guarantee convergence.
• Our method is based on optimal transport, or more specifically, multi-marginal optimal transport theory.