Understanding the dynamics of message passing algorithms: a free probability heuristics
This work provides theoretical insights into inference algorithms for dense models, but it is incremental as it recovers existing results.
The authors tackled the problem of analyzing the dynamics of message passing algorithms for dense probabilistic models using free probability heuristics, recovering known results like vanishing effective memories and analytical convergence rates for a toy Ising model.
We use freeness assumptions of random matrix theory to analyze the dynamical behavior of inference algorithms for probabilistic models with dense coupling matrices in the limit of large systems. For a toy Ising model, we are able to recover previous results such as the property of vanishing effective memories and the analytical convergence rate of the algorithm.