# Message-Passing Algorithms and Homology.

@article{Peltre2020MessagePassingAA, title={Message-Passing Algorithms and Homology.}, author={Olivier Peltre}, journal={arXiv: Mathematical Physics}, year={2020} }

This PhD thesis lays out algebraic and topological structures relevant for the study of probabilistic graphical models.
Marginal estimation algorithms are introduced as diffusion equations of the form $\dot u = \delta \varphi$. They generalise the traditional belief propagation (BP) algorithm, and provide an alternative for contrastive divergence (CD) or Markov chain Monte Carlo (MCMC) algorithms, typically involved in estimating a free energy functional and its gradient w.r.t. model… Expand

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