Stable Fixed Points of Loopy Belief Propagation Are Local Minima of the Bethe Free Energy

By Tom M. Heskes. 2002

162 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Discriminative Embeddings of Latent Variable Models for Structured Data (2016, neutral): “…discriminative tasks, and so as to W and u. Conceptually, the procedure starts with representing each datum by a graphical model constructed corresponding to its individual structure with sharing potential functions, and then, we embed these graphical models with the same feature mappings.”
Divergence measures and message passing (2005, background): “…1997) • Expectation propagation (Minka, 2001b) • Tree-reweighted message-passing (Wainwright et al., 2005b) • Fractional belief propagation (Wiegerinck & Heskes, 2002) • Power EP (Minka, 2004) One way to understand these algorithms is to view their cost functions as free-energy functions from…”
Constructing free-energy approximations and generalized belief propagation algorithms (2005, background): “More recently, Heskes [48] has analyzed the same question using the connection to the Bethe free energy, but his sufficient conditions for uniqueness also take into consideration the topology of the factor graph.”
A Fully-Connected Layered Model of Foreground and Background Flow (2013, methodology): “First, we mix the distributions at the current and the previous iterations, similar to damped BP [11]:”
MRF Energy Minimization and Beyond via Dual Decomposition (2011, background): “However, despite the fact that there has been a lot of work on trying to provide a better theoretical analysis of BP-based algorithms [57], [51], [50], [15], an important drawback of these methods remains that their theoretical optimality and/or convergence properties are not yet well understood and”
Compressive phase retrieval via generalized approximate message passing (2012, unknown): “, [47])”
Learning in Markov Random Fields with Contrastive Free Energies (2005, background): “Fortunately, algorithms have been developed that do not rely on messages but directly minimize the Bethe free energy as a function of the marginals [14, 20, 4].”
Graphical Model Inference in Optimal Control of Stochastic Multi-Agent Systems (2008, background): “In particular, more advanced variations on the algorithm (Heskes, Albers, & Kappen, 2003; Teh & Welling, 2001; Yuille, 2002) are guaranteed to converge to local minima of the Bethe free energy (Heskes, 2003).”