Loopy Belief Propagation: Convergence and Effects of Message Errors

By A. Ihler, John W. Fisher III, Alan S. Willsky. 2005

370 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Yoshua Bengio
2. Le Song
3. Wanli Ouyang
4. Yi Yang
5. Dacheng Tao
6. Trevor Darrell
7. Xiaogang Wang
8. Luc Van Gool

Citations in the corpus

• Kernel Belief Propagation (2011, methodology): “The convergence of kernel BP is a further challenging topic for future work (Ihler et al., 2005).”
• Bayesian Compressive Sensing Via Belief Propagation (2008, unknown): “Accounting for CS-BP iterations, overall computation is .”
• Estimating the "Wrong" Graphical Model: Benefits in the Computation-Limited Setting (2006, background): “The behavior of sum-product is relatively well understood in certain settings, including graphs with single cycles (Weiss, 2000), Gaussian models (Freeman and Weiss, 2001; Rusmevichientong and Roy, 2000) and Ising models (Tatikonda and Jordan, 2002; Ihler et al., 2005; Mooij and Kappen, 2005a).”
• Mutual CRF-GNN for Few-shot Learning (2021, background): “It converges in most cases but cannot be theoretically confirmed, which leads to divergence in some cases [2, 1].”
• Graphical Models, Exponential Families, and Variational Inference (2008, methodology): “[199] provide sufficient conditions for convergence, based on contraction arguments such as those used for ordinary sumproduct [225, 87, 175, 115].”
• Bayesian Predictive Beamforming for Vehicular Networks: A Low-Overhead Joint Radar-Communication Approach (2020, methodology): “Note that this part of factor graph has cycles, we have to implement the message passing algorithms for a few iterations [30].”
• Residual Belief Propagation: Informed Scheduling for Asynchronous Message Passing (2006, methodology): “We consider examples from two markedly different models in computational biology (Jaimovich et al., 2005; Yanover and Weiss, 2003).”
• Critical phenomena in complex networks (2007, background): “This phenomenon in the networks with aggregation was studied by Alava and Dorogovtsev (2005).”
• Cloud-Assisted Data Fusion and Sensor Selection for Internet of Things (2016, background): “For example, while it is known that BP is only guaranteed to converge on tree graphs, loopy belief propagation has been shown to work well in most cases for graphs with loops [25].”
• Residual Splash for Optimally Parallelizing Belief Propagation (2009, background): “4 τ -APPROXIMATE INFERENCE It was shown by [Ihler et al., 2005] that message errors decay along paths.”
• Stereo Matching with Color-Weighted Correlation, Hierachical Belief Propagation and Occlusion Handling (2006, methodology): “Ihler [13] provided some theoretical analysis for the approximated sumproduct BP algorithms.”
• Particle Belief Propagation (2009, methodology): “For Markov chains, and assuming some degree of mixing as measured by Ihler et al. (2005b) Eq.”