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Accuracy Bounds for Belief Propagation

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Alexander T. Ihler

Artificial Intelligence · Submitted 20 Jun 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Using recent analysis of convergence and stability properties in BP and new results on approximations in binary systems, we derive a bound on the error in BP's estimates for pairwise Markov random fields over discrete valued random variables.

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arXiv ID1206.5277 (version 1)
Pith IDKKVWACPF, Pith's permanent record of this paper and its review
CitationAlexander T. Ihler. "Accuracy Bounds for Belief Propagation." arXiv:1206.5277 (2012). https://pith.science/paper/KKVWACPF
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,566 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.13 · human participants 0.02 · controlled comparison 0.16 · randomized assignment 0.01 · states quantitative result 0.63 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when this algorithm will perform well. Using recent analysis of convergence and stability properties in BP and new results on approximations in binary systems, we derive a bound on the error in BP's estimates for pairwise Markov random fields over discrete valued random variables. Our bound is relatively simple to compute, and compares favorably with a previous method of bounding the accuracy of BP.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. background 1.00 0.05 0.02 asserted 1.00
s1 However, little is known theoretically about when this algorithm will perform well. gap 1.00 0.06 0.02 asserted 1.00
s2 Using recent analysis of convergence and stability properties in BP and new results on approximations in binary systems, we derive a bound on the error in BP's estimates for pairwise Markov random fields over discrete valued random variables. contribution 0.84 0.96 0.70 asserted 1.00
s3 Our bound is relatively simple to compute, and compares favorably with a previous method of bounding the accuracy of BP. result 0.75 0.87 0.28 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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not examined
  • full text
  • figures and tables
  • references and citing sentences
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  • P abstract
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  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when this algorithm will perform well. Using recent analysis of convergence and stability properties in BP and new results on approximations in binary systems, we derive a bound on the error in BP's estimates for pairwise Markov random fields over discrete valued random variables. Our bound is relatively simple to compute, and compares favorably with a previous method of bounding the accuracy of BP.

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