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Linear response algorithms for approximate inference in graphical models.

Max Welling1, Yee Whye Teh

  • 1Department of Computer Science, University of Toronto, Canada. willing@cs.toronto.edu

Neural Computation
|March 10, 2004
PubMed
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This summary is machine-generated.

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This study introduces novel algorithms to approximate pairwise probabilities in cyclic graphs, extending belief propagation (BP) for enhanced probabilistic inference in complex systems.

Area of Science:

  • Statistical inference
  • Graph theory
  • Machine learning

Background:

  • Belief propagation (BP) efficiently computes marginal probabilities on cyclic graphs.
  • BP lacks methods for computing joint distributions of distant nodes.
  • Approximating pairwise probabilities is crucial for advanced probabilistic modeling.

Purpose of the Study:

  • To develop novel algorithms for approximating joint probability distributions over distant nodes in cyclic graphs.
  • To extend the capabilities of belief propagation for more comprehensive probabilistic analysis.
  • To provide efficient methods for computing pairwise probabilities in graphical models.

Main Methods:

  • Developed two new algorithms based on the linear response theorem.
  • Proposed a novel propagation algorithm.

Related Experiment Videos

  • Introduced a matrix inversion-based algorithm.
  • Applied methods to Gaussian random fields.

    • Main Results:

    • The proposed propagation algorithm converges when BP converges to a stable fixed point.
    • Derived a propagation algorithm for computing the inverse of a matrix for Gaussian random fields.
    • Successfully approximated pairwise probabilities for distant nodes.

    Conclusions:

    • The new algorithms effectively approximate pairwise probabilities, overcoming limitations of standard BP.
    • These methods enhance the utility of BP for complex probabilistic inference tasks.
    • The derived matrix inversion algorithm offers an efficient approach for Gaussian random fields.