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Related Experiment Videos

A tighter bound for graphical models.

M A Leisink1, H J Kappen

  • 1Department of Biophysics, University of Nijmegen, NL 6525 EZ Nijmegen, The Netherlands.

Neural Computation
|August 23, 2001
PubMed
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We developed a novel method to improve bounds for Boltzmann machine neural networks using odd-order polynomials. This third-order bound significantly outperforms the standard mean-field approach, reducing approximation errors.

Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Statistical Physics

Background:

  • Boltzmann machine neural networks are powerful probabilistic models.
  • Accurate computation of the partition function is crucial for network analysis.
  • Existing methods like mean-field bounds have limitations in precision.

Purpose of the Study:

  • To introduce a generalized method for bounding the partition function of Boltzmann machines.
  • To extend the mean-field bound to higher-order polynomial approximations.
  • To evaluate the efficacy of the proposed third-order bound compared to existing methods.

Main Methods:

  • Developed a novel method to bound the partition function using any odd-order polynomial.
  • Extended the first-order mean-field bound to a third-order approximation.

Related Experiment Videos

  • Derived a third-order bound for the likelihood of sigmoid belief networks.

    • Main Results:

    • The third-order bound is demonstrated to be strictly superior to the mean-field bound.
    • Numerical experiments show a factor of two error reduction in relevant approximation regimes.
    • The method provides a more accurate estimation for complex network models.

    Conclusions:

    • The proposed odd-order polynomial bounding method offers a significant improvement over traditional techniques.
    • This advancement enhances the analytical capabilities of Boltzmann machines and sigmoid belief networks.
    • The findings are particularly valuable in regions where expansion-based approximations are typically applied.