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Model reductions for inference: generality of pairwise, binary, and planar factor graphs.

Frederik Eaton1, Zoubin Ghahramani

  • 1Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK. frederik@ofb.net

Neural Computation
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Summary
This summary is machine-generated.

This study introduces a novel method for translating algorithms between discrete statistical models, enhancing efficiency. A new "spectral reduction" technique allows for broader applicability beyond positive models, improving inference capabilities.

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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Statistical Modeling

Background:

  • Efficiently translating algorithms between discrete statistical models is a significant challenge.
  • Understanding the expressive power of different model classes is crucial for algorithm development.

Purpose of the Study:

  • To develop a solution for efficiently translating algorithms between discrete statistical models.
  • To investigate the expressive power of binary variable, pairwise factor, and planar topology models and their intersections.
  • To formalize and analyze the concept of
  • simple reduction
  • for marginal probability inference.

Main Methods:

  • Investigated seven subclasses of discrete factor graphs (binary variables, pairwise factors, planar topology, and their intersections).
  • Formalized a notion of
  • simple reduction
  • for marginal inference.
  • Developed a continuous
  • spectral reduction
  • based on polynomial interpolation.

Main Results:

  • Characterized the reducibility of each subclass, finding that binary pairwise factor graphs can only simply reduce positive models.
  • Demonstrated that the spectral reduction overcomes the limitations of simple reduction.
  • Experimental assessment of approximate inference algorithms on reduced models.

Conclusions:

  • The proposed spectral reduction offers a more general and powerful method for translating algorithms between discrete statistical models.
  • This work advances the understanding of model expressiveness and inference capabilities in machine learning.