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Consistent inference of a general model using the pseudolikelihood method.

Alexander Mozeika1, Onur Dikmen1, Joonas Piili2

  • 1Department of Information and Computer Science, Aalto University, P.O. Box 15400, FI-00076, Finland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 15, 2014
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Summary
This summary is machine-generated.

A new information theory approach connects maximum pseudolikelihood (MPL) inference with traditional likelihood functions for statistical physics models. This research demonstrates the consistency of the MPL method, even for complex, intractable models.

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Area of Science:

  • Statistical physics
  • Information theory
  • Computational statistics

Background:

  • Maximum pseudolikelihood (MPL) inference is a powerful technique for statistical models where the true likelihood function is computationally intractable.
  • Existing methods often rely on approximations or alternative statistical frameworks to handle these complex models.
  • A deeper theoretical understanding of the relationship between pseudolikelihood and likelihood is needed.

Purpose of the Study:

  • To establish a formal connection between pseudolikelihood and likelihood functions using information theory.
  • To rigorously demonstrate the consistency of the maximum pseudolikelihood (MPL) inference method.
  • To validate the applicability of MPL for general statistical models with intractable likelihoods.

Main Methods:

  • Utilizing principles from information theory to derive a mathematical relationship between pseudolikelihood and likelihood.
  • Applying theoretical analysis to prove the consistency of the MPL estimation procedure.
  • Generalizing the findings to encompass a broad class of statistical models.

Main Results:

  • A novel information-theoretic derivation explicitly links pseudolikelihood and likelihood functions.
  • The consistency of the maximum pseudolikelihood (MPL) method is formally proven for a general class of models.
  • The findings confirm the theoretical underpinnings and practical utility of MPL in statistical physics.

Conclusions:

  • The information-theoretic framework provides a rigorous justification for using maximum pseudolikelihood (MPL) inference.
  • The demonstrated consistency of MPL enhances its reliability for analyzing complex statistical physics models.
  • This work offers a foundational understanding for the broader application of MPL in statistical modeling.