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Marginal Consistency: Upper-Bounding Partition Functions over Commutative Semirings.

Tomás Werner

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |September 10, 2015
    PubMed
    Summary

    We developed a novel iterative algorithm to bound partition functions in artificial intelligence and pattern recognition. This method unifies existing algorithms and achieves marginal consistency for improved inference.

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    Area of Science:

    • Artificial Intelligence
    • Pattern Recognition
    • Theoretical Computer Science

    Background:

    • Many AI and pattern recognition tasks involve partition functions over commutative semirings.
    • Existing methods like max-sum diffusion offer approximate solutions for MAP inference.

    Purpose of the Study:

    • To propose a generalized iterative algorithm for upper bounding partition functions over commutative semirings.
    • To unify and extend existing message-passing and constraint propagation algorithms.

    Main Methods:

    • Generalizing max-sum diffusion to abstract commutative semirings.
    • Developing an iterative algorithm based on modifying factors to equalize overlapping marginals.
    • Introducing a hierarchy of marginal consistencies enforced by higher-arity identity factors.

    Main Results:

    • The proposed algorithm converges to a fixed point (marginal consistency) where an upper bound on the partition function monotonically decreases.
    • The abstract algorithm unifies algorithms like max-sum diffusion and constraint propagation.
    • A hierarchy of marginal consistencies is established, enforceable by adding identity factors.

    Conclusions:

    • The developed framework provides a unified approach to approximate inference over commutative semirings.
    • Marginal consistency is a key concept for achieving tighter bounds and improved inference.
    • The method has broad applicability across various semirings, including distributive lattices and max-sum/sum-product semirings.