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The entropy rate of Linear Additive Markov Processes.

Bridget Smart1,2, Matthew Roughan1, Lewis Mitchell1

  • 1School of Computer and Mathematical Sciences, University of Adelaide, Adelaide, South Australia, Australia.

Plos One
|April 5, 2024
PubMed
Summary

The Linear Additive Markov Process (LAMP) model

Area of Science:

  • Information Theory
  • Statistical Modeling
  • Machine Learning

Background:

  • Complex data often exhibits long-range dependencies.
  • Higher-order Markov processes can model these dependencies but have large parameter spaces.
  • A simpler model with theoretical tractability is needed.

Purpose of the Study:

  • To derive the theoretical entropy of a Linear Additive Markov Process (LAMP).
  • To compare the expressibility and parameter efficiency of LAMP models against higher-order Markov processes.
  • To apply the LAMP model for entropy rate estimation on real-world datasets.

Main Methods:

  • Theoretical derivation of entropy for LAMP models.
  • Comparison of LAMP model entropy with first-order Markov chains.

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  • Application of LAMP for entropy estimation on LastFM, BrightKite, Wikispeedia, and Reuters-21578 datasets.

    • Main Results:

    • The theoretical entropy rate of a LAMP model is equivalent to its underlying first-order Markov Chain.
    • LAMP models capture complex relationships with fewer parameters than higher-order models.
    • LAMP model entropy estimates were generally lower than alternatives, indicating better accommodation of structural dependencies.

    Conclusions:

    • LAMP models offer a computationally efficient and theoretically sound approach for modeling complex sequential data.
    • The equivalence of LAMP and first-order Markov chain entropy simplifies analysis.
    • LAMP provides more accurate entropy rate estimates for datasets with structural dependencies.