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Free energy evaluation using marginalized annealed importance sampling.

Muneki Yasuda1, Chako Takahashi1

  • 1Graduate School of Science and Engineering, Yamagata University, Yonezawa, Yamagata 992-8510, Japan.

Physical Review. E
|September 16, 2022
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This study introduces marginalized annealed importance sampling (mAIS) to approximate free energy in stochastic models. The new method, marginalized AIS, offers improved statistical efficiency over standard annealed importance sampling (AIS) under specific conditions.

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Area of Science:

  • Physics
  • Machine Learning
  • Computational Statistics

Background:

  • Accurate free energy evaluation is crucial in physics and machine learning.
  • Exact free energy calculation is often computationally intractable due to the partition function.
  • Annealed importance sampling (AIS) offers an approximation method.

Purpose of the Study:

  • To propose a novel approach for free energy approximation.
  • To enhance the efficiency of existing annealed importance sampling methods.
  • To introduce marginalized annealed importance sampling (mAIS).

Main Methods:

  • Development of the marginalized annealed importance sampling (mAIS) algorithm.
  • Theoretical analysis of mAIS statistical efficiency.
  • Numerical investigation of mAIS performance.

Main Results:

  • mAIS is demonstrated to be a viable alternative to standard AIS.
  • The statistical efficiency of mAIS is rigorously analyzed.
  • mAIS proves more effective than AIS under certain conditions.

Conclusions:

  • mAIS provides a more statistically efficient method for free energy approximation.
  • The findings contribute to computational methods in physics and machine learning.
  • This research validates the effectiveness of marginalized AIS.