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The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
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Resummed mean-field inference for strongly coupled data.

Hugo Jacquin1, A Rançon2

  • 1Laboratoire de Physique Statistique, École Normale Supérieure, UMR CNRS 8550, 24 rue Lhomond, 75005 Paris, France.

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We developed a new approximation method for inferring model parameters from noisy data. This robust technique improves upon existing methods and offers stable inference even with limited data.

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Area of Science:

  • Statistical Physics
  • Machine Learning
  • Computational Science

Background:

  • Accurate parameter inference is crucial for statistical models like the Ising and Potts models.
  • Traditional mean-field methods often struggle with noisy data and sampling instability.
  • Existing approaches based on small correlation expansions or Bethe free energy lack robustness.

Purpose of the Study:

  • To introduce a novel, resummed mean-field approximation for robust parameter inference.
  • To enhance the stability and accuracy of inference from noisy correlation functions.
  • To provide a computationally efficient and analytically tractable inference method.

Main Methods:

  • Resummed mean-field approximation based on log-likelihood expansion diagrams.
  • Iterative algorithm involving matrix operations for N auxiliary variables.
  • Testing on the Sherrington-Kirkpatrick model under external fields and couplings.

Main Results:

  • The proposed method outperforms standard and regularized mean-field inference.
  • Inference remains stable against sampling noise, unlike previous methods.
  • The algorithm demonstrates stability across the entire phase diagram of the tested model.
  • Consistent estimation of data entropy and generation of artificial data.

Conclusions:

  • The resummed mean-field approximation offers a stable and efficient approach for parameter inference.
  • This method overcomes limitations of prior techniques in handling noisy data.
  • The approach facilitates accurate model parameter estimation and data generation for complex systems.