Adaptive and self-averaging Thouless-Anderson-Palmer mean-field theory for probabilistic modeling

Area of Science:

• Statistical Physics
• Machine Learning
• Computational Science

Background:

• The Thouless-Anderson-Palmer (TAP) mean-field approach is a cornerstone in disorder physics.
• Conventional TAP methods require knowledge of the distribution of couplings between random variables.
• Applying TAP to real-world probabilistic models with concrete coupling sets remains a challenge.

Purpose of the Study:

• To generalize the TAP mean-field approach for broader applicability.
• To develop a method that adapts to concrete sets of couplings, rather than requiring distribution knowledge.
• To enhance the accuracy of approximate average computations in probabilistic models for real data.

Main Methods:

• Generalization of the Thouless-Anderson-Palmer (TAP) mean-field theory.
• Adaptation of the method to work with specific, given sets of couplings.
• Validation through theoretical analysis on toy models and simulations on real data models.

Main Results:

• The generalized approach reproduces established replica symmetric results for toy models in the thermodynamic limit.
• Simulations on a real data model show improved prediction accuracy compared to conventional TAP methods.
• The method demonstrates applicability to probabilistic models utilizing real-world data.

Conclusions:

• The generalized TAP approach offers a more practical and accurate tool for analyzing probabilistic models with real data.
• This work extends the utility of mean-field techniques in disorder physics to applied computational problems.
• The developed method provides a significant improvement over existing TAP techniques for real-world applications.