ACE: adaptive cluster expansion for maximum entropy graphical model inference.

Area of Science:

• Computational biology
• Statistical physics
• Machine learning

Background:

• Graphical models, including Ising/Potts models (Markov random fields), are vital for interpreting correlations in biological data, such as protein structure prediction and neural activity.
• Exact inference of these models is computationally intractable, necessitating accurate approximation methods.

Purpose of the Study:

• To introduce the adaptive cluster expansion (ACE) method for rapid and precise inference of Ising or Potts models from correlation data.
• To address overfitting by constructing sparse interaction networks that accurately reproduce observed correlations within statistical error.

Main Methods:

• Adaptive Cluster Expansion (ACE) algorithm for model inference.
• Combination of ACE with Boltzmann Machine Learning (BML) for slow convergence cases.
• Comparison with Gaussian and pseudo-likelihood inference methods on biological and artificial datasets.

Main Results:

• ACE accurately reconstructs known model parameters and provides superior statistical descriptions of biological and artificial data.
• ACE-inferred models better capture both low- and higher-order correlations compared to faster approximate methods.
• Alternative methods (Gaussian, pseudo-likelihood) identify network structure but often fail to accurately estimate interaction strengths.

Conclusions:

• ACE offers a significant improvement over existing approximate inference methods for Ising/Potts models.
• The method's accuracy in parameter estimation leads to more reliable generative models for complex biological systems.
• ACE provides a robust tool for analyzing correlation data in diverse scientific domains.