Graphical models are often employed to interpret patterns of correlations observed in data through a network of interactions between the variables. Recently, Ising/Potts models, also known as Markov random fields, have been productively applied to diverse problems in biology, including the prediction of structural contacts from protein sequence data and the description of neural activity patterns. However, inference of such models is a challenging computational problem that cannot be solved exactly. Here we describe the adaptive cluster expansion (ACE) method to quickly and accurately infer Ising or Potts models based on correlation data. ACE avoids overfitting by constructing a sparse network of interactions sufficient to reproduce the observed correlation data within the statistical error expected due to finite sampling. When convergence of the ACE algorithm is slow, we combine it with a Boltzmann Machine Learning algorithm (BML). We illustrate this method on a variety of biological and artificial data sets and compare it to state-of-the-art approximate methods such as Gaussian and pseudo-likelihood inference.We show that ACE accurately reproduces the true parameters of the underlying model when they are known, and yields accurate statistical descriptions of both biological and artificial data. Models inferred by ACE have substantially better statistical performance compared to those obtained from faster Gaussian and pseudo-likelihood methods, which only precisely recover the structure of the interaction network.
['John P. Barton', 'Eleonora De Leonardis', 'Alice Coucke', 'Simona Cocco']
ACE: adaptive cluster expansion for maximum entropy graphical model inference