1Departments of Chemical Engineering and Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA2Ragon Institute of Massachusetts General Hospital, Massachusetts Institute of Technology and Harvard, Cambridge, MA 02139, USA3Laboratoire de Physique Statistique de L’Ecole Normale Supérieure, CNRS, Ecole Normale Supérieure & Université P.&M. Curie, Paris, France4Computational and Quantitative Biology, UPMC, UMR 7238, Sorbonne Université, Paris, France5Laboratoire de Physique Théorique de L’Ecole Normale Supérieure, CNRS, Ecole Normale Supérieure & Université P.&M. Curie, Paris, France
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Motivation: 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 datasets and compare it to state-of-the-art approximate methods such as Gaussian and pseudo-likelihood inference.Results: 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 more accurately describe the statistics of the data, including both the constrained low-order correlations and unconstrained higher-order correlations, compared to those obtained by faster Gaussian and pseudo-likelihood methods. These alternative approaches can recover the structure of the interaction network but typically not the correct strength of interactions, resulting in less accurate generative models.Availability and implementation: The ACE source code, user manual and tutorials with the example data and filtered correlations described herein are freely available on GitHub at https://github.com/johnbarton/ACE.Contacts:firstname.lastname@example.org, email@example.comSupplementary information: Supplementary data are available at Bioinformatics online.