Persistent contrastive divergence permits the inference of high-quality models.

A and B Comparing single amino acid frequencies (left), pairwise amino acid frequencies (center) and covariances (right) computed from natural sequences (Pfam alignment) and from Markov chain Monte Carlo (MCMC) samples generated from Markov random field (MRF) models trained with either pseudo-likelihood maximization (A) or persistent contrastive divergence (PCD) (B) for protein 1bkrA in the PSICOV dataset. C Mean precision of contacts, predicted as (APC corrected) L2 norm of pair couplings of a MRF trained with either pseudo-likelihood maximization or PCD. D Distribution of run times in minutes when learning MRF models with CCMpredPy (run on 4 cores). The median runtime in minutes with pseudo-likelihood is 7 minutes and with PCD is 43.5 minutes. Dashed line in boxplots represents the mean, solid line represents the median of the distribution. C and D are computed over the 150 proteins in the PSICOV dataset.