Fig. 3. ACE outperforms plmDCA in recovering the single variable frequencies for models describing (a) ER005, (b) LP S<sub>B</sub>, (c) PF00014, (d) HIV.

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Fig. 3. ACE outperforms plmDCA in recovering the single variable frequencies for models describing (a) ER005, (b) LP S<sub>B</sub>, (c) PF00014, (d) HIV p7 and (e) cortical activity. The results for plmDCA are obtained with the regularization γ=0.01, which gives better results for the correlations than lower values of the regularization strength (see Supplementary Materials) From: ACE: adaptive cluster expansion for maximum entropy graphical model inference Bioinformatics. 2016;32(20):3089-3097. doi:10.1093/bioinformatics/btw328 Bioinformatics | © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 4. Fit for models describing (a) ER005, (b) LP S<sub>B</sub>, (c) PF00014, (d) HIV p7 and (e) cortical activity. ACE recovers the connected pair correlations cij(a,b)=pij(a,b)−pi(a)pj(b) (left). The inferred model also successfully captures higher order correlations present in the data, such as the connected three-body correlations (center) and the probability P(k) of observing a configuration with k differences from the consensus configuration (right) From: ACE: adaptive cluster expansion for maximum entropy graphical model inference Bioinformatics. 2016;32(20):3089-3097. doi:10.1093/bioinformatics/btw328 Bioinformatics | © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 6. (a) Contact map for PF00014 inferred by ACE Fig. 6. (a) Contact map for PF00014 inferred by ACE. Here, we show the top 100 predicted contacts, with true predictions in orange and false predictions in blue. Other contact residues in the crystal structure are shown in gray. For true positives and other contact residues, close contacts (<6Å) are darkly shaded and further contacts (<8Å) are lightly shaded. The upper and lower triangular parts of the contact map give predictions for the inferred model with strong regularization/no compression (γ = 1) and weak regularization/high compression (γ=2/B), respectively. (b) Precision (number of true predictions divided by the total number of predictions) as a function of the number of contact predictions for close contact residues that are widely separated on the protein backbone (i−j>4). Results using ACE compare favorably with those from DCA (Morcos et al., 2011) and are competitive with those from plmDCA (Ekeberg et al., 2014) (Color version of this figure is available at Bioinformatics online.) From: ACE: adaptive cluster expansion for maximum entropy graphical model inference Bioinformatics. 2016;32(20):3089-3097. doi:10.1093/bioinformatics/btw328 Bioinformatics | © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 1. Convergence of the cluster expansion as a function of the threshold t for (a) ER005, (b) LP S<sub>B</sub>, (c) PF00014, (d) HIV p7 and (e) cortical data. As the threshold is lowered, the cross-entropy S approaches a constant value. In all cases except for LP S<sub>B</sub> the normalized maximum error ϵmax reaches 1 through the cluster expansion alone. For LP S<sub>B</sub> a Monte Carlo learning procedure is used to refine the inferred parameters and reach ϵmax≃1 From: ACE: adaptive cluster expansion for maximum entropy graphical model inference Bioinformatics. 2016;32(20):3089-3097. doi:10.1093/bioinformatics/btw328 Bioinformatics | © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 2. ACE accurately recovers the true fields h (left) and couplings J (right) corresponding to Potts states with pi(a)≥0.05 for the ER05 model. Error bars denote standard deviation in estimated parameters due to finite sampling From: ACE: adaptive cluster expansion for maximum entropy graphical model inference Bioinformatics. 2016;32(20):3089-3097. doi:10.1093/bioinformatics/btw328 Bioinformatics | © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 5. Histograms of the data (MSA) and model (MC) energy distributions for (a) ER005, (b) LP S<sub>B</sub>, (c) PF00014, (d) HIV p7 and (e) cortical activity. Monte Carlo sampling of the inferred Potts model describing each set of data yields a distribution of energies similar to the empirical distribution, a further check on the consistency of the model fit beyond the fitting of correlations (Color version of this figure is available at Bioinformatics online.) From: ACE: adaptive cluster expansion for maximum entropy graphical model inference Bioinformatics. 2016;32(20):3089-3097. doi:10.1093/bioinformatics/btw328 Bioinformatics | © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com