Figure 5. The dependence of the KL divergences and the normalized distance measure, .

Data was generated from a third order model, as explained in the section “Generating synthetic data” (Methods), and fit to pairwise maximum entropy models and independent models. All data points correspond to averages over marginalizations of the true distribution (see text for details). The red points were computed directly using Eqs. (1), (3) and (4); the blue points are the zeroth order estimates, , , and , in rows 1, 2 and 3, respectively. The three columns correspond to , 0.029, and 0.037, from left to right. (A, B, C) (). Predictions from the perturbative expansion are in good agreement with the measurements up to , indicating that the data is in the perturbative regime. (D, E, F) (). Predictions from the perturbative expansion are in good agreement with the measurements up to , indicating that the data is only partially in the perturbative regime. (G, H, I) (). Predictions from the perturbative expansion are not in good agreement with the measurements, even for small , indicating that the data is outside the perturbative regime.