Comparison of the generalization performances of three predictors. Top row: linear method. Middle row: linear method with a non-linear pre-processing. Bottom row: random forest. All results are computed on the Horsehead pillar, i.e., the test set. Left column: joint Probability Distribution Function (PDF) of the predicted column density and of the observed one. The contours are the PDF isocontours enclosing 25, 50, and 75% of the datapoints. Points whose density falls below these values are shown as black dots. The oblique lines have a slope of 1. They indicates ratio values of 1.0 (plain), 0.5 and 2.0 (dashed), 0.1 and 10.0 (dotted). Right column: histogram of the ratio of the predicted column density over the observed one on a logarithmic scale. The dotted lines show the Gaussian of same mean and width.