Training and cross-validating a model

The purpose of this vignette is to show how to train and cross-validate SDeMo models.

using SpeciesDistributionToolkit
using CairoMakie
using PrettyTables

We will work on the demo data:

X, y, C = SDeMo.__demodata()

([14.25 9.85 10.05 11.85 10.45 15.25 10.65 9.75 9.65 10.65 9.65 11.85 11.65 8.55 15.85 11.35 9.25 8.15 10.85 11.55 10.55 10.95 11.35 10.85 11.35 9.45 8.75 8.55 8.55 10.25 13.15 9.05 9.25 10.85 12.55 16.65 10.15 9.65 10.35 10.05 8.15 7.05 7.85 9.75 10.35 9.25 8.75 10.15 10.25 8.45 6.25 6.25 8.65 9.95 10.85 12.25 12.65 12.05 8.65 9.55 9.65 8.85 6.55 10.85 8.25 8.55 9.15 8.95 7.25 7.75 13.55 14.75 12.45 11.05 8.95 10.05 8.95 9.35 7.25 12.05 10.55 10.15 8.65 10.25 10.65 8.25 8.95 8.15 6.55 11.85 9.75 8.75 14.15 9.85 10.45 9.15 8.85 10.95 7.95 7.55 7.65 8.15 4.45 9.45 9.15 11.85 8.45 9.35 7.85 7.75 8.65 8.75 7.25 5.65 7.05 9.25 10.05 8.15 11.35 8.05 10.45 12.55 7.75 8.65 8.95 8.25 9.15 8.95 6.95 6.05 7.35 6.95 9.55 8.95 12.45 11.65 15.25 9.05 9.05 9.55 8.85 9.45 8.95 7.05 7.65 8.45 7.95 7.55 9.55 8.75 10.55 8.45 9.75 9.75 10.05 9.15 7.45 6.45 8.35 9.05 8.15 6.95 4.55 6.15 5.45 9.95 8.65 10.95 7.65 9.35 10.15 10.25 9.45 8.45 7.25 9.15 6.65 7.45 7.45 5.85 14.85 9.15 11.25 9.95 8.15 9.15 10.05 10.55 9.15 7.85 9.55 7.25 8.65 7.95 7.25 7.55 7.65 6.75 9.55 10.55 5.35 7.15 8.75 9.85 10.45 9.75 8.55 9.95 6.55 8.75 9.55 8.25 8.35 8.55 7.35 8.55 8.35 9.85 8.35 8.35 9.45 10.05 10.75 9.95 1.25 7.55 9.85 9.35 9.25 9.55 7.75 6.05 9.05 8.05 9.55 8.25 14.65 9.45 10.55 8.55 8.15 7.55 8.75 9.35 10.55 10.95 10.55 6.25 7.35 8.85 9.95 10.05 8.35 9.95 8.15 7.25 9.95 8.75 12.45 12.25 9.65 6.85 7.85 8.35 10.45 11.15 10.65 10.45 7.85 9.25 10.15 9.55 7.15 9.95 9.45 7.75 10.45 9.95 10.55 11.25 9.55 11.35 10.75 8.85 10.35 9.55 10.55 11.15 16.05 12.25 10.15 9.45 10.55 7.65 11.55 8.45 10.75 10.35 13.35 12.45 8.85 9.55 10.95 6.15 7.55 9.35 11.25 10.05 9.65 10.55 11.25 12.35 8.45 8.55 10.55 7.35 5.15 6.65 8.15 9.65 11.65 8.75 11.15 12.25 9.65 11.35 12.55 12.05 8.95 7.65 9.95 9.15 6.85 6.05 8.35 9.95 11.65 10.75 11.35 12.95 9.95 12.25 12.45 11.35 8.75 7.15 9.05 9.15 3.95 7.05 8.65 10.55 7.05 11.75 8.15 12.45 10.65 11.65 11.55 11.25 12.25 10.55 9.55 7.45 8.35 5.35 5.95 8.15 9.05 10.75 12.45 12.15 11.95 7.15 8.55 7.15 9.05 9.65 13.15 8.85 5.95 6.45 7.75 8.05 9.05 9.75 10.75 11.65 13.35 12.05 12.95 5.95 7.15 7.95 5.75 7.45 8.35 8.95 10.95 13.25 8.65 6.55 7.55 9.25 7.35 8.85 10.75 12.35 11.25 5.75 1.55 7.65 9.35 8.15 6.45 7.15 7.95 7.25 7.75 10.45 9.35 9.05 6.85 6.25 13.25 9.25 8.35 3.25 9.75 10.05 6.75 8.85 9.85 8.45 7.55 7.75 9.65 8.85 10.45 8.95 7.45 9.15 8.05 6.05 4.85 9.05 9.95 10.65 8.25 6.55 8.55 9.85 8.15 7.55 6.75 6.55 8.15 7.75 9.45 7.45 13.55 11.85 8.45 5.85 4.05 9.25 7.65 11.15 7.75 8.25 10.65 8.85 6.65 6.85 7.85 8.75 5.85 8.05 9.95 8.75 10.85 11.25 10.45 10.15 8.05 10.75 9.95 10.05 9.35 11.85 10.95 8.05 10.85 13.95 10.85 7.95 8.65 10.65 7.45 9.75 10.05 2.95 10.95 12.55 12.55 7.85 6.55 6.75 8.85 8.75 8.55 6.65 8.05 8.65 10.95 10.85 7.75 12.65 11.15 8.55 8.75 7.95 8.35 9.95 9.05 10.45 9.75 6.95 13.05 12.95 11.45 10.05 5.05 9.65 10.55 10.45 11.65 8.55 7.85 12.45 12.65 12.95 12.65 16.25 9.25 10.95 8.85 11.95 13.45 13.85 6.95 7.25 6.65 9.65 10.05 11.45 8.75 14.15 13.35 7.35 6.85 8.15 8.25 6.45 7.35 8.35 8.65 11.15 12.45 13.35 10.25 7.85 6.95 8.85 9.75 7.45 8.15 8.45 9.65 10.85 11.25 12.15 13.15 12.25 15.75 10.95 10.85 12.35 12.65 6.75 7.75 8.15 8.25 9.45 9.45 9.55 8.05 7.75 8.95 11.45 12.95 14.15 12.95 14.05 12.05 10.55 11.15 12.45 10.55 10.15 8.45 10.45 10.55 8.75 9.55 8.55 8.95 8.95 12.55 12.85 16.55 11.45 10.55 12.25 9.95 9.35 9.05 8.95 8.75 10.65 11.25 10.85 10.35 10.15 9.85 8.15 11.85 14.35 11.45 11.85 11.95 11.55 11.55 10.85 8.95 9.15 10.15 9.55 7.65 7.75 7.95 7.65 9.25 10.35 10.85 11.15 10.95 9.45 8.65 9.85 10.35 13.45 16.35 11.85 11.45 10.75 11.35 10.55 9.95 7.55 8.65 8.65 8.85 9.75 9.25 12.55 12.45 12.55 8.35 9.05 10.45 11.75 14.25 10.45 9.85 9.85 10.05 9.85 7.15 7.35 8.55 7.75 11.95 12.15 10.15 9.05 7.55 8.95 10.65 13.15 9.95 9.45 9.35 9.55 10.15 11.05 6.35 6.95 7.75 8.35 9.55 9.75 11.65 9.75 10.45 10.95 11.65 8.75 9.25 8.85 7.15 8.75 8.55 10.35 12.25 13.65 10.55 11.65 12.45 9.55 9.45 7.65 7.65 8.65 9.25 8.85 8.65 10.75 11.75 16.75 13.85 9.05 8.35 9.25 9.35 9.45 9.35 9.05 10.95 11.15 11.15 9.25 10.05 11.85 14.55 12.45 10.25 12.05 11.65 11.15 11.85 13.75 13.65 13.25 12.95 12.15 12.25 13.55 16.55 12.55 9.35 10.15 13.35 14.15 7.35 13.05 14.65 8.05 12.95 10.65 13.15 11.75 16.55 16.55 16.05 15.75 16.15 16.35 15.95 14.95 16.45 16.05 15.85 15.05 16.05 15.65 16.35 16.55 15.75 16.15 15.95 13.75 15.55 15.95 15.75 16.45 15.65 14.55 14.15 15.05 14.25 16.45 16.75 15.05 15.25 14.55 16.25 16.45 16.15 15.75 15.05 15.85 16.65 15.85 14.85 15.25 15.95 15.45 13.65 14.45 15.45 16.25 15.95 14.95 15.65 15.85 16.05 15.85 16.25 14.95 16.35 14.05 14.45 15.45 16.15 16.65 14.35 14.65 14.75 14.95 15.35 16.35 16.45 16.15 15.65 14.95 15.35 15.45 15.05 16.65 16.45 14.95 13.65 15.05 15.25 15.95 16.05 16.55 13.95 16.05 15.55 15.85 16.35 14.25 16.55 14.55 15.25 16.65 16.55 14.15 14.75 16.15 14.65 10.55 14.45 16.65 15.15 16.55 16.05 15.45 14.55 11.15 11.05 14.05 16.55 15.35 16.35 15.45 16.45 16.25 15.95 15.85 16.55 12.45 15.75 11.25 16.65 16.35 16.65 13.75 15.45 16.35 16.15 16.55 16.25 12.65 15.45 16.45 13.85 15.05 14.65 15.95 13.95 15.25 16.75 16.35 15.65 14.25 16.85 16.45 16.35 16.65 16.05 13.95 16.55 14.25 16.35 16.05 15.05 16.55 16.55 15.75 14.65 16.15 16.25 16.45 13.65 16.75 16.05 14.65 14.95 16.55 15.45 13.65 14.85 16.15 16.15 15.85 14.75 16.05 15.65 16.65 16.15 15.35 15.05 16.55 16.45 16.55 16.25 15.55 15.45 15.15 14.95 16.05 15.55 13.25 14.15 15.25 13.65 15.85 16.25 14.35 15.45 15.95 14.95 14.55 16.15 16.35 15.65 12.15 13.45 16.35 15.25 14.45 16.25 15.55 14.35 15.65 15.85 14.85 14.55 11.25 11.35 15.85 11.15 15.95 15.05 15.55 14.35 14.45 12.85 14.95 15.65 15.15 13.05 15.45 15.85 14.95 16.05 15.65 14.45 13.35 16.35 13.35 12.55 12.55 15.25 13.95 13.35 10.55 12.55 11.95 15.95 14.25 15.65 14.95 16.05 13.35 11.75 14.15 15.95 11.45 14.15 16.35 16.35 16.25 16.25 12.95 15.15 16.85 14.45 13.65 14.95 14.15 16.65 15.35 14.65 15.55 14.55 10.65 13.05 5.15 16.45 14.15 15.75 16.05 13.75 14.45 12.45 16.45 15.75 13.65 12.25 12.55 16.85 14.45 15.45 12.45 15.45 16.45 15.45 15.65 10.55 11.65 8.85 11.95 10.85 12.45 14.95 15.15 15.65 9.35 13.15 10.75 11.85 13.25 14.15 14.15 13.35 9.85 12.05 12.55 15.55 16.55 12.85 12.95 12.35 10.75 11.45 12.85 16.65 15.15 12.45 12.25 12.55 16.55 16.35 5.95 12.95 16.55 16.65 11.95 10.45 11.95 13.05 15.85 16.45 16.15 16.15 15.85 8.75 14.75 14.15 15.75 15.35 15.85 13.15 8.05 7.65 14.75 13.95 16.05 15.65 16.15 16.45 12.35 7.45 9.25 15.05 15.15 15.25 15.05 9.75 15.55 13.75 14.75 10.35 13.25 15.55 14.85 15.85 16.25 13.35 13.65 14.55 15.15 14.95 13.35 15.45 16.45 16.15 7.75 15.65 16.05 16.35 6.45 16.15 16.45 8.35 15.25 9.95 12.45 15.65 16.75 11.95 15.45 14.05 15.75 7.15 14.95 14.75 12.85 11.25 15.85 16.55 14.15 10.15 9.25 16.25 15.85 16.25 16.15 16.75 11.25 8.05 15.55 16.05 16.55 13.95 14.05 13.95 14.05 15.35 16.75 12.95 9.65 11.55 10.05 16.45 13.15 13.05 12.75 9.65 16.25 13.05 12.45 9.85 13.35 14.75 11.35 15.15 16.85 16.65 14.85 13.25 14.05 13.55 16.55 16.65 12.85 15.85 11.95 12.45 15.75 16.45 15.65 13.55 14.05 13.85 16.45 16.75 16.25 15.55 12.15 16.35 16.25 16.65 16.15 14.05 9.55 15.65 16.95 13.95 15.35 14.55 9.95 9.25 15.45 16.25 10.85 10.05 12.25 15.65 15.35 16.95 14.55 15.55 15.95 15.95 15.35 14.15 14.85 14.95 16.65 15.25 15.05 15.75 16.05 12.65 12.45 13.45 9.45 11.55 15.55 16.25 16.25 15.65 16.15 14.55 15.25 16.35 16.15 15.05 16.15 14.45 14.05 15.55 16.15 14.95 14.25 12.35 15.95 14.95 16.25 16.55 16.85 15.75 15.35 16.65 14.35 13.75 12.25 14.55 15.35 15.05 12.85 15.25 12.55 16.15 17.05 16.05 16.45 16.55 16.35 14.75 14.35 12.95 11.65 13.85 15.05 15.25 15.65 17.05 16.65 11.55 15.45 12.45 15.25 16.75 16.85 16.55 16.85 16.55 16.25 12.35 14.75 11.65 12.15 11.05 9.85 11.15 11.45 12.15 13.65 14.65 14.55 16.45 16.95 16.95 16.45 14.65 12.55 11.75 12.55 16.95 16.95 16.95 16.85 16.75 16.15 16.15 15.55 13.45 13.55 11.15 12.25 15.75 15.55 17.05 16.85 16.75 16.35 16.45 16.25 14.35 13.05 13.25 15.35 12.75 14.55 16.45 16.95 16.85 16.45 16.25 16.25 16.15 14.85 14.95 13.25 10.95 15.75 14.35 16.05 13.55 11.75 10.65 12.15 13.65 15.55 15.55 15.85 16.25 16.85 15.55 10.15 16.15 16.35 16.35 16.45 11.35 14.65 16.65 16.55 16.55 11.95 16.35 16.55 12.35 15.85 16.65 16.65 16.55 16.65 16.05 14.05 15.45 15.65 16.15 16.45 16.15 15.45 12.05 16.55 16.65 16.35 15.95 16.05 16.55 16.85 16.85 16.65 15.95 15.75 11.05 15.35 13.25 16.25 16.85 15.95 14.35 12.35 15.75 16.45 16.25 15.55 16.25 15.85 15.05 14.15 16.25 16.45 12.85 15.35 15.85 16.35 16.55 16.65 16.85 14.75 15.05 15.95 16.35 16.45 16.65 16.65 16.65 16.65 16.05 15.65 15.95 16.25 16.55 16.55 16.65 16.65 16.65 16.35 16.25 16.25 15.95 16.25 16.55 16.65 16.65 16.65 16.65 16.85 16.55 16.55 16.55 16.85 16.55 16.35 16.55 16.45 16.65 16.65 16.65 16.65 16.65 16.55 16.65; 3.4 4.4 4.5 4.6 4.7 5.1 5.5 5.6 5.6 5.7 5.7 5.8 6.0 6.1 5.6 6.2 6.2 6.2 6.2 6.0 5.9 6.2 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.2 6.1 6.1 6.1 6.0 5.1 6.3 6.4 6.4 6.4 6.4 6.4 6.5 6.4 6.4 6.5 6.6 6.5 6.6 6.6 6.6 6.6 6.6 6.6 6.4 6.2 5.8 6.4 6.7 6.7 6.7 6.7 6.7 6.6 6.8 6.8 6.8 6.8 6.8 6.8 6.4 6.0 6.5 6.6 6.7 6.7 6.9 6.9 6.9 6.3 6.8 6.8 6.8 6.8 7.1 7.1 7.1 7.0 7.1 6.6 6.5 6.5 5.6 6.6 6.9 7.0 7.0 7.0 7.2 7.2 7.2 7.1 7.1 7.1 6.5 6.9 7.1 7.2 7.3 7.3 7.3 7.3 7.3 7.2 6.9 6.9 6.7 6.7 7.1 7.3 7.3 7.3 7.4 7.4 7.4 7.4 7.4 7.4 7.4 7.4 7.3 7.3 7.0 6.8 6.4 7.2 7.3 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.4 7.4 6.9 7.6 7.6 7.6 7.6 7.7 7.6 7.6 7.6 7.6 7.6 7.5 7.5 7.5 7.5 7.4 7.4 7.3 7.8 7.7 7.8 7.8 7.7 7.7 7.7 7.7 7.7 7.7 7.6 7.6 7.5 7.4 7.4 7.8 7.9 7.9 7.9 7.9 7.8 7.8 7.8 7.8 7.8 7.8 7.5 7.5 7.5 7.4 7.4 6.9 6.9 8.0 8.1 8.0 8.0 8.0 7.9 7.9 7.9 7.8 7.8 7.6 7.6 7.6 7.5 7.5 7.4 7.4 7.0 6.9 8.2 8.2 8.1 8.1 8.0 8.0 8.0 7.8 7.7 7.7 7.6 7.6 7.5 7.5 7.4 7.2 7.1 7.0 6.9 8.3 8.3 8.3 8.3 8.3 8.1 8.1 8.1 8.1 8.1 8.1 7.8 7.8 7.7 7.7 7.6 7.6 7.3 7.3 7.2 7.1 7.0 8.4 8.4 8.4 8.2 8.2 8.2 8.2 8.2 8.2 8.1 7.9 7.8 7.8 7.7 7.7 7.4 7.3 7.2 7.1 8.5 8.5 8.5 8.2 8.2 8.2 7.9 7.8 7.5 7.4 7.2 6.2 8.6 8.6 8.6 8.6 8.4 8.3 7.9 7.9 7.1 9.1 8.7 8.7 8.7 8.7 8.5 8.4 8.4 8.4 8.3 8.0 7.5 7.4 9.0 8.8 8.8 8.7 8.6 8.6 8.5 8.5 8.5 8.4 8.1 8.0 7.5 9.0 9.0 9.0 9.0 8.9 8.9 8.8 8.8 8.8 8.6 8.6 8.6 8.0 8.0 7.6 7.5 9.1 9.1 8.9 8.9 8.9 8.9 8.9 8.9 8.9 8.7 8.6 8.5 8.3 8.0 7.7 7.5 9.2 9.2 9.1 9.1 9.0 9.0 9.0 9.0 9.0 8.9 8.9 8.7 8.3 8.2 8.1 7.6 7.4 8.9 8.8 8.8 8.7 8.4 8.2 9.1 9.1 9.0 9.0 8.9 8.9 8.8 8.4 8.3 8.2 8.1 7.7 9.1 9.0 9.0 9.0 8.9 8.9 8.9 8.3 8.3 9.1 9.0 9.0 9.0 8.9 8.9 8.9 8.8 8.8 8.7 9.2 9.1 9.1 9.1 9.1 9.1 9.1 9.0 9.0 8.9 8.8 8.8 8.8 8.7 8.4 9.3 9.3 9.3 9.2 9.2 9.1 9.1 9.1 9.1 9.1 9.0 9.0 9.0 8.9 8.8 8.8 9.3 9.3 9.3 9.3 9.3 9.2 9.2 9.2 9.2 9.2 9.2 9.1 9.1 9.1 9.1 9.1 9.0 8.9 8.9 8.6 8.2 9.3 9.3 9.4 9.4 9.3 9.3 9.2 9.2 9.2 9.2 9.1 9.1 9.1 8.9 8.9 9.3 9.4 9.4 9.3 9.3 9.2 9.2 9.0 8.4 4.8 9.3 9.4 9.3 9.3 9.0 5.0 6.9 9.5 9.3 9.4 9.4 9.5 9.5 9.4 9.4 9.4 9.4 9.3 9.3 9.3 9.3 9.2 9.2 9.2 9.2 9.4 9.4 9.4 9.5 9.5 9.4 9.4 9.4 9.3 9.3 9.3 9.2 9.2 9.4 9.4 9.5 9.4 9.4 9.4 9.4 9.2 9.4 9.4 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 3.2 9.3 9.4 9.5 9.5 9.5 9.5 9.2 9.2 9.3 9.3 9.4 9.5 9.5 9.5 7.5 9.0 9.1 9.1 9.2 9.2 9.3 9.3 9.4 9.4 9.5 4.9 6.8 8.9 9.0 9.1 9.1 9.2 9.3 9.3 9.4 9.4 9.4 9.4 9.4 9.5 2.6 6.7 7.3 9.1 9.2 9.4 8.9 8.9 8.9 9.0 9.2 9.3 9.3 9.3 9.3 9.3 9.4 9.5 9.6 9.4 7.5 7.2 7.5 9.2 8.8 8.8 8.9 8.9 9.0 9.2 9.2 9.2 9.3 9.3 9.4 9.5 2.5 6.9 7.2 9.0 8.8 8.7 8.8 8.8 8.8 8.9 8.9 9.1 9.2 9.2 9.2 9.3 9.4 9.5 7.4 8.4 8.9 9.0 9.1 9.2 9.2 8.8 8.7 8.7 8.7 8.7 8.7 8.7 8.8 8.8 8.8 8.8 9.1 9.2 9.3 9.3 9.4 9.4 4.8 7.3 7.6 8.5 8.9 9.0 9.2 9.2 9.2 8.7 8.8 8.8 8.8 8.9 9.0 9.0 9.3 9.3 9.3 9.4 9.4 8.1 9.0 9.0 9.1 9.1 8.7 8.7 8.7 8.8 9.0 9.1 9.1 9.2 9.2 9.3 9.3 9.3 8.3 8.9 9.0 9.0 9.1 9.1 8.6 8.7 9.1 9.1 9.2 9.2 9.3 8.9 9.0 9.0 9.1 9.0 8.5 8.6 8.6 9.0 9.1 9.1 9.2 9.2 8.9 9.0 9.0 8.9 8.5 8.5 8.5 8.6 8.6 9.0 9.0 9.0 9.1 4.7 8.9 8.8 8.4 8.5 8.6 8.8 8.9 8.9 9.0 8.7 8.3 8.4 8.5 8.9 7.7 8.0 8.7 8.4 8.6 8.5 8.5 8.1 8.4 8.4 8.4 8.4 8.4 8.5 4.6 8.2 8.2 8.0 8.0 8.2 8.1 8.2 8.2 7.9 6.4 7.7 6.9 5.9 2.4 2.6 2.7 2.8 2.1 2.7 2.9 3.1 2.2 3.0 3.2 2.9 3.0 3.2 3.3 2.2 2.3 3.2 3.5 3.5 3.4 3.4 3.4 2.4 2.4 3.2 3.7 3.7 3.9 3.8 3.7 4.0 4.0 2.5 2.6 2.6 3.3 3.3 4.1 4.1 4.0 2.6 2.6 2.8 3.4 4.3 4.3 4.2 2.7 2.8 2.9 4.4 4.2 2.8 4.5 4.3 2.9 2.9 3.7 4.7 4.6 4.3 2.9 3.1 3.0 4.8 4.8 4.8 4.4 3.0 3.1 3.0 3.1 3.2 4.1 4.6 4.6 3.1 3.3 3.9 5.0 5.0 3.3 3.4 3.4 3.3 5.0 4.9 4.9 3.4 3.5 5.1 3.5 3.6 3.6 3.6 3.5 4.7 3.8 3.8 4.5 5.4 5.3 4.7 3.9 3.9 3.8 4.4 5.1 5.4 5.4 4.1 3.9 4.2 4.7 5.6 5.1 3.9 4.2 4.3 4.2 4.3 4.8 5.7 2.4 2.7 2.9 4.5 4.5 4.5 4.5 4.4 4.3 4.4 4.6 4.3 4.7 4.7 4.7 4.5 5.5 6.0 2.3 2.5 2.8 4.9 4.7 2.3 2.4 4.6 4.9 5.1 4.9 5.0 2.4 2.6 3.4 4.8 4.9 5.1 5.2 5.1 5.1 5.1 5.7 2.3 2.6 3.5 3.6 5.0 5.4 5.5 5.5 5.3 5.7 3.0 3.8 5.6 5.6 2.5 5.8 5.8 5.8 2.4 2.5 2.6 2.8 3.1 3.4 3.6 3.9 4.2 6.1 6.2 6.2 6.2 6.5 6.2 2.9 4.1 4.5 5.8 5.9 6.1 6.5 6.5 6.6 6.7 6.5 2.7 6.1 6.4 6.8 6.9 6.9 6.7 3.1 4.4 6.3 7.1 7.1 6.9 7.4 3.2 4.9 7.1 7.4 7.1 7.3 5.4 3.0 4.3 7.5 3.0 3.6 4.4 5.5 6.1 7.7 6.5 6.9 7.4 7.7 7.9 8.3 8.4 8.3 8.1 8.1 8.1 3.2 4.9 5.4 6.7 7.5 7.8 8.6 5.1 6.5 8.8 8.5 5.3 3.5 3.7 6.4 8.4 9.0 5.2 3.0 9.0 9.2 8.8 5.5 2.9 3.0 6.1 8.1 9.1 8.8 8.3 2.4 3.3 3.9 4.1 5.3 5.8 8.9 2.6 4.8 5.9 9.3 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5.05 5.95 6.25 5.55 6.45 6.25 4.35 3.55 4.75 4.35 6.95 6.45 9.85 8.95 12.45 6.45 6.35 6.75 6.15 6.75 6.15 4.35 4.95 5.75 5.35 5.05 6.85 6.05 7.85 5.75 6.95 7.05 7.25 6.35 4.75 3.85 5.65 6.25 5.45 4.35 2.05 3.55 2.85 7.25 5.95 8.15 4.95 6.65 7.35 7.45 6.75 5.75 4.55 6.45 4.05 4.85 4.85 3.25 11.95 6.45 8.35 7.15 5.45 6.35 7.25 7.75 6.35 5.15 6.75 4.55 5.95 5.35 4.65 4.95 5.15 4.35 6.75 7.75 2.75 4.45 5.95 7.05 7.65 6.95 5.85 7.15 3.95 6.05 6.85 5.55 5.65 5.85 4.75 6.05 5.85 7.05 5.55 5.55 6.65 7.15 7.95 7.05 -1.25 4.85 7.05 6.65 6.55 6.75 5.05 3.55 6.45 5.45 6.95 5.75 11.65 6.65 7.65 5.75 5.35 4.85 5.95 6.45 7.65 8.05 7.75 3.55 4.65 6.15 7.15 7.25 5.65 7.35 5.55 4.65 7.35 6.25 9.65 9.25 6.75 4.15 5.05 5.55 7.55 8.25 7.75 7.55 5.15 6.45 7.35 6.85 4.45 7.25 6.85 5.25 7.75 7.05 7.65 8.25 6.75 8.45 7.85 6.15 7.55 6.85 7.85 8.45 13.45 9.25 7.25 6.55 7.55 4.85 8.55 5.75 7.85 7.75 10.55 9.35 5.95 6.65 7.95 3.45 4.75 6.45 8.25 7.15 6.85 7.85 8.55 9.45 5.55 5.65 7.55 4.55 2.45 3.85 5.25 6.75 8.65 5.95 8.35 9.45 6.95 8.45 9.55 9.15 6.05 4.75 6.95 6.25 4.05 3.25 5.45 6.95 8.75 7.85 8.55 10.15 7.05 9.25 9.35 8.25 5.75 4.25 6.15 6.25 1.25 4.25 5.75 7.55 4.35 8.85 5.45 9.65 7.75 8.65 8.55 8.25 9.15 7.55 6.55 4.55 5.45 2.55 3.15 5.25 6.15 7.85 9.45 9.35 9.25 4.25 5.65 4.35 6.15 6.85 10.15 5.85 3.15 3.65 4.85 5.15 6.15 6.75 7.85 8.75 10.35 9.15 10.15 3.15 4.25 5.05 3.05 4.55 5.45 6.05 8.05 10.25 5.65 3.65 4.65 6.25 4.55 5.95 7.75 9.25 8.15 3.05 -1.05 4.75 6.35 5.15 3.55 4.25 5.05 4.35 4.85 7.35 6.45 6.15 4.05 3.45 10.25 6.35 5.55 0.55 6.65 6.95 3.95 5.85 6.75 5.45 4.65 4.85 6.65 5.95 7.35 6.05 4.55 6.15 5.05 3.25 2.15 6.05 6.85 7.55 5.25 3.65 5.55 6.75 5.25 4.65 3.85 3.75 5.25 4.85 6.45 4.65 10.45 8.95 5.55 3.15 1.35 6.25 4.75 8.05 4.85 5.25 7.55 5.85 3.75 3.95 4.95 5.85 3.15 5.25 6.85 5.75 7.75 8.15 7.35 7.15 5.25 7.85 8.05 7.05 6.25 8.65 7.85 5.15 8.85 11.55 8.05 5.15 5.75 7.55 4.55 6.65 6.95 0.35 7.85 9.35 9.35 4.85 3.75 3.85 5.95 5.85 5.65 3.95 5.15 5.65 7.85 7.75 4.85 9.45 8.05 5.55 5.75 5.05 5.45 7.05 6.25 7.45 6.65 4.05 9.75 9.75 8.25 7.05 2.45 6.65 7.45 7.35 8.45 5.55 4.85 9.25 9.45 9.75 9.35 14.65 6.35 7.85 5.75 8.75 10.15 10.55 4.15 4.45 3.85 6.65 7.05 8.25 5.65 10.85 10.75 4.65 4.15 5.35 5.45 3.65 4.55 5.45 5.75 8.05 9.25 11.35 7.95 5.15 4.25 6.05 6.85 4.65 5.25 5.55 6.65 7.75 8.15 8.95 9.95 9.05 14.25 8.55 8.35 9.45 9.75 4.05 5.05 5.45 5.45 6.55 6.55 6.65 5.25 4.85 6.05 8.35 9.75 10.75 9.65 10.75 9.35 8.15 8.65 9.55 7.65 7.35 5.75 7.55 7.65 5.85 6.65 5.75 6.05 6.05 9.35 9.55 15.15 8.95 8.05 9.35 7.25 6.65 6.35 6.25 5.95 7.75 8.35 7.85 7.35 7.25 6.95 5.25 8.75 11.05 8.95 9.05 9.05 8.75 8.65 8.05 6.25 6.45 7.45 6.75 4.95 5.05 5.35 5.05 6.55 7.55 7.95 8.25 7.95 6.55 5.75 6.85 7.35 10.25 14.25 9.35 8.85 8.05 8.55 7.75 7.15 4.85 5.95 5.95 6.15 6.95 6.45 9.45 9.35 9.45 5.55 6.15 7.45 8.65 10.95 7.85 7.05 7.15 7.25 7.05 4.55 4.75 5.85 5.15 8.95 9.15 7.25 6.15 4.75 6.05 7.65 9.95 7.35 6.75 6.55 6.75 7.35 8.25 3.85 4.35 4.95 5.55 6.65 6.85 8.65 7.05 7.65 8.15 8.75 6.05 6.55 6.25 4.65 5.95 5.75 7.35 9.15 10.45 7.75 8.75 9.55 6.85 6.75 5.05 5.05 5.95 6.55 6.05 5.85 7.85 8.65 14.65 10.85 6.35 5.75 6.55 6.65 6.65 6.45 6.25 7.95 8.35 8.45 6.55 7.35 8.85 11.85 9.75 7.55 9.15 8.85 8.35 9.05 10.85 10.65 10.35 10.15 9.35 9.45 10.55 14.25 9.75 6.65 7.45 10.55 11.35 4.75 10.25 11.75 5.55 10.45 7.95 10.55 9.35 14.85 15.05 14.55 14.05 14.75 14.75 14.35 13.25 15.05 14.35 14.05 13.35 14.35 13.85 14.55 15.15 14.35 14.45 14.15 11.95 13.75 14.15 14.05 15.05 14.15 12.85 12.25 13.15 12.35 14.55 14.85 13.05 13.35 12.95 14.75 14.95 14.45 13.95 13.05 13.95 14.65 14.25 13.35 13.65 14.15 13.35 11.65 12.35 13.85 14.55 14.35 12.85 13.65 14.25 13.95 13.85 14.85 13.35 14.55 11.95 12.35 13.35 14.65 15.15 12.75 12.45 12.65 12.75 13.25 14.85 14.85 14.45 13.95 13.25 13.35 13.35 12.95 15.15 14.85 13.05 11.45 12.85 13.65 14.35 14.35 14.85 11.75 13.85 13.35 14.25 14.75 11.95 14.95 12.85 13.55 14.85 14.85 11.95 13.05 14.45 12.65 8.25 12.15 14.45 13.35 14.85 14.15 13.45 12.35 8.85 8.75 12.25 14.65 13.35 14.25 12.95 14.15 14.65 14.15 14.05 14.65 10.45 13.65 8.85 15.45 15.05 15.15 11.95 13.65 14.45 14.25 14.55 14.25 10.55 13.35 14.65 11.95 13.15 12.75 13.85 11.65 12.75 15.45 15.05 14.25 12.35 14.65 15.25 15.05 14.75 14.15 11.95 14.45 12.05 15.05 14.75 13.45 14.75 14.65 13.85 12.65 14.05 14.05 14.35 11.35 15.45 14.75 13.05 13.35 14.65 13.45 11.55 12.75 13.95 13.65 14.45 13.15 14.05 13.35 15.35 14.05 13.05 12.75 15.25 15.15 15.25 14.95 14.15 13.95 13.55 13.35 14.35 13.35 10.95 11.85 12.95 11.35 13.35 14.85 12.65 13.75 13.85 12.95 12.45 13.95 14.05 13.35 9.85 11.05 14.95 13.15 12.35 13.95 13.15 11.95 13.15 14.35 13.05 12.45 8.85 8.95 13.25 8.45 14.55 13.25 13.25 11.85 11.85 10.25 12.55 14.25 13.45 10.35 13.95 14.35 13.15 14.05 13.55 11.65 10.75 14.05 11.05 10.15 9.75 12.65 11.25 10.65 7.75 9.65 9.05 14.55 12.45 13.65 12.75 13.65 10.95 9.05 12.35 13.75 8.65 11.15 13.95 14.85 14.65 14.15 10.35 12.35 14.45 12.95 10.85 12.15 11.05 14.25 13.85 13.15 13.45 12.05 7.75 9.95 2.45 15.05 12.55 14.05 14.35 11.85 12.45 9.45 15.05 13.85 11.55 9.45 9.65 14.35 12.95 13.65 9.95 12.95 14.95 13.45 13.35 7.85 8.95 6.15 8.95 7.95 9.25 13.35 13.15 13.25 6.55 10.15 7.75 9.15 11.05 11.75 11.55 10.65 6.85 9.25 9.95 13.05 14.35 11.15 10.35 9.65 7.85 8.55 9.85 15.25 12.65 9.75 9.45 9.85 14.05 14.85 3.25 10.25 14.15 14.25 9.35 7.55 9.05 10.35 13.65 15.15 13.65 13.75 13.55 5.95 11.75 11.35 13.15 12.95 14.45 10.55 5.25 4.95 11.65 11.25 13.45 13.25 13.95 14.35 9.55 4.65 6.35 11.95 12.35 12.85 12.75 6.95 12.85 11.25 12.95 7.45 10.05 13.15 12.65 13.65 14.85 10.15 10.55 11.55 12.75 12.75 10.15 13.05 15.05 14.65 5.05 13.35 13.75 14.95 3.85 13.95 14.95 5.75 11.95 7.45 9.95 13.35 15.25 8.85 12.25 10.85 13.45 4.55 11.75 11.55 9.75 8.75 13.65 14.45 10.95 7.35 6.65 14.75 14.25 14.55 14.45 14.85 8.15 5.45 13.25 13.85 14.75 10.65 10.75 10.85 10.95 13.05 15.25 10.05 6.65 8.45 7.25 14.15 10.05 9.95 9.55 6.75 14.65 9.95 9.35 6.95 10.35 11.65 8.65 12.85 15.15 14.85 12.35 10.15 11.05 10.85 14.95 15.05 9.75 13.25 9.15 9.45 13.25 14.55 12.65 10.75 11.15 10.85 14.65 14.35 13.65 12.55 9.45 13.85 14.35 14.05 13.45 11.25 6.85 13.75 14.65 11.15 12.35 11.55 7.25 6.55 12.55 13.65 8.15 7.45 9.55 13.15 13.85 14.65 11.75 12.65 13.05 13.55 13.75 12.55 13.35 13.45 14.65 12.45 12.25 12.95 13.15 9.95 9.75 10.65 6.95 8.95 13.25 14.05 14.35 13.85 14.35 13.05 13.75 14.95 14.75 12.25 13.25 11.65 11.75 13.25 14.05 13.15 12.55 10.75 14.45 13.45 14.85 14.05 14.15 12.85 12.55 13.75 11.55 11.05 9.55 11.95 13.45 13.15 11.25 13.75 11.05 14.75 14.45 13.25 13.55 13.65 13.45 11.95 11.85 10.85 10.15 12.35 13.65 13.95 14.35 14.35 13.85 9.05 12.85 10.85 13.85 14.05 14.05 13.65 13.95 13.75 13.55 9.85 12.35 9.95 10.55 9.45 8.45 9.75 9.95 10.75 12.15 13.25 13.15 13.75 14.15 14.15 13.75 12.05 10.05 10.05 10.95 14.05 14.15 14.15 14.15 13.95 13.45 13.55 13.15 11.25 11.55 9.75 10.75 14.25 14.25 14.25 14.15 14.05 13.75 13.75 13.65 11.85 10.65 10.85 13.45 11.35 13.05 15.05 14.25 14.15 13.85 13.65 13.65 13.55 12.35 12.45 10.85 8.75 13.35 12.05 14.05 11.95 10.25 9.25 10.65 12.25 14.15 14.15 14.45 14.95 14.25 13.15 8.05 14.05 14.35 14.35 14.45 9.95 13.15 14.05 13.95 13.95 9.75 14.25 14.55 10.95 14.55 14.05 14.05 13.95 14.05 13.65 11.75 14.05 14.25 14.75 15.05 13.75 13.05 9.95 14.65 14.75 14.85 14.55 14.65 15.25 14.35 14.35 14.25 13.55 13.45 9.05 13.85 11.85 14.85 14.35 13.65 12.25 10.35 13.55 14.25 14.85 14.15 13.95 13.65 12.85 12.05 14.05 14.35 10.85 13.15 13.75 14.25 14.55 14.75 14.45 12.65 12.95 13.85 14.25 14.35 14.65 14.35 14.35 14.35 13.95 13.55 13.85 14.15 14.45 14.45 14.65 14.75 14.45 14.25 14.15 14.15 13.95 14.15 14.45 14.55 14.65 14.65 14.75 14.55 14.35 14.35 14.45 14.55 14.45 14.35 14.55 14.35 14.55 14.65 14.75 14.65 14.65 14.55 14.65; 20.75 16.75 17.05 18.75 17.45 22.25 17.85 17.05 16.95 17.95 16.95 19.15 19.05 15.85 23.15 18.75 16.65 15.55 18.25 18.95 17.95 18.35 18.75 18.25 18.75 16.85 16.15 15.95 16.05 17.65 20.65 16.45 16.65 18.25 19.95 23.75 17.55 17.05 17.85 17.55 15.55 14.55 15.25 17.25 17.85 16.75 16.15 17.65 17.65 15.95 13.75 13.75 16.15 17.35 18.35 19.75 19.85 19.45 16.15 17.05 17.15 16.35 14.05 18.25 15.65 16.05 16.65 16.55 14.75 15.35 21.05 22.25 19.95 18.55 16.35 17.55 16.45 16.85 14.75 19.55 18.05 17.65 16.15 17.65 18.25 15.75 16.55 15.75 14.15 19.45 17.25 16.25 21.45 17.25 17.95 16.65 16.35 18.55 15.55 15.15 15.25 15.75 11.95 17.05 16.75 19.35 15.95 16.85 15.45 15.35 16.25 16.45 14.85 13.15 14.65 16.85 17.65 15.75 18.85 15.55 18.05 20.25 15.35 16.25 16.65 15.95 16.85 16.65 14.65 13.65 15.05 14.55 17.15 16.55 19.95 19.25 22.95 16.75 16.75 17.25 16.55 17.15 16.65 14.65 15.35 16.15 15.65 15.15 17.25 16.45 18.25 16.15 17.45 17.55 17.75 16.85 15.15 14.05 16.05 16.75 15.85 14.65 12.15 13.75 13.05 17.65 16.35 18.65 15.35 17.15 17.85 18.05 17.25 16.15 14.95 16.95 14.35 15.15 15.15 13.45 22.75 16.95 19.05 17.75 15.85 16.95 17.85 18.35 16.85 15.65 17.25 14.95 16.45 15.65 14.85 15.15 15.15 14.35 17.35 18.35 13.05 14.85 16.55 17.65 18.35 17.55 16.35 17.75 14.25 16.45 17.35 15.95 16.05 16.25 14.95 16.15 15.95 17.65 16.15 16.15 17.25 17.85 18.65 17.75 8.75 15.25 17.65 17.15 16.95 17.25 15.45 13.65 16.65 15.65 17.15 15.85 22.65 17.35 18.45 16.45 15.95 15.35 16.65 17.15 18.45 18.75 18.45 13.95 15.05 16.65 17.75 17.85 16.05 17.65 15.75 14.85 17.55 16.35 20.25 20.25 17.55 14.65 15.65 16.25 18.35 19.05 18.55 18.35 15.65 17.05 17.95 17.35 14.85 17.65 17.15 15.35 18.05 17.85 18.45 19.25 17.45 19.25 18.65 16.65 18.15 17.35 18.25 18.85 23.55 20.35 18.15 17.35 18.55 15.45 19.55 16.25 18.65 17.95 21.25 20.55 16.75 17.55 18.95 13.95 15.45 17.25 19.15 18.05 17.55 18.35 19.05 20.35 16.35 16.55 18.55 15.15 12.85 14.45 16.05 17.55 19.65 16.55 19.15 20.05 17.25 19.25 20.55 20.05 16.85 15.55 17.95 17.05 14.75 13.85 16.15 17.85 19.65 18.55 19.15 20.75 17.85 20.25 20.65 19.45 16.65 15.05 17.05 17.15 11.65 14.85 16.55 18.45 14.95 19.65 15.85 20.25 18.55 19.65 19.55 19.35 20.45 18.65 17.55 15.35 16.25 13.15 13.75 16.05 16.95 18.65 20.45 20.05 19.75 14.95 16.45 15.05 16.95 17.65 21.15 16.85 13.75 14.25 15.65 15.95 17.05 17.65 18.75 19.65 21.35 20.05 20.85 13.75 14.95 15.85 13.55 15.25 16.25 16.85 18.95 21.35 16.55 14.35 15.45 17.25 15.25 16.75 18.85 20.45 19.25 13.55 9.15 15.55 17.35 16.05 14.25 15.05 15.85 15.05 15.55 18.45 17.35 16.95 14.75 14.05 21.35 17.25 16.35 10.85 17.75 18.05 14.65 16.85 17.85 16.35 15.45 15.65 17.65 16.85 18.45 16.95 15.35 17.15 15.95 13.95 12.65 17.05 17.95 18.75 16.15 14.35 16.45 17.85 16.05 15.45 14.65 14.45 16.05 15.65 17.35 15.35 21.65 19.75 16.35 13.65 11.75 17.35 15.55 19.25 15.65 16.15 18.75 16.75 14.45 14.75 15.75 16.65 13.75 16.05 18.05 16.75 19.05 19.45 18.55 18.25 15.95 18.75 16.65 18.15 17.35 20.05 19.05 15.95 17.65 21.25 18.85 15.85 16.65 18.75 15.45 17.85 18.15 10.65 19.05 20.75 20.75 15.75 14.45 14.65 16.95 16.65 16.45 14.45 15.95 16.65 19.15 19.05 15.75 20.95 19.35 16.55 16.75 15.95 16.35 17.95 17.05 18.55 17.75 14.85 21.35 21.25 19.55 18.15 12.75 17.65 18.65 18.65 19.85 16.55 15.75 20.75 20.95 21.25 20.85 22.55 17.25 19.05 16.85 20.15 21.75 22.15 14.75 15.05 14.45 17.65 18.05 19.65 16.75 22.45 20.85 15.15 14.65 16.05 16.15 14.25 15.15 16.25 16.65 19.35 20.65 20.25 17.65 15.65 14.65 16.75 17.65 15.25 15.95 16.35 17.65 18.95 19.45 20.35 21.45 20.45 21.95 18.25 18.35 20.35 20.75 14.65 15.55 15.95 16.05 17.35 17.35 17.55 15.95 15.55 16.95 19.55 21.15 22.45 21.25 22.25 19.75 18.05 18.75 20.55 18.45 18.05 16.25 18.35 18.55 16.65 17.55 16.45 16.95 16.95 20.75 21.05 22.65 18.85 18.05 20.15 17.85 17.25 16.85 16.75 16.55 18.65 19.25 18.85 18.35 18.15 17.85 16.05 20.05 22.65 19.05 19.65 19.95 19.55 19.55 18.95 16.95 17.05 18.05 17.35 15.35 15.45 15.75 15.45 17.15 18.25 18.85 19.15 18.85 17.45 16.55 17.85 18.45 21.65 23.15 19.45 19.15 18.65 19.35 18.55 18.05 15.55 16.65 16.45 16.65 17.55 17.05 20.55 20.45 20.55 16.25 16.95 18.45 19.85 22.55 18.15 17.85 17.85 18.05 17.85 14.85 15.05 16.25 15.45 19.95 20.25 18.15 16.85 15.35 16.75 18.65 21.35 17.75 17.35 17.35 17.55 18.15 19.15 13.95 14.55 15.55 16.15 17.45 17.65 19.75 17.75 18.45 19.05 19.75 16.65 16.95 16.55 14.75 16.55 16.25 18.25 20.35 21.75 18.55 19.65 20.55 17.45 17.15 15.25 15.25 16.35 17.05 16.65 16.45 18.75 19.65 23.55 21.95 16.95 16.05 16.95 17.15 17.15 17.05 16.85 18.85 19.15 18.95 16.95 17.85 19.75 22.45 20.25 18.15 19.85 19.65 19.05 19.85 21.65 21.55 21.15 20.95 20.05 20.25 21.45 23.45 20.35 17.05 17.85 21.25 22.15 14.85 21.05 22.65 15.55 20.35 18.15 20.65 18.85 22.85 22.65 22.25 21.95 21.95 22.45 22.25 21.25 22.25 22.25 22.15 21.25 22.25 21.95 22.65 22.45 21.75 22.45 22.35 20.25 21.95 22.35 22.15 22.45 21.65 20.95 20.75 21.65 20.95 23.05 23.25 21.75 21.95 20.75 22.35 22.55 22.55 22.05 21.75 22.55 23.25 21.95 21.05 21.45 22.25 22.15 20.45 21.25 21.65 22.45 22.25 21.75 22.35 21.95 22.85 22.65 22.25 21.25 22.85 20.95 21.35 22.25 22.15 22.75 20.75 21.55 21.65 21.85 22.25 22.45 22.75 22.35 21.95 21.35 22.05 22.45 21.95 22.65 22.65 21.65 20.75 22.15 21.45 22.15 22.25 22.85 21.05 23.15 22.55 22.05 22.65 21.35 22.75 20.95 21.55 22.95 22.95 21.05 21.15 22.55 21.55 17.75 21.65 23.65 21.55 23.05 22.55 22.25 21.55 18.35 18.25 20.55 23.05 22.05 23.25 22.75 23.55 22.55 22.35 22.35 23.05 19.25 22.65 18.45 22.45 22.25 22.55 20.35 22.05 22.85 22.65 23.05 22.85 19.45 22.25 22.75 20.45 21.65 21.35 22.65 21.15 22.55 22.55 22.15 21.65 20.95 23.85 22.25 22.15 23.05 22.55 20.65 23.35 21.15 22.15 21.95 21.15 23.05 23.05 22.35 21.35 23.05 23.15 23.45 20.95 22.55 21.95 20.85 21.25 23.05 22.25 20.55 21.75 23.15 23.45 21.85 20.95 22.75 22.75 22.45 22.95 22.45 22.25 22.35 22.25 22.45 22.25 21.65 21.65 21.35 21.25 22.35 22.45 20.35 21.25 22.35 20.75 23.15 22.25 20.65 21.85 22.65 21.75 21.35 23.05 23.25 22.65 19.35 20.75 22.25 22.05 21.45 23.25 22.65 21.55 23.15 21.85 21.25 21.45 18.55 18.65 23.25 18.85 21.95 21.65 22.65 21.65 22.05 20.45 22.15 21.65 21.45 20.65 21.45 22.05 21.35 22.65 22.45 22.25 20.95 23.35 20.55 19.85 20.25 22.65 21.55 21.05 18.25 20.45 19.85 22.05 20.85 22.25 21.95 23.25 20.65 19.55 20.75 22.85 19.25 22.25 23.55 22.55 22.45 23.15 20.45 22.85 24.05 20.55 21.35 22.75 22.25 23.95 21.35 20.85 22.35 21.95 18.45 21.15 12.85 22.25 20.35 21.95 22.35 20.45 21.25 20.55 22.35 22.25 20.45 20.05 20.55 24.15 20.55 21.95 19.75 22.95 22.35 22.15 22.75 18.15 19.45 16.75 19.95 18.85 20.65 21.05 21.85 22.85 17.25 21.25 18.75 19.65 20.25 21.25 21.65 21.05 17.85 19.85 20.15 22.95 23.65 19.25 20.55 20.15 18.75 19.45 21.05 22.55 22.45 20.05 20.05 20.25 23.85 22.45 13.85 20.75 23.85 23.85 19.65 18.55 19.75 20.75 22.85 22.25 23.55 23.35 22.95 16.75 22.65 21.95 23.25 22.55 21.95 20.95 15.95 15.65 22.95 21.55 23.55 22.75 23.05 23.35 20.15 15.35 17.25 23.15 22.75 22.45 22.15 17.75 23.15 21.15 21.35 18.35 21.45 22.65 21.85 22.75 22.25 21.45 21.85 22.45 22.35 21.95 21.45 22.65 22.55 22.15 15.65 22.75 23.15 22.45 14.25 22.95 22.45 16.25 23.45 17.45 19.85 22.75 22.75 20.15 23.65 22.05 22.85 15.05 23.05 22.85 20.85 18.65 22.85 23.35 22.25 18.05 16.75 22.45 22.15 22.55 22.45 23.25 19.35 15.75 22.65 22.95 23.05 22.05 22.25 22.05 22.05 22.45 22.85 21.05 17.55 19.55 17.85 23.65 21.25 21.15 20.75 17.55 22.45 21.05 20.45 17.75 21.35 22.75 18.95 22.15 23.25 23.15 22.35 21.25 21.95 21.15 22.75 22.95 20.75 23.45 19.75 20.35 23.15 22.95 23.85 21.55 21.95 21.75 22.95 24.05 23.95 23.65 19.95 23.55 22.85 24.25 23.85 21.85 17.25 22.45 24.05 21.85 23.25 22.45 17.55 16.85 23.15 23.75 18.45 17.65 19.85 22.85 21.45 24.15 22.35 23.35 23.85 23.05 21.65 20.45 21.15 21.05 23.35 23.15 22.85 23.65 23.95 20.35 20.05 21.15 16.85 19.05 22.65 23.05 22.85 22.15 22.55 20.65 21.35 22.25 22.05 22.95 23.95 22.15 21.15 22.45 22.85 21.45 20.65 18.55 22.15 20.95 22.25 24.05 24.65 23.75 23.35 24.55 22.05 21.35 19.75 21.95 21.85 21.55 19.25 21.45 18.65 22.25 24.65 23.85 24.45 24.45 24.25 22.35 21.65 19.85 17.85 20.05 21.05 21.25 21.65 24.65 24.55 18.85 22.85 18.85 21.35 24.45 24.85 24.55 24.75 24.25 23.95 19.65 22.05 18.05 18.55 17.35 15.95 17.35 17.55 18.25 19.65 20.75 20.45 24.25 24.85 24.75 24.15 22.05 19.75 18.25 18.75 24.85 24.85 24.75 24.55 24.45 23.65 23.65 22.75 20.45 20.35 17.35 18.25 21.75 21.55 24.85 24.45 24.45 23.95 23.95 23.65 21.55 20.15 20.35 21.95 18.85 20.65 22.35 24.55 24.45 23.95 23.65 23.55 23.45 22.15 22.15 20.35 17.95 22.85 21.35 22.55 19.85 17.95 16.85 18.25 19.65 21.55 21.45 21.75 22.15 24.45 22.75 17.15 22.95 23.05 22.95 22.95 17.45 20.75 24.05 23.95 23.85 18.95 23.05 23.15 18.55 21.85 24.05 24.05 23.95 23.95 23.25 21.05 21.55 21.65 22.05 22.35 23.35 22.45 18.95 23.15 23.15 22.35 22.05 22.05 22.55 24.25 24.15 23.95 23.05 22.75 17.85 21.45 19.35 22.25 24.25 23.05 21.25 19.15 22.65 23.25 22.25 21.55 23.35 22.85 21.85 20.95 23.05 23.25 19.55 22.15 22.65 23.15 23.35 23.15 24.05 21.45 21.85 22.75 23.15 23.15 23.25 23.75 23.65 23.65 22.85 22.45 22.75 23.05 23.25 23.25 23.25 23.15 23.65 23.15 23.05 22.95 22.75 22.95 23.25 23.35 23.25 23.25 23.15 23.85 23.35 23.35 23.25 23.85 23.45 23.05 23.25 23.05 23.25 23.25 23.15 23.25 23.25 23.15 23.25; 20.85 16.75 17.05 18.75 17.45 22.25 17.85 17.05 16.95 17.95 16.95 19.15 19.05 15.85 23.15 18.75 16.65 15.55 18.25 18.95 17.95 18.35 18.75 18.25 18.75 16.85 16.15 15.95 16.05 17.65 20.65 16.45 16.65 18.25 19.95 23.75 17.55 17.05 17.85 17.55 15.55 14.55 15.25 17.25 17.85 16.75 16.15 17.65 17.65 15.95 13.75 13.75 16.15 17.35 18.35 19.75 19.85 19.45 16.15 17.05 17.15 16.35 14.05 18.25 15.65 16.05 16.65 16.55 14.75 15.35 21.05 22.25 19.95 18.55 16.35 17.55 16.45 16.85 14.75 19.55 18.05 17.65 16.15 17.65 18.25 15.75 16.55 15.75 14.15 19.45 17.25 16.25 21.45 17.25 17.95 16.65 16.35 18.55 15.55 15.15 15.25 15.75 11.95 17.05 16.75 19.35 15.95 16.85 15.45 15.35 16.25 16.45 14.85 13.15 14.65 16.85 17.65 15.75 18.85 15.55 18.05 20.25 15.35 16.25 16.65 15.95 16.85 16.65 14.65 13.65 15.05 14.55 17.15 16.55 19.95 19.25 22.95 16.75 16.75 17.25 16.55 17.15 16.65 14.65 15.35 16.15 15.65 15.15 17.25 16.45 18.25 16.15 17.45 17.55 17.75 16.85 15.15 14.05 16.05 16.75 15.85 14.65 12.15 13.75 13.05 17.65 16.35 18.65 15.35 17.15 17.85 18.05 17.25 16.15 14.95 16.95 14.35 15.15 15.15 13.45 22.75 16.95 19.05 17.75 15.85 16.95 17.85 18.35 16.85 15.65 17.25 14.95 16.45 15.65 14.85 15.15 15.15 14.35 17.35 18.35 13.05 14.85 16.55 17.65 18.35 17.55 16.35 17.75 14.25 16.45 17.35 15.95 16.05 16.25 14.95 16.15 15.95 17.65 16.15 16.15 17.25 17.85 18.65 17.75 8.75 15.25 17.65 17.15 16.95 17.25 15.45 13.65 16.65 15.65 17.15 15.85 22.65 17.35 18.45 16.45 15.95 15.35 16.65 17.15 18.45 18.75 18.45 13.95 15.05 16.65 17.75 17.85 16.05 17.65 15.75 14.85 17.55 16.35 20.25 20.25 17.55 14.65 15.65 16.25 18.35 19.05 18.55 18.35 15.65 17.05 17.95 17.35 14.85 17.65 17.15 15.35 18.05 17.85 18.45 19.25 17.45 19.25 18.65 16.65 18.15 17.35 18.25 18.85 23.55 20.35 18.15 17.35 18.55 15.45 19.55 16.25 18.65 17.95 21.25 20.55 16.75 17.55 18.95 13.95 15.45 17.25 19.15 18.05 17.55 18.35 19.05 20.35 16.35 16.55 18.55 15.15 12.85 14.45 16.05 17.55 19.65 16.55 19.15 20.05 17.25 19.25 20.55 20.05 16.85 15.55 17.95 17.05 14.75 13.85 16.15 17.85 19.65 18.55 19.15 20.75 17.85 20.25 20.65 19.45 16.65 15.05 17.05 17.15 11.65 14.85 16.55 18.45 14.95 19.65 15.85 20.25 18.55 19.65 19.55 19.35 20.45 18.65 17.55 15.35 16.25 13.15 13.75 16.05 16.95 18.65 20.45 20.05 19.75 14.95 16.45 15.05 16.95 17.65 21.15 16.85 13.75 14.25 15.65 15.95 17.05 17.65 18.75 19.65 21.35 20.05 20.85 13.75 14.95 15.85 13.55 15.25 16.25 16.85 18.95 21.35 16.55 14.35 15.45 17.25 15.25 16.75 18.85 20.45 19.25 13.55 9.15 15.55 17.35 16.05 14.25 15.05 15.85 15.05 15.55 18.45 17.35 16.95 14.75 14.05 21.35 17.25 16.35 10.85 17.75 18.05 14.65 16.85 17.85 16.35 15.45 15.65 17.65 16.85 18.45 16.95 15.35 17.15 15.95 13.95 12.65 17.05 17.95 18.75 16.15 14.35 16.45 17.85 16.05 15.45 14.65 14.45 16.05 15.65 17.35 15.35 21.65 19.75 16.35 13.65 11.75 17.35 15.55 19.25 15.65 16.15 18.75 16.75 14.45 14.75 15.75 16.65 13.75 16.05 18.05 16.75 19.05 19.45 18.55 18.25 15.95 18.75 16.75 18.15 17.35 20.05 19.05 15.95 17.75 21.25 18.85 15.85 16.65 18.75 15.45 17.85 18.15 10.65 19.05 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15.55 16.65 16.45 16.65 17.55 17.05 20.55 20.45 20.55 16.25 16.95 18.45 19.85 22.55 18.15 17.85 17.85 18.05 17.85 14.85 15.05 16.25 15.45 19.95 20.25 18.15 16.85 15.35 16.75 18.65 21.35 17.75 17.35 17.35 17.55 18.15 19.15 13.95 14.55 15.55 16.15 17.45 17.65 19.75 17.75 18.45 19.05 19.75 16.65 16.95 16.55 14.75 16.55 16.25 18.25 20.35 21.75 18.55 19.65 20.55 17.45 17.15 15.25 15.25 16.35 17.05 16.65 16.45 18.75 19.65 23.75 21.95 16.95 16.05 16.95 17.15 17.15 17.05 16.85 18.85 19.15 18.95 16.95 17.85 19.75 22.45 20.25 18.15 19.85 19.65 19.05 19.85 21.65 21.55 21.15 20.95 20.05 20.25 21.45 23.55 20.35 17.05 17.85 21.25 22.15 14.85 21.05 22.65 15.55 20.35 18.15 20.65 18.85 23.05 22.85 22.45 22.15 22.25 22.65 22.45 21.45 22.55 22.45 22.35 21.45 22.45 22.15 22.85 22.75 22.05 22.65 22.55 20.35 22.15 22.55 22.35 22.75 21.85 21.15 20.85 21.75 21.05 23.15 23.45 21.75 22.05 20.95 22.55 22.75 22.75 22.25 21.85 22.65 23.35 22.15 21.25 21.65 22.45 22.25 20.55 21.25 21.85 22.65 22.45 21.75 22.45 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42.320693915200025), (9.529027019700015, 42.354027248400016), (9.529027019700015, 42.404027248200016), (9.529027019700015, 42.445693914700016), (9.529027019700015, 42.50402724780002), (9.529027019700015, 42.55402724760002), (9.537360353000015, 42.41236058150002), (9.545693686300016, 42.28736058200002), (9.545693686300016, 42.29569391530002), (9.545693686300016, 42.320693915200025)])

We will limit the model to two variables for the sake of illustration. We will train a simple decision tree with two variables:

sdm = SDM(RawData, DecisionTree, X, y)

❎  RawData → DecisionTree → P(x) ≥ 0.5

Note that the models are all composed of a transformer, and then a classifier; this means that SDeMo can be reasonably easy to extend (by defining a train! and a predict method for additional types you would like to include).

variables!(sdm, [1, 12])

2-element Vector{Int64}:
  1
 12

The cross-validation of a model requires a series of training/validation indices, and there are several convenience functions implemented:

folds = kfold(sdm)

10-element Vector{Tuple{Vector{Int64}, Vector{Int64}}}:
 ([3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 89, 90, 91, 92, 93, 95, 96, 97, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 170, 171, 172, 173, 175, 176, 177, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 196, 197, 198, 199, 200, 201, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 219, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 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691, 692, 693, 694, 695, 696, 697, 698, 699, 700, 702, 703, 704, 705, 707, 708, 709, 710, 711, 712, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 725, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 740, 742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 789, 790, 791, 792, 793, 794, 795, 797, 798, 799, 800, 801, 802, 803, 807, 808, 809, 810, 811, 812, 813, 814, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 828, 829, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 860, 861, 862, 863, 865, 866, 867, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884, 885, 886, 887, 889, 890, 891, 892, 893, 894, 895, 897, 898, 899, 900, 901, 902, 903, 904, 905, 907, 908, 909, 910, 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1109, 859, 1314, 987, 1227, 1056, 804, 1127, 989, 1404, 959, 906, 1134, 1447, 1070, 1514, 915, 1290])

Stratification

By default, the sets of testing and training indices will always be stratified, so that they have the same prevalence. This is also true when using bagging for homogeneous ensemble models.

We can cross-validate this model with:

cv = crossvalidate(sdm, folds);

This returns the confusion matrices for the validation and training sets, in a named tuple:

mcc(cv.validation)

0.7942252359807807

mcc(cv.training)

0.8073850345507727

SDeMo has methods for the most common measures on a confusion matrix. For example, the true-skill statistics is:

trueskill(cv.training)

0.8007902628503606

And Cohen's κ:

κ(cv.training)

0.8026065763895343

It is a good idea to compare the value of different measures to some null classifiers:

measures = [mcc, ppv, npv, plr, nlr]
cvresult = [measure(set) for measure in measures, set in cv]
nullresult = [measure(null(sdm)) for measure in measures, null in [coinflip, noskill]]
pretty_table(
    hcat(string.(measures), hcat(cvresult, nullresult));
    alignment = [:l, :c, :c, :c, :c],
    backend = :markdown,
    column_labels = ["Measure", "Validation", "Training", "Coin-flip", "No-skill"],
    formatters = [fmt__printf("%5.3f", [2, 3, 4, 5])],
)

Measure	Validation	Training	Coin-flip	No-skill
mcc	0.794	0.807	0.022	0.000
ppv	0.863	0.866	0.511	0.511
npv	0.939	0.948	0.511	0.489
plr	6.771	6.248	1.044	1.000
nlr	0.063	0.053	0.958	1.000

Note that crossvalidate does not train the model. The point of crossvalidate is to decide whether the model should be trained. If the performance is good enough, training the model with all data is done with:

train!(sdm)

☑️  RawData → DecisionTree → P(x) ≥ 0.255

Training the model will automatically optimize the threshold, using the MCC as a measure of optimal predictive ability.

If you want to optimize the threshold using cross-validation, there is a specific method for that:

threshold!(sdm, folds; optimality=mcc)

☑️  RawData → DecisionTree → P(x) ≥ 0.559

It works by finding the value of the threshold that optimizes the average performance across folds, and can be used with any measure of performance you want to optimize.