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Table 2.

Feature importances using various machine learning models and statistics.

Feature OLS Lasso Stability RanFor RFEOLS RFErf MIC Corr Mean
B2 0.0076 0.0048 0.0 0.0049 0.2 0.6 0.0000 0.1019 0.1149
B2Bx 0.6345 0.2577 0.0 1.0000 0.8 1.0 1.0000 0.9972 0.8362
B2By 0.0871 0.0240 0.0 0.0000 0.6 0.0 0.3979 0.1210 0.1538
Bx 1.0000 1.0000 1.0 0.4404 1.0 0.8 1.0000 0.9982 0.7793
By 0.0818 0.0000 0.0 0.0000 0.4 0.4 0.4048 0.1179 0.1756
BxBy 0.0000 0.0145 0.0 0.0001 0.0 0.2 0.2089 0.1366 0.0700


All the numbers are normalized such that they are positive and lie between 0 and 1 for the sake of comparison. Stability column refers to randomized LASSO where the LASSO shrinkage coefficient is randomly varied for different features and the feature that is most robust to this variation survives. RFE stands for Recursive Feature Elimination where a model is trained with all features and the top ranking feature is given the most significance, while the bottom ranking one gets the smallest score. We applied this to both OLS and random forests, and reverse sorted the entries to give the highest score to top ranking feature. MIC stands for Maximal Information Coefficient and computes a normalized measure of the mutual information between two variables scaled between 0 and 1. It gives a quantitative measure of the question: how much information about some variable Y can be obtained through some variable X? MIC is capable of capturing non-linear relationships that Pearson correlation (Corr) cannot. In the last column we take the mean over all models that represents the synthesis of several models (linear, non-linear) to show that and are the two strongest features.

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