Model-agnostic variable importance metric

Question

I use genetic / evolutionary algorithms in python's TPOT package to find the overall best model (GBM, RF, SVM, elastic net, etc) and its tuning parameters. Now I need a way to measure each variable's contribution to the chosen model's predictive performance. How can I do this in a model-agonistic way?

My current approach is to retrain the best model architecture after holding out each of the variables. For example, if my variables are [a,b,c] I'll retrain on [a,b], [a,c], and [b,c]. I define the removed variable associated with the worst performing model as the most important variable and I define the variable's predictive contribution as the decrease in predictive performance. I measure all variable's predictive performance this way. Is there anything obviously wrong with this approach? Is there a better approach? I'm familiar with variable importance in decision trees, and p-values in linear models, but I need a model agnostic approach.

Answer 1

Have you looked at the permutation importance approach in the eli5 package?

The idea is that instead of retraining the model without the feature, which is computationally expensive, they replace each feature in turn with random noise in the test set. To get random noise that is drawn from the same distribution as the original feature, they just randomly shuffle that feature.

Note that, as with feature importance in decision trees, this measure is biased against categorical variables with low cardinality.