Scikit-learn SelectFromModel - actually obtain the feature importance scores of underlying predictor

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I was trying to estimate the feature importance for the classification task I have at hand. What is important for me is to get specific numbers which represent importance of each feature, not just 'pick X features which are most important'.

Obvious choice was to use the tree-based methods which provide nice feature_importances_ method to obtain importance of each feature. But I wasn't satisfied with the results of the tree-base classifiers. I learned that SelectFromModel method is capable to eliminate not important features based on the importance score and successfully does that for SVM or Linear models as well.

I wonder, is there any way to obtain specific importance score from SelectFromModel for each feature instead of just getting a list of most important features?

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