关于scikit-learn随机森林特征重要性计算逻辑的技术问询

Great questions—let’s break this down clearly for both classification and regression scenarios:

1. Classification Scenario: Gini Impurity & Ensemble Aggregation #

Your initial hunch is on track: for a single decision tree in classification, feature importance is tied to how much the feature reduces Gini impurity (or entropy, if you set criterion="entropy") when splitting nodes. Here’s the full picture for the ensemble:

• For one decision tree:
  • Every time a feature is used to split a node, calculate the impurity reduction (the difference between the parent node’s impurity and the weighted average of its child nodes’ impurities).
  • Multiply that reduction by the fraction of total samples passing through that split node—this gives more weight to splits that affect a larger portion of the data.
  • Sum these weighted reductions across all splits where the feature was used to get its importance score for that single tree.
• For the Random Forest ensemble:
  It’s not a simple average of each tree’s feature scores. Instead, we sum up the weighted impurity reductions for each feature across all trees in the forest. Then we normalize these totals so all feature importance scores add up to 1—this makes comparing relative importance straightforward.

2. Regression Scenario: MSE Reduction #

You nailed this one! Regression trees in Random Forest use Mean Squared Error (MSE) reduction to measure feature importance. The process mirrors classification, just with MSE replacing Gini/entropy:

• For one regression tree:
  • When a feature is used to split a node, compute the reduction in MSE (parent node MSE minus the weighted average of child nodes’ MSE).
  • Multiply that reduction by the fraction of total samples in the split node.
  • Sum these values across all splits using the feature to get its single-tree importance score.
• For the ensemble:
  We sum these weighted MSE reductions across all trees, then normalize the totals to get final feature importance scores that sum to 1.

Quick Side Note #

Scikit-learn’s feature_importances_ attribute handles all this aggregation and normalization automatically—so when you access it, you’re getting the final, ready-to-compare scores for the entire forest.

内容的提问来源于stack exchange，提问作者companyyy