Understanding Feature Importance
📌 Feature Importance in machine learning refers to calculating the importance of each feature (column) relative to a specific algorithm.
🧐 It is a technique used in feature selection to identify and retain the most useful features while discarding less relevant ones, thereby improving model performance and reducing training time.
📊 Feature importance provides interpretability, explaining why a model makes certain predictions (e.g., why a loan application was rejected).

Calculating Feature Importance with Random Forest (Code Example)
💻 The speaker demonstrated calculating feature importance using Random Forest Classifier on the MNIST dataset.
🖼️ Visualization confirmed that central pixels in the image data had significantly higher feature importance scores than peripheral pixels, as they are crucial for digit classification.
🔢 After training the model, calling `rf.feature_importances_` yields an array where each element corresponds to the importance score of a feature (pixel column).

Mathematical Basis: Feature Importance in Decision Trees
🧠 To understand Random Forest importance, one must first grasp how it's calculated in a single Decision Tree (using criteria like Gini Impurity).
⚖️ Feature importance in a Decision Tree is defined as the total reduction in the criterion (like Gini Impurity) achieved by splits based on that feature across all nodes where the feature was used for splitting.
🔗 When calculating feature importance for a specific feature, you sum the importance scores of all nodes split by that feature and divide by the sum of importance scores of all nodes in the tree.

Node Importance Calculation (Gini Impurity Basis)
➗ The importance of a single node is calculated using the formula: $\text{Node Importance} = (\text{Samples}_{\text{node}} / \text{Total Samples}) \times (\text{Impurity}_{\text{node}} - \text{Weighted Average of Child Impurities})$.
🔢 For a small dataset example, the calculation demonstrated that the feature used at the root node received a higher importance score (e.g., 0.38) compared to the feature used in a subsequent split (e.g., 0.18).
1️⃣ A key property when using normalized importance scores is that the sum of importance for all features will always equal 1.

Feature Importance in Random Forest vs. Single Tree
🌲 Random Forest computes feature importance by taking the average of the feature importance scores calculated by each individual Decision Tree within the forest.
🧮 If a Random Forest consists of $N$ trees, the final feature importance for a feature is the average of its importance scores across those $N$ trees.

Key Points & Insights
➡️ Feature importance helps interpret model decisions, which is vital in critical applications like finance or healthcare.
⚠️ Be cautious: Gini Importance (Impurity-based importance) can be misleading for high cardinality features (features with many unique values).
💡 For datasets containing high cardinality features, consider using alternative methods like Permutation Importance (available via `sklearn.inspection.permutation_importance`) for more reliable results.

📸 Video summarized with SummaryTube.com on Nov 27, 2025, 15:37 UTC