Mean Decrease Impurity

Description

Mean Decrease Impurity (MDI) quantifies a feature's importance in tree-based models (e.g., Random Forests, Gradient Boosting Machines) by measuring the total reduction in impurity (e.g., Gini impurity, entropy) across all splits where the feature is used. Features that lead to larger, more consistent reductions in impurity are considered more important, indicating their effectiveness in creating homogeneous child nodes and improving predictive accuracy.

Example Use Cases

Explainability

Determining the most influential genetic markers in a decision tree model predicting disease susceptibility, by identifying which markers consistently lead to the purest splits between healthy and diseased patient groups.

Assessing the key factors driving customer purchasing decisions in an e-commerce random forest model, revealing which product attributes or customer demographics are most effective in segmenting buyers.

Limitations

MDI is inherently biased towards features with more unique values or those that allow for more splits, potentially overestimating their true importance.
It is only applicable to tree-based models and cannot be directly used with other model architectures.
The importance scores can be unstable, varying significantly with small changes in the training data or model parameters.
MDI does not account for feature interactions, meaning it might not accurately reflect the importance of features that are only relevant when combined with others.

Resources

Trees, forests, and impurity-based variable importance

Research Paper•Erwan Scornet•Jan 13, 2020

A Debiased MDI Feature Importance Measure for Random Forests

Research Paper•Xiao Li et al.•Jun 26, 2019

Variable Importance in Random Forests | Towards Data Science

Tutorial

Interpreting Deep Forest through Feature Contribution and MDI Feature Importance

Research Paper•Yi-Xiao He, Shen-Huan Lyu, and Yuan Jiang•May 1, 2023

optuna.importance.MeanDecreaseImpurityImportanceEvaluator ...

Documentation

Related Techniques

Name	Description	Assurance Goals
Integrated Gradients	Integrated Gradients is an attribution technique that explains a model's prediction by quantifying the contribution of each input feature. It works by accumulating gradients along a straight path from a user-defined baseline input (e.g., a black image or an all-zero vector) to the actual input. This path integral ensures that the attributions satisfy fundamental axioms like completeness (attributions sum up to the difference between the prediction and the baseline prediction) and sensitivity (non-zero attributions for features that change the prediction). The output is a set of importance scores, often visualised as heatmaps, indicating which parts of the input were most influential for the model's decision.	Explainability
Layer-wise Relevance Propagation	Layer-wise Relevance Propagation (LRP) explains neural network predictions by working backwards through the network to show how much each input feature contributed to the final decision. It follows a simple conservation rule: the total contribution scores always add up to the original prediction. Starting from the output, LRP distributes 'relevance' backwards through each layer using different rules depending on the layer type. This creates a detailed breakdown showing which input features helped or hindered the prediction, making it easier to understand why the network made a particular decision.	Explainability Transparency
Occlusion Sensitivity	Occlusion sensitivity tests which parts of the input are important by occluding (masking or removing) them and seeing how the model's prediction changes. For example, portions of an image can be covered up in a sliding window fashion; if the model's confidence drops significantly when a certain region is occluded, that region was important for the prediction.	Explainability
Area Under Precision-Recall Curve	Area Under Precision-Recall Curve (AUPRC) measures model performance by plotting precision (the proportion of positive predictions that are correct) against recall (the proportion of actual positives that are correctly identified) at various classification thresholds, then calculating the area under the resulting curve. Unlike accuracy or AUC-ROC, AUPRC is particularly valuable for imbalanced datasets where the minority class is of primary interest---a perfect score is 1.0, whilst random performance equals the positive class proportion. By focusing on the precision-recall trade-off, it provides a more informative assessment than overall accuracy for scenarios where false positives and false negatives have different costs, especially when positive examples are rare.	Reliability Transparency Fairness
Runtime Monitoring and Circuit Breakers	Runtime monitoring and circuit breakers establish continuous surveillance of AI/ML systems in production, tracking critical metrics such as prediction accuracy, response times, input characteristics, output distributions, and system resource usage. When monitored parameters exceed predefined safety thresholds or exhibit anomalous patterns, automated circuit breakers immediately trigger protective actions including request throttling, service degradation, system shutdown, or failover to backup mechanisms. This approach provides real-time defensive capabilities that prevent cascading failures, ensure consistent service reliability, and maintain transparent operation status for stakeholders monitoring system health.	Safety Reliability Transparency
Classical Attention Analysis in Neural Networks	Classical attention mechanisms in RNNs and CNNs create alignment matrices and temporal attention patterns that show how models focus on different input elements over time or space. This technique analyses these traditional attention patterns, particularly in encoder-decoder architectures and sequence-to-sequence models, where attention weights reveal which source elements influence each output step. Unlike transformer self-attention analysis, this focuses on understanding alignment patterns, temporal dependencies, and encoder-decoder attention dynamics in classical neural architectures.	Explainability