Evaluation Metrics

Evaluation Metrics

Evaluation Metrics are quantitative measures used to assess the performance of machine learning models. Choosing the right metric is essential for understanding how well a model performs, especially in classification and regression problems.

Why Are Evaluation Metrics Important?

• Provide objective criteria to compare different models.
• Help detect issues like overfitting or underfitting.
• Guide model improvement and selection.
• Reflect the business or real-world importance of model predictions.

Types of Evaluation Metrics

1. Classification Metrics

These metrics evaluate models that predict discrete categories (classes).

• Accuracy: Proportion of correct predictions over total predictions.

 :$\text{Accuracy}=\frac{TP+TN}{TP+TN+FP+FN}$

• Precision: Proportion of true positives among all predicted positives.

 :$\text{Precision}=\frac{TP}{TP+FP}$

• Recall (Sensitivity): Proportion of true positives among all actual positives.

 :$\text{Recall}=\frac{TP}{TP+FN}$

• F1 Score: Harmonic mean of precision and recall, balancing both.

 :$F1=2\times \frac{\text{Precision}\times \text{Recall}}{\text{Precision}+\text{Recall}}$

• Specificity: Proportion of true negatives among all actual negatives.

 :$\text{Specificity}=\frac{TN}{TN+FP}$

• ROC AUC: Area under the Receiver Operating Characteristic curve, measuring true positive rate vs false positive rate across thresholds.

• Precision-Recall AUC (AUPRC): Area under the Precision-Recall curve, especially useful for imbalanced data.

2. Regression Metrics

Used for models predicting continuous values.

• Mean Absolute Error (MAE): Average absolute difference between predicted and actual values.

 :$MAE=\frac{1}{n}\sum _{i=1}^n|y_i-{\hat{y}}_i|$

• Mean Squared Error (MSE): Average squared difference, penalizes larger errors more.

 :$MSE=\frac{1}{n}\sum _{i=1}^n(y_i-{\hat{y}}_i{)}^2$

• Root Mean Squared Error (RMSE): Square root of MSE, in same units as output.

 :$RMSE=\sqrt{MSE}$

• R-squared (R²): Proportion of variance explained by the model.

 :$R^2=1-\frac{\sum (y_i-{\hat{y}}_i{)}^2}{\sum (y_i-\overline{y}{)}^2}$

Choosing the Right Metric

• Imbalanced Classification: Use Precision, Recall, F1 Score, or AUPRC instead of accuracy.
• Cost-Sensitive Tasks: Consider metrics that weigh errors differently.
• Regression: Use MAE or RMSE based on error tolerance.

Related Pages

• Confusion Matrix
• Precision
• Recall
• F1 Score
• ROC Curve
• AUC Score
• Imbalanced Data
• Cost-Sensitive Learning

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