Confusion Matrix for Two-Class Classifiers

• One challenge in machine learning is skew (percentage of positive samples): $$\alpha =\frac{P}{P+N}$$
• If the $\alpha$ isn’t near .5, we describe it as a skewed data set.
• Skewed data creates challenges both for training and evaluating classifiers.
• How might we address it???

Training: Oversampling, Undersampling, SMOTE

SMOTE - Synthetic Minority Oversampling Technique

Evaluation Metrics

• Confusion matrix tells the whole story BUT, we often want a single number to summarize our performance.
  • Accuracy $=\frac{\text{Correct Predictions}}{\text{Total Predictions}}=\frac{TP+TN}{TP+TN+FP+FN}$
    • Sensitive to skew, doesn’t distinguish between types of error:
      • Type I Error: False Positive
      • Type II Error: False Negative
  • True Positive Rate (TPR)/Recall = Percentage of positives that are classified as positives = $\frac{TP}{TP+FN}$
  • False Positive Rate (FPR) = Percentage of negatives that are classified as positives = $\frac{FP}{FP+TN}$
    • These distinguish error type, but don’t help with skew
  • Precision = Correct predictions over the total number of positive predictions = $\frac{TP}{TP+FP}$
    • Meaningful even for highly skewed data, since it only considers positive predictions.
  • There are also more complicated measures that attempt to combine strengths of those above. E.g.:
    • F1 Score = $\frac{2\times precision\times recall}{precision+recall}$
    • Both precision and recall must be high for the F1 score to be high.

Classifiers Scores + ROC Curves + AUC

• Many classifiers are able to produce a score $s(\mathbf{x})$ that indicates the model’s confidence that $\mathbf{x}$ is in the positive class.
• This allows us to adjust our classifier’s behavior by changing the classification threshold.

• Receiver Operating Characteristic (ROC) curve shows the impact of different threshold values:

  

  (Image credit: https://glassboxmedicine.com/2019/02/23/measuring-performance-auc-auroc/

• The Area Under the Curve (AUC) provides a single summary value (generally between .5 and 1.0) of the behavior across all possible thresholds