Machine Learning metrics are quantitative measures used to evaluate how well a model performs.
They help answer questions like:
- How accurate is my model?
- Is it making more false alarms or missing key detections?

Understanding metrics is essential for comparing models, diagnosing errors, and improving reliability.
In this presentation, we will explore common classification metrics, their mathematical definitions, and visual representations that make them intuitive to understand.

The foundation of all classification metrics is the confusion matrix, which summarizes predictions versus actual outcomes.

From these four values, we can compute accuracy, precision, recall, and more.

\[ Accuracy = \frac{TP + TN}{TP + TN + FP + FN} \] \[ Precision = \frac{TP}{TP + FP}, \quad Recall = \frac{TP}{TP + FN} \]

Accuracy measures overall correctness, while Precision and Recall reveal how well the model identifies positives.

\[ F1 = 2 \times \frac{Precision \times Recall}{Precision + Recall} \] \[ \text{TPR} = \frac{TP}{TP + FN}, \quad \text{FPR} = \frac{FP}{FP + TN} \]

The F1-score balances precision and recall, while the True Positive Rate (TPR) and False Positive Rate (FPR) are key for ROC analysis.

\[ P(\text{Positive} \mid \text{Predicted Positive}) = \text{Precision},\quad P(\text{Predicted Positive} \mid \text{Positive}) = \text{Recall} \] These metrics are deeply rooted in conditional probability and Bayes’ Theorem.
They provide a bridge between statistics and machine learning, allowing us to interpret model predictions probabilistically.

metrics <- function(tp, fp, fn) {
  precision <- tp / (tp + fp)
  recall    <- tp / (tp + fn)
  f1        <- 2 * precision * recall / (precision + recall)
  c(precision = round(precision, 3),
    recall    = round(recall, 3),
    f1        = round(f1, 3))
}
metrics(88, 12, 15)

## precision    recall        f1 
##     0.880     0.854     0.867

• Machine learning metrics turn model performance into measurable insights.
  
• Precision and Recall highlight the trade-off between exactness and coverage.
  
• ROC curves visualize this balance across thresholds.

Mastering these metrics ensures that ML models are not only accurate but trustworthy and interpretable.