# Accuracy

**Definition**: The proportion of total correct predictions.

### Confusion Matrix

| | Predicted Positive | Predicted Negative |
|---------------|--------------------|--------------------|
| **Actual Positive** | True Positive (TP) | False Negative (FN) |
| **Actual Negative** | False Positive (FP) | True Negative (TN) |

### Formula

> Accuracy = (TP + TN) / (TP + FP + FN + TN)

### Key Points

| Feature | Explanation |
|----------------------|--------------------------------------------------|
| **Type** | Overall correctness |
| **Range** | 0.0 ~ 1.0 |
| **Ideal Value** | 1.0 |
| **Limitation** | Misleading in imbalanced datasets |
| **Example** | If 95% of data is negative, predicting all negative gives 95% accuracy (but it's a bad model) |

---

## F1-Score

**Definition**: The harmonic mean of **precision** and **recall**, giving a balanced metric when class distribution is uneven.

### Related Metrics

| Metric | Formula | What It Means |
|------------|--------------------------|------------------------------------------|
| Precision | TP / (TP + FP) | Out of all predicted positives, how many are correct |
| Recall | TP / (TP + FN) | Out of all actual positives, how many did we catch? |
| F1-Score | 2 × (Precision × Recall) / (Precision + Recall) | Balances precision and recall |

### Key Points

| Feature | Explanation |
|----------------------|--------------------------------------------------|
| **Type** | Balance between precision & recall |
| **Range** | 0.0 ~ 1.0 |
| **Ideal Value** | 1.0 |
| **Use Case** | Imbalanced classification tasks (e.g. anomaly, disease detection) |
| **Limitation** | Ignores true negatives |

---

## AUC (Area Under ROC Curve)

**Definition**: Measures the model’s ability to distinguish between positive and negative classes across all possible thresholds.

### ROC Curve Explanation

| Term | Formula | Interpretation |
|-----------------------|--------------------------|-----------------------------------------|
| TPR (Recall) | TP / (TP + FN) | True Positive Rate (sensitivity) |
| FPR | FP / (FP + TN) | False Positive Rate |
| AUC | Area under the ROC curve | 1.0 means perfect, 0.5 means random |

### Key Points

| Feature | Explanation |
|----------------------|--------------------------------------------------|
| **Type** | Threshold-independent probability ranking |
| **Range** | 0.0 ~ 1.0 |
| **Ideal Value** | 1.0 |
| **Use Case** | Probabilistic classifiers, risk scoring models |
| **Benefit** | Does not require picking a threshold |

---

## Summary Comparison

| Metric | Focus Area | Ideal Value | Threshold-Dependent | Sensitive to Imbalance? |
|------------|----------------------|-------------|----------------------|--------------------------|
| Accuracy | Overall correctness | 1.0 | Yes | Yes |
| F1-Score | Precision + Recall | 1.0 | Yes | No |
| AUC | Class ranking | 1.0 | No | No |

---

## 📝 When to Use What?

| Scenario | Recommended Metric(s) |
|--------------------------------------|----------------------------|
| Balanced dataset | Accuracy |
| Imbalanced dataset (e.g. 1:10 ratio) | F1-Score, AUC |
| Need to rank predictions | AUC |
| Medical diagnosis | F1-Score (catch positives), AUC |
| Binary classification with class overlap | AUC, F1-Score |