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# System prepended metadata

title: Accuracy

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# 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) |

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## 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                          |

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## 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             |

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## 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                    |

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## 📝 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       |