# Part II: Precision/Recall and Sensitivity/Specificity

In the previous article on evaluation metrics for classification problems we explained that accuracy is a very useful metric and very easy to interpret. However, if the dataset we have is not balanced, it will be completely useless.

We also defined what a confusion matrix is, in which we defined four categories among our predictions: True Positives, True Negatives, False Positives and False Negatives. We can use this information to evaluate our model despite having imbalanced data.

## Precision-Recall

On the one hand, **precision** indicates the proportion of the relevant or positive samples predicted by our model that are actually positive.

$$ \text{Precision} = \frac{TP}{TP + FP} $$

On the other hand, **recall** indicates the proportion of relevant or positive samples predicted by the model with respect to all the actual positive samples.

$$ \text{Recall} = \frac{TP}{TP + FN} $$

The following picture illustrates both metrics:

As mentioned before, these metrics are robust against imbalanced data. A way of taking both into account to evaluate the model is considering the **Fbeta-score**:

$$ F_{ \beta}\text{ -}score = \frac{(1 + \beta^2) \times Precision \times Recall}{\beta^2 \times Precision + Recall} $$

The Fbeta-score is defined as the harmonic mean of the precision and recall. The beta parameter can be tuned depending on the situation:

- If the objective of the analyst is to reduce the FP results, then a small beta should be chosen to increase the importance of the precision in the metric
- If the emphasis is made on reducing the FN, then a large beta must be selected to increase the relevance of the recall in the metric
- For achieving a balanced performance on both FP and FN, then beta equal to 1 will be the obvious value for beta. In this scenario, this metric receives the name of
**F1-score**(being the most common case) and the previous equation can be rewritten as:

$$ F_1\text{-}score = 2 \times \frac{Precision \times Recall}{Precision + Recall} $$

## Sensitivity-Specificity

Another way of evaluating a model is by means of sensitivity and specificity. These metrics are also robust against imbalanced datasets.

**Sensitivity** indicates how well the positive class was predicted and it is equivalent to the recall:

$$ \text{Sensitivity} = \frac{TP}{TP + FN} $$

**Specificity** is the complement metric and it indicates how well the negative class was predicted:

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

In the same way as with precision and recall, both metrics can be combined, this time with the so-called **geometric mean** or **G-Mean**:

$$ \text{G-Mean} = \sqrt{Sensitivity \times Specificity} $$

## 0 Comments