Evaluate the performance of a classification model using F2 score

The F2 score is a metric used to evaluate the performance of a classification model. It is a balance between precision and recall, with a higher weight given to recall. The F2 score can be calculated using the following formula:

F2 = (5 * recall * precision) / (4 * recall + precision)

The F2 score is often used in situations where false negatives (items that should have been classified as positive but were classified as negative) are more costly than false positives. This is because the F2 score puts more emphasis on recall, which is the number of true positives divided by the sum of the true positives and false negatives.

In the context of this competition, the F2 score will be calculated for each predicted row, and then the mean F2 score will be calculated by averaging all of the individual F2 scores. This means that the overall performance of the model will be evaluated by considering the F2 score for each individual prediction, rather than just looking at the overall accuracy of the model.

Implement the F2 score in Python

To implement the F2 score in Python, you will need to calculate the precision and recall for each class, then combine them using the F2 formula provided above. Here is an example of how this could be done:

def f2_score(y_true, y_pred):
    # Calculate the precision and recall for each class
    precisions = []
    recalls = []
    for i in range(n_classes):
        # Calculate the precision for class i
        true_positives = sum((y_pred == i) & (y_true == i))
        false_positives = sum((y_pred == i) & (y_true != i))
        precision = true_positives / (true_positives + false_positives)
        precisions.append(precision)

        # Calculate the recall for class i
        true_positives = sum((y_pred == i) & (y_true == i))
        false_negatives = sum((y_pred != i) & (y_true == i))
        recall = true_positives / (true_positives + false_negatives)
        recalls.append(recall)

    # Calculate the mean F2 score
    f2_scores = []
    for i in range(n_classes):
        f2 = (5 * recalls[i] * precisions[i]) / (4 * recalls[i] + precisions[i])
        f2_scores.append(f2)
    mean_f2 = sum(f2_scores) / n_classes
    return mean_f2

In this example, y_true and y_pred are the true labels and predicted labels for the data, respectively. n_classes is the number of unique classes in the data. The F2 score is calculated for each class and then averaged to get the mean F2 score.

It is important to note that this implementation assumes that the classes are balanced, meaning that there are roughly equal numbers of samples in each class. If the classes are imbalanced, you may need to use a different metric, such as the F1 score or the Matthews correlation coefficient (MCC), which are more robust to imbalanced classes.