In classification problems, there's a tradeoff between precision and recall.

If you forgot what precision and recall are, here's a good analogy to recap.

Let's say you're fishing with a huge net. You cast it and catch 80 fishes out of the 100. That's 80% recall. However, you also catch 80 rocks in the process, that's 50% precision.

You can use a smaller net, and target a pocket of the lake with only fish and no rocks, but you only get 20 of the fish, but no rocks. That's 20% recall and 100% precision.

Get the idea?

Recall = what proportion of the things you catch are actually fish (true). (ex1: 80 / 100)

Precision = of those you catch, what proportion are fish. (ex1: 80 / 80 + 80)

To balance between these two metrics, we optimize the F1 score, which is their harmonic mean.

However, in some cases, precision would be more important than recall, and vice versa.

Here's where the F Beta scofe comes in handy.

We can adjust the value of Beta to assign higher weight to either precision or recall.

Below is a toy example.

from sklearn.metrics import fbeta_score

# define two models
y_true           = [1, 1, 1, 1, 1, 0, 0, 0, 0, 0] # half positive
y_pred_precision = [1, 1, 1, 0, 0, 0, 0, 0, 0, 0] # perfect precision, two false negatives
y_pred_recall    = [1, 1, 1, 1, 1, 1, 1, 1, 0, 0] # perfect recall, three false positives

perfect_precision = [y_true, y_pred_precision]
perfect_recall    = [y_true, y_pred_recall]

# the two models score similarly when beta = 1
print(fbeta_score(*perfect_precision, beta=1))
print(fbeta_score(*perfect_recall, beta=1))

# higher perfect precision scores
print(fbeta_score(*perfect_precision, beta=0.5))
print(fbeta_score(*perfect_recall, beta=0.5))

# higher perfect recall scores
print(fbeta_score(*perfect_precision, beta=2))
print(fbeta_score(*perfect_recall, beta=2))

The beta parameter determines the weight of recall in the combined score.

beta < 1 lends more weight to precision, while beta > 1 favors recall (beta -> 0 considers only precision, beta -> +inf only recall).