Please explain what a confusion matrix is.
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Confusion matrix

The confusion matrix is a representation of Model classification metrics.

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Implementation

from sklearn.metrics import classification_report

y_bin_preds = np.array(y_pred) > 0.5
print("Confusion Matrix:\n", classification_report(y_test, y_bin_preds, target_names=["pos", "neg"])) # target names: 0, 1, 2, ..., str labels in that order

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Please provide the formulas for Accuracy, Precision and Recall. Please also explain when to use each.
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Formulas

Metric	Formula	Description	Pros / Cons / Use Case
Accuracy	$\frac{c o r r e c t_p r e d i c t i o n s}{a l l_p r e d i c t i o n s}$	The proportion of total predictions that were correct. See implementation example.	Simple but it is misleading if the dataset is imbalanced!
Precision	$\frac{T P}{T P + F P}$	The proportion of positive predictions that were actually correct.	Use when false positives are costly. Example: Spam detection
Recall	$\frac{T P}{T P + F N}$	The proportion of actual positives that were correctly identified.	Use when false negatives are costly. Example: medical diagnose
F1 Score	$\frac{2 \times p r e c i s i o n \times r e c a l l}{p r e c i s i o n + r e c a l l}$	A balance of Precision and Recall, all in one metric.	Considers both FP and FN. If the model fails in either direction, it will give a bad score; ideal for imbalanced datasets.
If you are interested in more than the True/False prediction, you want predictions that take the models performance into account. If these are differentiable, then they can be and are used as Loss functions

Please provide the formula for the f1 score and when to use it.
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Formulas

Metric	Formula	Description	Pros / Cons / Use Case
Accuracy	$\frac{c o r r e c t_p r e d i c t i o n s}{a l l_p r e d i c t i o n s}$	The proportion of total predictions that were correct. See implementation example.	Simple but it is misleading if the dataset is imbalanced!
Precision	$\frac{T P}{T P + F P}$	The proportion of positive predictions that were actually correct.	Use when false positives are costly. Example: Spam detection
Recall	$\frac{T P}{T P + F N}$	The proportion of actual positives that were correctly identified.	Use when false negatives are costly. Example: medical diagnose
F1 Score	$\frac{2 \times p r e c i s i o n \times r e c a l l}{p r e c i s i o n + r e c a l l}$	A balance of Precision and Recall, all in one metric.	Considers both FP and FN. If the model fails in either direction, it will give a bad score; ideal for imbalanced datasets.
If you are interested in more than the True/False prediction, you want predictions that take the models performance into account. If these are differentiable, then they can be and are used as Loss functions