Logistic regression — classify at a threshold

Background

A logistic-regression model outputs a probability $p = \mathbb{P}(y=1 \mid \mathbf{x}) \in (0, 1)$. To turn that into a hard class label you compare it to a threshold — by default $0.5$:

$$\hat{y} = \begin{cases} 1 & p \ge t \\ 0 & p < t \end{cases}$$

The default $t = 0.5$ is the neutral choice; raising or lowering it trades precision against recall.

Problem statement

Implement classify(probs, threshold=0.5) that converts predicted probabilities into 0/1 labels, predicting class 1 when $p \ge t$.

Input

• probs — array-like of probabilities in $[0, 1]$.
• threshold — float, default 0.5. Predict class 1 when $p \ge \text{threshold}$.

Output

Returns an np.ndarray of integer labels (0 or 1), the same length as probs.

Examples

Example 1 — default 0.5 threshold

Input:  probs = [0.2, 0.5, 0.8, 0.49, 0.51]
Output: [0 1 1 0 1]

Explanation: $0.5 \ge 0.5$ so it rounds up to class 1; $0.49 < 0.5$ stays class 0.

Example 2 — stricter threshold

Input:  probs = [0.2, 0.5, 0.8, 0.49, 0.51], threshold = 0.7
Output: [0 0 1 0 0]

Explanation: only $0.8$ clears the higher bar of $0.7$.

Constraints

• Use >= so a probability exactly at the threshold is class 1.
• Return integer labels (0/1), not booleans or floats.

Notes

• The threshold is a decision knob, separate from the model. Shifting it changes which mistakes you make (false positives vs false negatives) without retraining.