Decision Boundary & Metrics

Decision Boundary & Classification Metrics

A logistic regression model outputs a probability $\hat{p} \in (0,1)$. To make a hard prediction (0 or 1) we apply a threshold $\tau$ (usually 0.5):

$\hat{y} = \begin{cases} 1 & \text{if } \hat{p} \geq \tau \\ 0 & \text{otherwise} \end{cases}$

Evaluation Metrics

Once we have hard predictions we can measure quality with:

where TP = true positives, TN = true negatives, FP = false positives, FN = false negatives.

Zero-division: if the denominator is zero, return 0.0.

Your Task

Implement:

• classify(x, w, b, threshold=0.5) → 0 or 1
• accuracy(y_pred, y_true) → fraction of correct predictions
• precision(y_pred, y_true) → TP / (TP + FP), 0.0 on zero-division
• recall(y_pred, y_true) → TP / (TP + FN), 0.0 on zero-division