ML Coding: Logistic Regression from Scratch

Implement core pieces of binary logistic regression from scratch. Given training data X (shape n x d) and labels y (0/1), implement: Forward pass: p = sigmoid(Xw + b) Loss: Binary Cross Entropy (log loss) Gradient descent updates for w, b Provide the mathematical definition of Binary Cross Entropy and explain why it is equivalent to minimizing the negative log-likelihood. Derive the derivative of sigmoid(z). Bonus Compute a confusion matrix (TP/FP/TN/FN) from ground-truth labels and predicted labels (or probabilities + threshold). Example Input 4 2 200 0.1 0 0 0 0 1 0 1 0 0 1 1 1 Output (parameters printed; values may vary depending on iterations/lr)