Lecture 9 models P(y=1|x) with a sigmoid instead of directly predicting 0 or 1, learns parameters with cross-entropy and convex optimization, and extends naturally to softmax regression.
Week 3 connects text features, sigmoid probabilities, cross-entropy loss, and gradient descent, producing a classifier whose feature contributions remain inspectable.
Chapter 2 derives logistic loss from a sigmoid probability model, then contrasts it with the perceptron and extends it through softmax and Newton's method.
HW4 joins probabilistic interpretation, cross-entropy gradients, and implementation into one traceable training pipeline.