Logistic Regression and Maximum Likelihood

Linear regression assumes a continuous, Gaussian-noise target — the wrong model for a binary outcome like "did this loan default?" This note builds the classification analogue: logistic regression, which reuses the MLE argument from Topic 1 with a Bernoulli, rather than Gaussian, label distribution, arriving at a different loss function (cross-entropy, not squared error) and an update rule that looks — not coincidentally — identical in form to LMS.