The Exponential Family and Generalized Linear Models

Two lessons ago the exact same gradient-ascent update rule appeared for two seemingly different problems — regression and classification — and the "reading the result" notes flagged this as no coincidence. This note explains why: both are instances of a single template, the generalized linear model (GLM), built from any distribution in the exponential family. Once this template is in hand, deriving a new model for a new output type (counts, categorical labels, non-negative durations) is mechanical rather than a fresh derivation each time.