Syllabus Map

• Study map: Syllabus Study Map

Core Idea

• Likelihood treats parameters as unknowns and observed data as fixed.
• MLE picks parameters that maximize observed-data likelihood.

Key Formula

Usually optimize:

Why This Matters for ML

• MLE is the statistical foundation of many classical ML estimators.
• Log-likelihood turns products into sums, enabling stable optimization and gradient methods.
• Logistic regression and many generative models are trained by maximizing likelihood objectives.
• Understanding likelihood is key for comparing models and defining principled losses.