Younes — Introduction to Machine Learning

laurent-younes's graduate text from the Department of Applied Mathematics and Statistics at johns-hopkins-university, posted to arXiv as 2409.02668 (stat.ML, cs.LG) on 4 September 2024 and revised 13 May 2025 (v2, dated 15 May inside; 674 pages, CC BY 4.0). The held copy in raw/ is v2. Arrived by Telegram 2026-09-17.

What kind of book it is

The preface says so plainly: a viewpoint "mainly focused on the mathematical and statistical aspects of the subject," written so that a reader of the packages "will be able to assess their prerequisites and limitations, and to extend them." Measure theory is kept to a few marked places with elementary readings offered beside them. There are no exercises — the word does not occur in 674 pages — which puts it at the opposite end from lindholm-machine-learning-first-course's course-with-problems and from the corpus's textbook rule of thumb that the exercises carry the course.

The shape (23 chapters)

Three chapters of prerequisites — notation and background (linear algebra, topology, calculus, probability including the measure-theoretic case), matrix analysis (trace inequality, norms, low-rank approximation), and a 60-page optimization chapter that goes from descent and line search through SGD and Adam, Lagrange and KKT, subgradients and proximal methods, to duality, augmented Lagrangians and ADMM. Then the subject proper:

• Prediction (ch. 4–11): bias and variance via sieves and kernel density estimation; the Bayes predictor and empirical risk minimisation; reproducing kernels; linear regression; linear classification; nearest neighbours; trees; neural nets in one chapter of 18 pages.
• Generative and probabilistic methods (ch. 12–19): comparing distributions; Monte-Carlo sampling; Markov random fields and inference on them; Bayesian networks; latent variables and variational methods; learning graphical models; deep generative methods.
• Unsupervised (ch. 20–22): clustering (48 pages), factor analysis and dimension reduction (52 pages), manifold learning and visualisation.
• Theory (ch. 23): concentration inequalities and generalization bounds.

The weighting is the argument. Graphical models get ~140 pages and neural networks 18; "transformer" and "attention" appear, but as words inside the deep-generative chapter, not as a subject. This is statistical learning as a mathematician teaches it, with optimization as the engine and probability as the language, and deep learning as one method among the others.

What it adds here

The spoke's two textbooks were a first course for engineers (lindholm-machine-learning-first-course) and MacKay's information-theoretic route in (information-theory-inference-learning-algorithms). This is the third register: the graduate mathematical foundations, with the optimization theory the other two assume and the graphical-model tradition MacKay treats and Lindholm does not. For open question 4 (the middle layer) it supplies what Lindholm's syllabus lacked — the theory chapter that says why a learner generalizes, with bounds — and still nothing on pretraining, data or evaluation as practice, which stay unsourced. Cross-spoke: the optimization chapter overlaps optimization-algorithms-wiki's gradient-based corner and mathematics-wiki's textbook pedagogy line; neither should duplicate it.

Tier T1 — a full graduate text by a named academic, openly licensed, held in full.

Related

laurent-younes · johns-hopkins-university · lindholm-machine-learning-first-course · information-theory-inference-learning-algorithms · fine-tuning · synthesis