High-Dimensional Statistics (arxiv.org)

Philippe Rigollet has posted a comprehensive set of lecture notes for MIT’s course 18.657, "High-Dimensional Statistics," on arXiv, updating material originally prepared at Princeton in 2013–14. The notes are a rigorous, course-length treatment of the mathematical foundations that underpin modern high-dimensional inference and learning; the arXiv entry also links to associated demos and supplementary media that can aid hands‑on study. For the AI/ML community this is a valuable reference: it synthesizes non-asymptotic statistical tools and conceptual frameworks that are essential when dimensionality rivals or exceeds sample size. Key technical building blocks covered (and central to contemporary research) include concentration inequalities, random matrix theory, minimax risk ideas, and the analysis of regularized M‑estimators — the theory behind sparsity-promoting methods like Lasso, compressed sensing, and low‑rank matrix recovery. By collecting proofs, error bounds, and examples in one place, the notes help practitioners and researchers translate statistical guarantees into design and evaluation choices (sample complexity, tuning/regularization, uncertainty quantification) for high‑dimensional models used across ML applications.