[{"data":1,"prerenderedAt":4},["ShallowReactive",2],{"FNFRG3RVQJ":3},"\u003Ch1 align=\"center\">StatsMLlib\u003C/h1>\n\n\u003Ch4 align=\"center\">Verified probability, statistics, and learning theory in Lean 4\u003C/h4>\n\n\u003Cp align=\"center\">\n  \u003Ca href=\"https://github.com/leanprover/lean4/releases/tag/v4.33.0\">\u003Cimg src=\"https://img.shields.io/badge/Lean-v4.33.0-blue?style=for-the-badge\" alt=\"Lean v4.33.0\">\u003C/a>\n  \u003Ca href=\"./LICENSE\">\u003Cimg src=\"https://img.shields.io/badge/License-Apache%202.0-lightgrey?style=for-the-badge\" alt=\"Apache 2.0\">\u003C/a>\n  \u003Ca href=\"https://statsmllib.github.io/\">\u003Cimg src=\"https://img.shields.io/badge/Website-StatsMLlib-175b47?style=for-the-badge\" alt=\"StatsMLlib website\">\u003C/a>\n\u003C/p>\n\nStatsMLlib is a reusable Lean 4 library for probability, high-dimensional statistics, empirical\nprocesses, and statistical learning theory. It is built on Mathlib and organized as a subject-first,\nacyclic hierarchy rather than around individual projects or proof techniques.\n\nThe public source contains 90 modules and no `sorry`, `axiom`, `admit`, or `native_decide`.\n\n## Scope\n\n| Layer | Module root | Contents |\n| --- | --- | --- |\n| Measure theory | `StatsMLlib.MeasureTheory.*` | Integral, convergence, and L1 infrastructure |\n| Topology | `StatsMLlib.Topology.*` | Covering and packing numbers, separable suprema |\n| Analysis | `StatsMLlib.Analysis.*` | Metric entropy, chaining, normed-space covering estimates |\n| Linear algebra | `StatsMLlib.LinearAlgebra.*` | Singular values, variational principles, matrix perturbation |\n| Probability | `StatsMLlib.Probability.*` | Concentration, entropy methods, Gaussian analysis, random matrices |\n| Learning theory | `StatsMLlib.LearningTheory.*` | Empirical metrics, Rademacher complexity, uniform deviation |\n| Statistics | `StatsMLlib.Statistics.*` | Localized least squares, regression, and minimax guarantees |\n\nThe dependency order is foundational measure theory, topology, and linear algebra; then analysis;\nprobability; learning theory; and statistics. See [ARCHITECTURE.md](./ARCHITECTURE.md) for the\nownership policy and [FILE_TREE.md](./FILE_TREE.md) for the complete module index.\n\n## Selected results\n\n- Dudley's entropy integral and truncated Dudley bounds for sub-Gaussian processes\n- Efron–Stein, Hoeffding, McDiarmid, scalar Bernstein, Gaussian Poincare, and Gaussian log-Sobolev inequalities\n- Gaussian Lipschitz concentration, Hanson–Wright, and matrix Bernstein inequalities\n- Singular-value decomposition, Courant–Fischer, Eckart–Young–Mirsky, Weyl, and Davis–Kahan\n  perturbation results\n- Symmetrization, Massart's lemma, Rademacher complexity, and uniform-deviation bounds\n- Localized least-squares theory for linear and L1-constrained regression\n\nRepresentative declarations include `dudley`, `truncated_dudley_entropy_bound`, `efronStein`,\n`gaussian_lipschitz_concentration`, `bernstein_inequality`, `hanson_wright_inequality`,\n`RMT.matrix_bernstein_inequality_hdp_all`, `expectation_le_rademacher`, and\n`master_error_bound`.\n\n## Getting started\n\nStatsMLlib is pinned to Lean and Mathlib `v4.33.0`.\n\n```bash\n# Optional: download the Mathlib build cache.\nlake exe cache get\n\n# Build every StatsMLlib module.\nLEAN_NUM_THREADS=$(nproc) lake build\n\n# Build an individual module.\nLEAN_NUM_THREADS=$(nproc) lake build StatsMLlib.Probability.Process.Dudley\n```\n\nTo use the `v4.33.0` release from another Lake project:\n\n```lean\nrequire «StatsMLlib» from git\n  \"https://github.com/Lean-MoDS/StatsMLlib.git\" @ \"v4.33.0\"\n```\n\nThen import only the modules needed by the project:\n\n```lean\nimport StatsMLlib.Probability.Concentration.HansonWright\nimport StatsMLlib.LearningTheory.UniformDeviation.Bounds\n```\n\n## Contributing\n\nRead [CONTRIBUTING.md](./CONTRIBUTING.md) and the\n[Code of Conduct](./CODE_OF_CONDUCT.md) before opening a change. New code must preserve the subject\nownership rules, source attribution, complete-proof policy, and warning-free build.\n\n## Authors, copyright, and provenance\n\nStatsMLlib unifies material developed in the former SLT and FoML trees. Files retain their original\ncopyright and author headers. See [AUTHORS.md](./AUTHORS.md) for the organizer and contributor lists\nand the repository's copyright, authorship, and co-authorship policy; the individual source headers\nremain authoritative for file-level attribution.\n\n## License\n\nStatsMLlib is released under the [Apache License 2.0](./LICENSE). Copyright remains with the individual\nholders identified in the source files.\n",1788128299585]