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ML Formulas\n理論計算科学・機械学習・統計学などに出てくる等式・不等式を集めていきます\n\n# 運用方法\n\nGitHubのIssueで管理しています．1つのトピック（不等式・等式・定理など）に対して1つのMarkdownファイルを用意し，そこに「ステートメント」「証明の概要」「コメント」「出典」などを簡潔にまとめます．\n\n# How to contribute\n\n* ほしいエントリがある場合は「Issues」から新たなIssueから希望を挙げてください（エントリのドラフトもあるとベターです）\n* 既にあるエントリで誤植を見つけた場合にはIssueとして登録するか，Pull Requestで修正を送ってください．\n\n\n# 今後やりたいこと\n\n* Twitter Bot化\n\n# 今後登録を検討している数式リスト\n\nContribution welcome!\n\n* 機械学習・統計的学習理論\n  * 集中不等式\n    * [Markovの不等式](src/markov_inequality.md)\n    * [Chebyshevの不等式](src/chebyshev_inequality.md)\n    * [Chernoff bound](src/chernoff_bound.md)\n    * [Hoeffdingの不等式](src/hoeffding_inequality.md)\n    * [Bennetの不等式](src/bennett_inequality.md)\n    * [Bernsteinの不等式](src/bernstein_inequality.md)\n    * [Poisson分布の生成母関数とそのCramer変換](src/poisson_moment_generating_function.md)\n    * [Bernsteinの不等式](src/bernstein_inequality.md)\n    * Azuma's inequality\n    * [最大不等式](src/maximal_inequality.md)\n    * [Dudleyのエントロピーバウンド](src/dudley_entropy_bound.md)\n    * [Sudakov minoration](src/sudakov_minoration.md)\n    * [Generic chaining](src/generic_chaining.md)\n    * Talagrand's inequality\n    * Symmetrization\n    * [Efron--Stein不等式](src/efron_stein.md)\n    * [エントロピーの劣加法性](src/subadditivity_of_entropy.md)\n    * Log-Sobolev inequality\n    * [Gauss集中不等式](src/gaussian_concentration_inequality.md)\n    * Modified Log-Sobolev inequality\n    * McDiarmid's inequality (Bounded difference inequality)\n  * Donsker's variational representation of KL divergence\n  * ブーリアン関数\n    * [Hypercontractive不等式](src/hypercontractive_inequality.md)\n    * Kahn--Kalai--Linial（KKL）不等式\n    * Majority is the stablest定理\n  * Isoperimetric inequality\n  * 凸幾何学\n    * [Brunn-Minkowskiの不等式](src/brunn_minkowski_inequality.md)\n    * [Prekopa-Leindlerの不等式](src/prekopa_leindler_inequality.md)\n    * Andersonの不等式\n  * 情報理論\n    * [Fanoの不等式](src/fano_inequality.md)\n    * [Pinskerの不等式](src/pinsker_inequality.md)\n    * Birgeの不等式\n    * [Le Camの不等式](src/le_cam_inequality.md)\n    * Data processing inequality\n    * Strong data processing inequality\n  * 凸解析\n    * Jensen's inequality\n    * 種々の双対定理\n    * KKT条件 (学習理論のバウンドを出すときに0次最適性よりタイトになる傾向)\n    * Luo-Tseng error bound\n    * Lojasiewicz不等式\n* 確率論\n  * [Slepianの不等式](src/slepian_inequality.md)\n  * Gaussian correlation inequality\n  * [Berry--Esseenの定理](src/berry_esseen_univariate.md)\n  * [Dvoretzky--Kiefer--Wolfowitzの不等式](src/dvoretzky_kiefer_wolfowitz_inequality.md)\n* 確率過程・確率微分方程式\n  * Doobの不等式\n  * Borel-Cantelliの定理\n  * Levyの不等式\n  * 重複対数の法則\n* 統計学\n  * Cramer-Rao bound系 (オリジナル1変数版，Bhattacharya)\n  * Steinのパラドックス\n  * ミニマックスリスク \u003e= ベイズリスク\n  * [ミニマックス理論におけるLe Camの方法](src/le_cam_method.md)\n  * 分類問題のBayes errorをBhattacharya affinityとかchi^2-divergenceで抑えるもの (名前不明)\n* 関数解析\n  * Holder inequality\n  * Sobolev embedding\n  * Fatou's lemma\n  * 優収束定理\n  * 単調収束定理\n  * 項別微分\n  * 期待値を確率の積分で表示\n  * Kinchin-type inequality\n  * Poincare inequality\n  * Radon-Nikodymの定理\n* 線形代数\n  * Min-max theorem\n  * Cauchy's interacing theorem\n* elementaryな不等式\n  * 1 + x =\u003c e^x, a^2 + b^2 \u003e= abのような時々使う不等式\n* スペクトル理論\n  * Cheeger inequality\n* Majorization inequality系\n  * Muirheadの不等式\n* Koksma-Hlawka inequality (quai-Monte Carlo法に関係)\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdelta2323%2Fml-formulas","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fdelta2323%2Fml-formulas","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdelta2323%2Fml-formulas/lists"}