ReadTheDocs

README.md

@@ -1,5 +1,8 @@
 # ML Formulas
-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
+
+理論計算科学・機械学習・統計学などに出てくる等式・不等式を集めています．
+
+ページは[こちら](https://ml-formulas.readthedocs.io/ja/latest/index.html)
 
 # 運用方法
 
@@ -10,7 +13,6 @@ GitHubのIssueで管理しています．1つのトピック（不等式・等
 * 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）
 * 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．
 
-
 # 今後やりたいこと
 
 * Twitter Bot化
@@ -21,36 +23,36 @@ Contribution welcome!
 
 * 機械学習・統計的学習理論
   * 集中不等式
-    * [Markovの不等式](src/markov_inequality.md)
-    * [Chebyshevの不等式](src/chebyshev_inequality.md)
-    * [Chernoff bound](src/chernoff_bound.md)
-    * [Hoeffdingの不等式](src/hoeffding_inequality.md)
-    * [Bennetの不等式](src/bennett_inequality.md)
-    * [Bernsteinの不等式](src/bernstein_inequality.md)
-    * [Poisson分布の生成母関数とそのCramer変換](src/poisson_moment_generating_function.md)
-    * [Bernsteinの不等式](src/bernstein_inequality.md)
+    * [Markovの不等式](docs/source/concentration/markov_inequality.md)
+    * [Chebyshevの不等式](docs/source/concentration/chebyshev_inequality.md)
+    * [Chernoff bound](docs/source/concentration/chernoff_bound.md)
+    * [Hoeffdingの不等式](docs/source/concentration/hoeffding_inequality.md)
+    * [Bennetの不等式](docs/source/concentration/bennett_inequality.md)
+    * [Bernsteinの不等式](docs/source/concentration/bernstein_inequality.md)
+    * [Poisson分布の生成母関数とそのCramer変換](docs/source/concentration/poisson_moment_generating_function.md)
+    * [Bernsteinの不等式](docs/source/concentration/bernstein_inequality.md)
     * Azuma's inequality
-    * [最大不等式](src/maximal_inequality.md)
-    * [Dudleyのエントロピーバウンド](src/dudley_entropy_bound.md)
-    * [Sudakov minoration](src/sudakov_minoration.md)
-    * [Generic chaining](src/generic_chaining.md)
+    * [最大不等式](docs/source/concentration/maximal_inequality.md)
+    * [Dudleyのエントロピーバウンド](docs/source/concentration/dudley_entropy_bound.md)
+    * [Sudakov minoration](docs/source/concentration/sudakov_minoration.md)
+    * [Generic chaining](docs/source/concentration/generic_chaining.md)
     * Talagrand's inequality
     * Symmetrization
-    * [Efron--Stein不等式](src/efron_stein.md)
-    * [エントロピーの劣加法性](src/subadditivity_of_entropy.md)
+    * [Efron--Stein不等式](docs/source/concentration/efron_stein.md)
+    * [エントロピーの劣加法性](docs/source/concentration/subadditivity_of_entropy.md)
     * Log-Sobolev inequality
-    * [Gauss集中不等式](src/gaussian_concentration_inequality.md)
+    * [Gauss集中不等式](docs/source/concentration/gaussian_concentration_inequality.md)
     * Modified Log-Sobolev inequality
     * McDiarmid's inequality (Bounded difference inequality)
   * Donsker's variational representation of KL divergence
   * ブーリアン関数
-    * [Hypercontractive不等式](src/hypercontractive_inequality.md)
+    * [Hypercontractive不等式](docs/source/boolean/hypercontractive_inequality.md)
     * Kahn--Kalai--Linial（KKL）不等式
     * Majority is the stablest定理
   * Isoperimetric inequality
   * 凸幾何学
-    * [Brunn-Minkowskiの不等式](src/brunn_minkowski_inequality.md)
-    * [Prekopa-Leindlerの不等式](src/prekopa_leindler_inequality.md)
+    * [Brunn-Minkowskiの不等式](docs/source/convex_geometry/brunn_minkowski_inequality.md)
+    * [Prekopa-Leindlerの不等式](docs/source/convex_geometry/prekopa_leindler_inequality.md)
     * Andersonの不等式
   * 情報理論
     * Fano inequality
@@ -66,10 +68,10 @@ Contribution welcome!
     * Luo-Tseng error bound
     * Lojasiewicz不等式
 * 確率論
-  * [Slepianの不等式](src/slepian_inequality.md)
+  * [Slepianの不等式](docs/source/probability/slepian_inequality.md)
   * Gaussian correlation inequality
-  * [Berry--Esseenの定理](src/berry_esseen_univariate.md)
-  * [Dvoretzky--Kiefer--Wolfowitzの不等式](src/dvoretzky_kiefer_wolfowitz_inequality.md)
+  * [Berry--Esseenの定理](docs/source/probability/berry_esseen_univariate.md)
+  * [Dvoretzky--Kiefer--Wolfowitzの不等式](docs/source/probability/dvoretzky_kiefer_wolfowitz_inequality.md)
 * 確率過程・確率微分方程式
   * Doobの不等式
   * Borel-Cantelliの定理

docs/.gitignore

@@ -0,0 +1,2 @@
+build
+__pycache__

docs/Makefile

@@ -0,0 +1,20 @@
+# Minimal makefile for Sphinx documentation
+#
+
+# You can set these variables from the command line.
+SPHINXOPTS    =
+SPHINXBUILD   = python -msphinx
+SPHINXPROJ    = ml-formulas
+SOURCEDIR     = source
+BUILDDIR      = build
+
+# Put it first so that "make" without argument is like "make help".
+help:
+	@$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
+
+.PHONY: help Makefile
+
+# Catch-all target: route all unknown targets to Sphinx using the new
+# "make mode" option.  $(O) is meant as a shortcut for $(SPHINXOPTS).
+%: Makefile
+	@$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)

docs/make.bat

@@ -0,0 +1,36 @@
+@ECHO OFF
+
+pushd %~dp0
+
+REM Command file for Sphinx documentation
+
+if "%SPHINXBUILD%" == "" (
+	set SPHINXBUILD=python -msphinx
+)
+set SOURCEDIR=source
+set BUILDDIR=build
+set SPHINXPROJ=ml-formulas
+
+if "%1" == "" goto help
+
+%SPHINXBUILD% >NUL 2>NUL
+if errorlevel 9009 (
+	echo.
+	echo.The Sphinx module was not found. Make sure you have Sphinx installed,
+	echo.then set the SPHINXBUILD environment variable to point to the full
+	echo.path of the 'sphinx-build' executable. Alternatively you may add the
+	echo.Sphinx directory to PATH.
+	echo.
+	echo.If you don't have Sphinx installed, grab it from
+	echo.http://sphinx-doc.org/
+	exit /b 1
+)
+
+%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS%
+goto end
+
+:help
+%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS%
+
+:end
+popd

docs/source/_static/mathjaxconf.js

@@ -0,0 +1,6 @@
+window.MathJax = {
+    tex2jax: {
+	inlineMath: [['$','$'], ['\\(', '\\)']],
+	processEscapes: true
+    }
+};

docs/source/_templates/layout.html

@@ -0,0 +1,2 @@
+{% extends "!layout.html" %}
+{% set script_files = ["_static/mathjaxconf.js"] + script_files %}

docs/source/boolean/index.rst

@@ -0,0 +1,7 @@
+ブーリアン関数
+==============
+
+.. toctree::
+   :maxdepth: 1
+
+   hypercontractive_inequality.md

src/generic_chaining.md → docs/source/concentration/generic_chaining.md

@@ -8,7 +8,7 @@ $(T, d)$ を距離空間とする．
 
 $T$ の部分集合 $A$ の直径を $\mathrm{diam}(A) = \sup\_{s, t \in A} d(s, t)$ と表す．
 
-$T$ の分割 $\mathcal{A}$ とは，互いに交わらない $T$ の有限個の部分集合の族 $\mathcal{A} = \\{ A\_1, \ldots, A\_m \\}$ で，$\bigcup\_i A\_i = T$ となるものである．$T$ の分割 $\mathcal{A}$ および点 $t \in T$ に対して，$\mathcal{A}(t)$ によって $t$ を含む $\mathcal{A}$ の唯一の要素を表すとする．
+$T$ の分割 $\mathcal{A}$ とは，互いに交わらない $T$ の有限個の部分集合の族 $\mathcal{A} = \{ A_1, \ldots, A_m \}$ で，$\bigcup\_i A\_i = T$ となるものである．$T$ の分割 $\mathcal{A}$ および点 $t \in T$ に対して，$\mathcal{A}(t)$ によって $t$ を含む $\mathcal{A}$ の唯一の要素を表すとする．
 
 $T$ の分割からなる列 $\mathcal{A}_0, \mathcal{A}\_1, \ldots$ がネストしているとは，任意の $k \geq 1$ に対して $\mathcal{A}\_{k}$ が $\mathcal{A}\_{k-1}$ の細分になっていることをいう．
 分割の列 $\mathcal{A}\_{0}, \mathcal{A}\_{1}, \ldots$ がTalagrand列 (または許容列) であるとは，任意の $k \geq 1$ に対して，

docs/source/concentration/index.rst

@@ -0,0 +1,22 @@
+集中不等式
+==========
+
+.. toctree::
+   :maxdepth: 1
+
+   markov_inequality.md
+   chebyshev_inequality.md
+   chernoff_bound.md
+   hoeffding_inequality.md
+   bennett_inequality.md
+   bernstein_inequality.md
+   poisson_moment_generating_function.md
+   bernstein_inequality.md
+   maximal_inequality.md
+   dudley_entropy_bound.md
+   sudakov_minoration.md
+   generic_chaining.md
+   efron_stein.md
+   subadditivity_of_entropy.md
+   gaussian_concentration_inequality.md
+

docs/source/conf.py

@@ -0,0 +1,179 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+#
+# ml-formulas documentation build configuration file, created by
+# sphinx-quickstart on Sat Jun 30 22:46:42 2018.
+#
+# This file is execfile()d with the current directory set to its
+# containing dir.
+#
+# Note that not all possible configuration values are present in this
+# autogenerated file.
+#
+# All configuration values have a default; values that are commented out
+# serve to show the default.
+
+# If extensions (or modules to document with autodoc) are in another directory,
+# add these directories to sys.path here. If the directory is relative to the
+# documentation root, use os.path.abspath to make it absolute, like shown here.
+#
+import os
+import sys
+sys.path.insert(0, os.path.abspath('.'))
+
+from recommonmark.parser import CommonMarkParser
+
+source_parsers = {
+    '.md': CommonMarkParser,
+}
+
+# -- General configuration ------------------------------------------------
+
+# If your documentation needs a minimal Sphinx version, state it here.
+#
+# needs_sphinx = '1.0'
+
+# Add any Sphinx extension module names here, as strings. They can be
+# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
+# ones.
+extensions = ['mathjax']
+mathjax_path = 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.3/MathJax.js?config=TeX-AMS-MML_HTMLorMML'
+
+# Add any paths that contain templates here, relative to this directory.
+templates_path = ['_templates']
+
+# The suffix(es) of source filenames.
+# You can specify multiple suffix as a list of string:
+#
+source_suffix = ['.rst', '.md']
+# source_suffix = '.rst'
+
+# The master toctree document.
+master_doc = 'index'
+
+# General information about the project.
+project = 'ml-formulas'
+copyright = '2018, Kenta Oono'
+author = 'Kenta Oono'
+
+# The version info for the project you're documenting, acts as replacement for
+# |version| and |release|, also used in various other places throughout the
+# built documents.
+#
+# The short X.Y version.
+version = ''
+# The full version, including alpha/beta/rc tags.
+release = ''
+
+# The language for content autogenerated by Sphinx. Refer to documentation
+# for a list of supported languages.
+#
+# This is also used if you do content translation via gettext catalogs.
+# Usually you set "language" from the command line for these cases.
+language = 'ja'
+
+# List of patterns, relative to source directory, that match files and
+# directories to ignore when looking for source files.
+# This patterns also effect to html_static_path and html_extra_path
+exclude_patterns = []
+
+# The name of the Pygments (syntax highlighting) style to use.
+pygments_style = 'sphinx'
+
+# If true, `todo` and `todoList` produce output, else they produce nothing.
+todo_include_todos = False
+
+
+# -- Options for HTML output ----------------------------------------------
+
+# The theme to use for HTML and HTML Help pages.  See the documentation for
+# a list of builtin themes.
+#
+# html_theme = 'alabaster'
+html_theme = 'sphinx_rtd_theme'
+
+# Theme options are theme-specific and customize the look and feel of a theme
+# further.  For a list of options available for each theme, see the
+# documentation.
+#
+# html_theme_options = {}
+
+# Add any paths that contain custom static files (such as style sheets) here,
+# relative to this directory. They are copied after the builtin static files,
+# so a file named "default.css" will overwrite the builtin "default.css".
+html_static_path = ['_static']
+
+# Custom sidebar templates, must be a dictionary that maps document names
+# to template names.
+#
+# This is required for the alabaster theme
+# refs: http://alabaster.readthedocs.io/en/latest/installation.html#sidebars
+html_sidebars = {
+    '**': [
+        'about.html',
+        'navigation.html',
+        'relations.html',  # needs 'show_related': True theme option to display
+        'searchbox.html',
+        'donate.html',
+    ]
+}
+
+
+# -- Options for HTMLHelp output ------------------------------------------
+
+# Output file base name for HTML help builder.
+htmlhelp_basename = 'ml-formulasdoc'
+
+
+# -- Options for LaTeX output ---------------------------------------------
+
+latex_elements = {
+    # The paper size ('letterpaper' or 'a4paper').
+    #
+    # 'papersize': 'letterpaper',
+
+    # The font size ('10pt', '11pt' or '12pt').
+    #
+    # 'pointsize': '10pt',
+
+    # Additional stuff for the LaTeX preamble.
+    #
+    # 'preamble': '',
+
+    # Latex figure (float) alignment
+    #
+    # 'figure_align': 'htbp',
+}
+
+# Grouping the document tree into LaTeX files. List of tuples
+# (source start file, target name, title,
+#  author, documentclass [howto, manual, or own class]).
+latex_documents = [
+    (master_doc, 'ml-formulas.tex', 'ml-formulas Documentation',
+     'Kenta Oono', 'manual'),
+]
+
+
+# -- Options for manual page output ---------------------------------------
+
+# One entry per manual page. List of tuples
+# (source start file, name, description, authors, manual section).
+man_pages = [
+    (master_doc, 'ml-formulas', 'ml-formulas Documentation',
+     [author], 1)
+]
+
+
+# -- Options for Texinfo output -------------------------------------------
+
+# Grouping the document tree into Texinfo files. List of tuples
+# (source start file, target name, title, author,
+#  dir menu entry, description, category)
+texinfo_documents = [
+    (master_doc, 'ml-formulas', 'ml-formulas Documentation',
+     author, 'ml-formulas', 'One line description of project.',
+     'Miscellaneous'),
+]
+
+import tex_macro
+mathjax_preamble = tex_macro.macro

docs/source/convex_geometry/index.rst

@@ -0,0 +1,8 @@
+凸幾何学
+========
+
+.. toctree::
+   :maxdepth: 1
+
+   brunn_minkowski_inequality.md
+   prekopa_leindler_inequality.md