test_gibbs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 基本的なStochastic BlockModels(SBM)の事後分布計算\n",
    "\n",
    "Stochastic BlockModels(確率的ブロックモデル, SBM)は、対称/非対称グラフの両方へ適用可能な確率モデルであり、 **ノードのクラスタリングが推論可能なモデルである。** 基本的なSBMでは、具体的に以下のような状況を考える。\n",
    "\n",
    "## 対称グラフの場合のイメージ\n",
    "\n",
    "1. ある学校に $N$ 人の生徒がいて、 $N$ 人の交友関係を考えるとする\n",
    "1. アンケート等で調査した結果、生徒 $i$ と生徒 $j$ が友人関係とわかった場合、 $x_{ij} = 1$ とする\n",
    "1. 逆に生徒 $i$ と生徒 $j$ の間で交流がない場合は $x_{ij} = 0$ とする\n",
    "1. 学校内には $K$ 個のコミュニティがあると仮定する\n",
    "1. 各生徒は $K$ 個のコミュニティのうちの1つのみに属していると仮定する\n",
    "1. 生徒 $i$ と生徒 $j$ の交友関係は、生徒 $i$ の属するコミュニティと生徒 $j$ の属するコミュニティの関係で近似されると仮定する\n",
    "\n",
    "この状況で「各生徒はどのコミュニティに属しているか」を推論することが、SBMの目的の1つ。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "using LinearAlgebra, Distributions, Random, PGFPlotsX;\n",
    "using SpecialFunctions, Clustering;\n",
    "using ProgressMeter;\n",
    "using Mamba;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## データの生成\n",
    "\n",
    "前述の状況と同じ設定でデータ生成を行う。\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "  N &\\coloneqq 50,\n",
    "\\\\\n",
    "  K &\\coloneqq 4,\n",
    "\\\\\n",
    "  z=\\left(z_1,\\dots, z_N \\right) &\\quad \\text{$z_i\\in \\left\\{1,\\dots, K\\right\\}$は生徒 $i$ がどのコミュニティに属するかを表す},\n",
    "\\\\\n",
    "  \\Theta = \\left( \\theta_{kl} \\right) \\in \\mathbb{R}^{N\\times N}\n",
    "    &\\quad \\text{$\\theta_{kl}$ はコミュニティ $k$ とコミュニティ $l$ の人間同士で友人関係となる確率を表す。$\\theta_{lk} = \\theta_{kl}$}\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "Random.seed!(123);\n",
    "N = 50;\n",
    "K = 4;\n",
    "\n",
    "α₀ = ones(Int, K);\n",
    "a₀ = 1.0;\n",
    "b₀ = 1.0;\n",
    "\n",
    "γ = Dirichlet(α₀) |> rand;\n",
    "z = rand(Categorical(γ), N);\n",
    "Θ = zeros(K,K);\n",
    "for k in 1:K\n",
    "  for l in k:K\n",
    "    Θ[k,l] = Beta(a₀, b₀) |> rand;\n",
    "  end\n",
    "end\n",
    "for k in 1:K\n",
    "  for l in 1:k-1\n",
    "    Θ[k,l] = Θ[l,k];\n",
    "  end\n",
    "end\n",
    "\n",
    "X = zeros(Int, N, N);\n",
    "for i in 1:N\n",
    "  for j in i+1:N\n",
    "    X[i,j] = Bernoulli(Θ[z[i], z[j]]) |> rand |> Int;\n",
    "  end\n",
    "end\n",
    "X = X + X';"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 生成データの可視化\n",
    "\n",
    "黒色が友人関係であることを表し、白色は友人関係でないことを表す。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
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