GPLVMwithSCG.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 基本的なGPLVMの実装\n",
    "\n",
    "本資料は『ガウス過程と機械学習』に記載されるGPLVMのうち、最も基本的なものの実装メモです。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 前準備. 環境設定\n",
    "\n",
    "本資料は以下の環境で実行しています。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Julia Version 1.4.2\n",
      "Commit 44fa15b150* (2020-05-23 18:35 UTC)\n",
      "Platform Info:\n",
      "  OS: Linux (x86_64-pc-linux-gnu)\n",
      "  CPU: Intel(R) Core(TM) i5-8400 CPU @ 2.80GHz\n",
      "  WORD_SIZE: 64\n",
      "  LIBM: libopenlibm\n",
      "  LLVM: libLLVM-8.0.1 (ORCJIT, skylake)\n",
      "Environment:\n",
      "  JULIA_NUM_THREADS = 6\n"
     ]
    }
   ],
   "source": [
    "versioninfo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1mStatus\u001b[22m\u001b[39m `~/.julia/environments/v1.4/Project.toml`\n",
      " \u001b[90m [c52e3926]\u001b[39m\u001b[37m Atom v0.12.15\u001b[39m\n",
      " \u001b[90m [ad839575]\u001b[39m\u001b[37m Blink v0.12.3\u001b[39m\n",
      " \u001b[90m [d38c429a]\u001b[39m\u001b[37m Contour v0.5.3\u001b[39m\n",
      " \u001b[90m [a93c6f00]\u001b[39m\u001b[37m DataFrames v0.21.2\u001b[39m\n",
      " \u001b[90m [31c24e10]\u001b[39m\u001b[37m Distributions v0.23.4\u001b[39m\n",
      " \u001b[90m [e30172f5]\u001b[39m\u001b[37m Documenter v0.24.11\u001b[39m\n",
      " \u001b[90m [35a29f4d]\u001b[39m\u001b[37m DocumenterTools v0.1.6\u001b[39m\n",
      " \u001b[90m [f6369f11]\u001b[39m\u001b[37m ForwardDiff v0.10.10\u001b[39m\n",
      " \u001b[90m [34004b35]\u001b[39m\u001b[37m HypergeometricFunctions v0.2.3\u001b[39m\n",
      " \u001b[90m [7073ff75]\u001b[39m\u001b[37m IJulia v1.21.2\u001b[39m\n",
      " \u001b[90m [033835bb]\u001b[39m\u001b[37m JLD2 v0.1.13\u001b[39m\n",
      " \u001b[90m [e5e0dc1b]\u001b[39m\u001b[37m Juno v0.8.2\u001b[39m\n",
      " \u001b[90m [b964fa9f]\u001b[39m\u001b[37m LaTeXStrings v1.1.0\u001b[39m\n",
      " \u001b[90m [5424a776]\u001b[39m\u001b[37m Mamba v0.12.4\u001b[39m\n",
      " \u001b[90m [8314cec4]\u001b[39m\u001b[37m PGFPlotsX v1.2.6\u001b[39m\n",
      " \u001b[90m [14b8a8f1]\u001b[39m\u001b[37m PkgTemplates v0.7.4\u001b[39m\n",
      " \u001b[90m [f0f68f2c]\u001b[39m\u001b[37m PlotlyJS v0.13.1\u001b[39m\n",
      " \u001b[90m [92933f4c]\u001b[39m\u001b[37m ProgressMeter v1.3.1\u001b[39m\n",
      " \u001b[90m [6f49c342]\u001b[39m\u001b[37m RCall v0.13.7\u001b[39m\n",
      " \u001b[90m [df47a6cb]\u001b[39m\u001b[37m RData v0.7.2\u001b[39m\n",
      " \u001b[90m [2913bbd2]\u001b[39m\u001b[37m StatsBase v0.33.0\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "using Pkg\n",
    "Pkg.status()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "また連続変数、今回の場合は各データに対応する潜在変数ベクトル、カーネル関数のハイパーパラメタ、の最適化が必要な場合、Meiller, \"A Scaled Conjugate Gradient Algorithm for Fast Supervised Learning\" (1991) で提案されるSCGをここでは用います。採用理由は『ガウス過程と機械学習』で挙げられていたためです。簡単な記事は **ここ** に記載しているため、SCGに関する記述は本資料では割愛します。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 基本的なGPLVMの概要\n",
    "\n",
    "基本的なGPLVMは教師なし学習に分類される、PCAを非線形化した手法の1つです。各観測データに対応する低次元潜在変数ベクトルを導入し、各観測データは、潜在変数によるガウス過程から生じるという生成モデルを考えます。この時の事後対数尤度を最大とする潜在変数ベクトルを、勾配法等を用いて求めることで、各観測データに対応する低次元潜在変数を得ます。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 表記\n",
    "\n",
    "以降、特に明記がなければ以下の記号を用いることとします。記号自体はぶらないようにしていますが、スカラー値としての$K$と、グラム行列としての$\\boldsymbol{K}_{\\boldsymbol{X}}$が紛らわしかったりするため、参考にされる場合はご注意ください。\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "  N\\in\\mathbb{N} &\\quad\n",
    "    \\text{データ数}\n",
    "\\\\\n",
    "  D\\in\\mathbb{N} &\\quad\n",
    "    \\text{観測されたデータの次元数}\n",
    "\\\\\n",
    "  K\\in\\mathbb{N} &\\quad\n",
    "    \\text{潜在変数の次元数}\n",
    "\\\\\n",
    "  i=1\\dots N,\\; \\boldsymbol{y}_i\\in\\mathbb{R}^D &\\quad\n",
    "    \\text{$i$番目の観測データ}\n",
    "\\\\\n",
    "  d=1\\dots D,\\; \\boldsymbol{y}^{(d)}\\in\\mathbb{R}^{D} &\\quad\n",
    "    \\text{各観測データの$d$番目の要素のベクトル}\n",
    "\\\\\n",
    "  \\boldsymbol{Y}:= \\begin{pmatrix} \\boldsymbol{y}_1 & \\dots & \\boldsymbol{y}_N \\end{pmatrix}^{\\top} = \\begin{pmatrix} \\boldsymbol{y}^{(1)} & \\dots & \\boldsymbol{y}^{(D)} \\end{pmatrix} \\in\\mathbb{R}^{N\\times D} &\\quad\n",
    "    \\text{観測データによる行列}\n",
    "\\\\\n",
    "  i=1\\dots N,\\; \\boldsymbol{x}_i\\in\\mathbb{R}^K &\\quad\n",
    "    \\text{$i$番目の観測データに対応する潜在変数ベクトル}\n",
    "\\\\\n",
    "  \\boldsymbol{X} := \\begin{pmatrix} \\boldsymbol{x}_1 & \\dots & \\boldsymbol{x}_N \\end{pmatrix}^{\\top} &\\quad\n",
    "    \\text{潜在変数ベクトルによる行列}\n",
    "\\\\\n",
    "  k(\\cdot,\\cdot): \\mathbb{R}^D\\times \\mathbb{R}^D \\to \\mathbb{R} &\\quad\n",
    "    \\text{カーネル関数}\n",
    "\\\\\n",
    "  \\boldsymbol{K}_{\\boldsymbol{X}} := \\begin{pmatrix} k(\\boldsymbol{x}_l, \\boldsymbol{x}_m) \\end{pmatrix} &\\quad\n",
    "    \\text{カーネル法の意味でのグラム行列}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "また本資料では以下のカーネル関数を採用することとします。\n",
    "$$\n",
    "\\begin{align}\n",
    "  k(\\boldsymbol{x}_i, \\boldsymbol{x}_j) := \\tau^2 \\exp \\left\\{ -\\left( \\frac{\\left\\| \\boldsymbol{x}_i - \\boldsymbol{x}_j \\right\\|}{\\sigma} \\right)^2 \\right\\} + \\eta^2 \\delta_{i,j}\n",
    "\\end{align}\n",
    "$$\n",
    "ここで$\\delta_{i,j}$はクロネッカーのデルタとします。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 生成モデル\n",
    "\n",
    "本資料では計算過程の実装メモに注力するため、詳細は『ガウス過程と機械学習』を参照してもらうこととして割愛します。\n",
    "\n",
    "基本的なGPLVMでは、観測データにおける$d$番目の要素のベクトル$\\boldsymbol{y}^{(d)}$が、潜在変数による平均$0$のガウス過程から生じると仮定します。\n",
    "『ガウス過程と機械学習』P.190, 式(7.2), (7.3)を再掲すると、\n",
    "$$\n",
    "d=1\\dots D,\\; \\boldsymbol{y}^{(d)} \\sim \\mathcal{N}(0, \\boldsymbol{K}_{\\boldsymbol{X}} + \\sigma^2 I).\n",
    "$$\n",
    "\n",
    "また潜在変数$\\boldsymbol{x}_i, i=1\\dots N$の事前分布として、『ガウス過程と機械学習』では互いに独立して平均$0$のガウス分布に従うとしています。つまり、\n",
    "$$\n",
    "i=1\\dots N,\\; \\boldsymbol{x}_i \\sim \\mathcal{N}(0,I).\n",
    "$$\n",
    "\n",
    "基本的なGPLVMはこのモデルのもとで、事後対数尤度$\\log p(\\boldsymbol{X}\\mid \\boldsymbol{Y})$を最大にするような$\\boldsymbol{X}$とカーネル法のハイパーパラメタを求めます。ガウシアンGPLVMとの違いは、変分近似によって$\\boldsymbol{X}$の事後分布を求める点だと思われます。こちらはまだ確認してないです。\n",
    "\n",
    "事後対数尤度は以下のように、\n",
    "$$\n",
    "\\begin{align}\n",
    "  &p(\\boldsymbol{X} \\mid \\boldsymbol{Y}) \\propto p(\\boldsymbol{Y} \\mid \\boldsymbol{X}) p(\\boldsymbol{X})\n",
    ",\\\\\n",
    "  &\\Rightarrow \n",
    "  \\log p(\\boldsymbol{X} \\mid \\boldsymbol{Y}) = \\log p(\\boldsymbol{Y} \\mid \\boldsymbol{X}) + \\log p(\\boldsymbol{X}) + C\n",
    ",\\quad\n",
    "    \\text{$C$は定数}\n",
    ",\n",
    "\\end{align}\n",
    "$$\n",
    "であることから、第一、第二項に着目して最適化すれば良いことがわかります。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 勾配の導出例\n",
    "\n",
    "自動微分を使えばわざわざ手計算せずとも勾配を導出できるのですが、ここではあえて勾配を導出します。カーネル関数の選択に依存する箇所はそのことを明記するようにします。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 潜在変数による事後対数尤度の微分\n",
    "\n",
    "$n$番目の潜在変数ベクトル$\\boldsymbol{x}_n = \\begin{pmatrix} x_{n1} & x_{n2} & \\dots & x_{nK} \\end{pmatrix}$の$j$番目の要素 $x_{nj}$による事後対数尤度の微分を導出します。\n",
    "\n",
    "$$\n",
    "\\frac{\\partial}{\\partial x_{nj}} \\log p(\\boldsymbol{X} \\mid \\boldsymbol{Y}) = \\frac{\\partial}{\\partial x_{nj}} \\log p(\\boldsymbol{Y} \\mid \\boldsymbol{X}) + \\frac{\\partial}{\\partial x_{nj}} \\log p(\\boldsymbol{X})\n",
    "$$\n",
    "\n",
    "カーネル関数を考慮する前段階の第一項は『ガウス過程と機械学習』P.197, 式(7.29)に記述されています。上記で採用するとしたカーネル関数を考慮すると、第一項は以下のように記述できます。\n",
    "$$\n",
    "\\begin{align}\n",
    "  &\\frac{\\partial}{\\partial x_{nj}} \\log p(\\boldsymbol{Y} \\mid \\boldsymbol{X}) = 4\\sum_{l=1}^{N} \\frac{x_{lj} - x_{nj}}{\\sigma^2} k(\\boldsymbol{x}_l, \\boldsymbol{x}_n) G_{l,n}\n",
    ",\\\\\n",
    "  &\\text{where} \\quad\n",
    "    G := \\frac{1}{2} \\left( \\boldsymbol{K}_{\\boldsymbol{X}}^{-1}\\boldsymbol{Y}\\boldsymbol{Y}^{\\top}\\boldsymbol{K}_{\\boldsymbol{X}}^{-1} -D\\boldsymbol{K}_{\\boldsymbol{X}}^{-1} \\right)\n",
    ".\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "また第二項についても、$\\log p(\\boldsymbol{X}) = -\\frac{1}{2}\\sum_{i=1}^{N} \\boldsymbol{x}_{i}^{\\top} \\boldsymbol{x}_{i} - \\frac{1}{2}KN\\log 2\\pi$であるため、\n",
    "$$\n",
    "\\frac{\\partial}{\\partial x_{nj}}\\log p(\\boldsymbol{X}) = -x_{nj}\n",
    "$$\n",
    "となり、これら2つから$\\frac{\\partial}{\\partial x_{nj}} \\log p(\\boldsymbol{X} \\mid \\boldsymbol{Y})$が求まります。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### ハイパーパラメタによる事後対数尤度の微分\n",
    "\n",
    "こちらも計算ミスに気をつけながら$\\log p(\\boldsymbol{X} \\mid \\boldsymbol{Y})$を微分するだけで導出できます。$\\log p(\\boldsymbol{X})$にはハイパーパラメタが含まれていないため、$\\log p(\\boldsymbol{Y} \\mid \\boldsymbol{X})$のみに着目できます。上記で採用したカーネル関数を考慮するとそれぞれ、\n",
    "$$\n",
    "\\begin{align}\n",
    "  &\\frac{\\partial}{\\partial \\tau} \\log p(\\boldsymbol{Y} \\mid \\boldsymbol{X}) = \\sum_{l=1}^{N}\\sum_{m=1}^{N} L_{lm} G_{lm}\n",
    ",\\\\\n",
    "  &\\frac{\\partial}{\\partial \\sigma} \\log p(\\boldsymbol{Y} \\mid \\boldsymbol{X}) = \\sum_{l=1}^{N}\\sum_{m=1}^{N} H_{lm} G_{lm}\n",
    ",\\\\\n",
    "  &\\frac{\\partial}{\\partial \\eta} \\log p(\\boldsymbol{Y} \\mid \\boldsymbol{X}) = 2\\eta \\sum_{l=1}^{N} G_{ll}\n",
    ",\\\\\n",
    "  &\\text{where} \\quad\n",
    "    L := \\begin{pmatrix} 2\\tau \\exp \\left[ -\\sigma^{-2} \\left( \\boldsymbol{x}_l - \\boldsymbol{x}_m \\right)^{\\top} \\left( \\boldsymbol{x}_l - \\boldsymbol{x}_m \\right) \\right] \\end{pmatrix}_{lm}\n",
    "\\end{align}\n",
    "$$\n",
    "となります。これら勾配を使って、最急降下法等を適用して最適な$\\boldsymbol{X}, \\tau, \\sigma, \\eta$を得ます。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 計算例\n",
    "\n",
    "『ガウス過程と機械学習』でも使われている\"送油データ\"に対してGPLVMを適用して、低次元潜在変数表現を獲得してみます。\n",
    "その際、変数をどのような順で更新を繰り返すかで、同じ初期値でも結果に影響を与えるかに関心があったため、以下3通りの計算を行います。\n",
    "1. 各潜在変数ベクトルごと($n=1\\dots N$)に、他変数を固定して逐次更新\n",
    "2. 潜在変数ベクトルの各要素ごと($j=1\\dots L$)に、他変数を固定して逐次更新\n",
    "3. すべての潜在変数の更新と、ハイパーパラメタの更新を反復\n",
    "\n",
    "**ここで重要な点は各潜在変数ベクトルの初期値の選び方です。** 私が実装した限りでは、初期値を乱数で与えると、意味のありそうな解に収束せず局所解にハマってしまう印象でした。したがって以下では、観測データに対して古典的なPCAを適用して得られる低次元表現を初期値とします。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SCG (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 実行の前準備\n",
    "\n",
    "using LinearAlgebra, LaTeXStrings, PGFPlotsX, Random, Distributions, ForwardDiff, DelimitedFiles\n",
    "function SCG(init, f::Function, ∇f::Function; σ=1e-4, MaxLoop=50)\n",
    "  D = length(init)\n",
    "  xₖ = zeros(D)\n",
    "  xₖ .= init\n",
    "  λₖ = 1e-6\n",
    "  λ̄ₖ = 0.0\n",
    "  rₖ = -∇f(xₖ)\n",
    "  pₖ = rₖ\n",
    "  success = true\n",
    "\n",
    "  for loop in 1:MaxLoop\n",
    "    if success\n",
    "      σₖ = σ/norm(pₖ)\n",
    "      sₖ = (∇f(xₖ+σₖ.*pₖ) - ∇f(xₖ)) / σₖ\n",
    "      δₖ = dot(pₖ, sₖ)\n",
    "    end\n",
    "\n",
    "    δₖ = δₖ + (λₖ - λ̄ₖ)*norm(pₖ)^2\n",
    "    if δₖ <= 0.0\n",
    "      λ̄ₖ = 2*(λₖ - δₖ/norm(pₖ)^2)\n",
    "      δₖ = -δₖ + λₖ*norm(pₖ)^2\n",
    "      λₖ = λ̄ₖ\n",
    "    end\n",
    "\n",
    "    μₖ = dot(pₖ, rₖ)\n",
    "    αₖ = μₖ/δₖ\n",
    "    Δₖ = 2*δₖ*( f(xₖ) - f(xₖ+αₖ.*pₖ) )/μₖ^2\n",
    "    if Δₖ >= 0.0\n",
    "      xₛ = xₖ+αₖ.*pₖ\n",
    "      rₛ = - ∇f(xₛ)\n",
    "      λ̄ₛ = 0.0\n",
    "      success = true\n",
    "      if loop % D == 0\n",
    "        pₛ = rₛ\n",
    "      else\n",
    "        βₖ = (norm(rₛ)^2 - dot(rₛ, rₖ)) / μₖ\n",
    "        pₛ = rₛ + βₖ.*pₖ\n",
    "      end\n",
    "\n",
    "      if Δₖ >= 0.75\n",
    "        λₖ = λₖ/4.0\n",
    "      end\n",
    "      xₖ = xₛ\n",
    "      rₖ = rₛ\n",
    "      pₖ = pₛ\n",
    "      λ̄ₖ = λ̄ₛ\n",
    "    else\n",
    "      λ̄ₖ = λₖ\n",
    "    end\n",
    "\n",
    "    if Δₖ < 0.25\n",
    "      λₖ = λₖ + δₖ*(1-Δₖ)/norm(pₖ)^2\n",
    "    end\n",
    "  end\n",
    "\n",
    "  return(xₖ)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 送油データ R等のパッケージから各自利用していただければ幸いです。\n",
    "originY = readdlm(\"oil.dat\")\n",
    "Y = originY .- mean(originY, dims=1)\n",
    "## 送油各データのラベル情報\n",
    "labels = readdlm(\"oil.labels\") .|> Int |> vec\n",
    "(N,D) = size(Y)\n",
    "K = 2\n",
    "\n",
    "## 古典的なPCAの適用\n",
    "eigret = eigen(Y'*Y)\n",
    "ords = sortperm(eigret.values, rev=true)\n",
    "vals = eigret.values[ords]\n",
    "## V\\in\\mathbb{R}^{N\\times D} 主成分ベクトルの行列\n",
    "V = eigret.vectors[:,ords];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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       "<path style=\"fill-rule:nonzero;fill:rgb(59.999084%,39.99939%,19.999695%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(44.999695%,29.998779%,14.99939%);stroke-opacity:1;stroke-miterlimit:10;\" d=\"M 25.833454 65.844359 C 25.833454 66.943983 24.941232 67.836205 23.841608 67.836205 C 22.73807 67.836205 21.845849 66.943983 21.845849 65.844359 C 21.845849 64.744734 22.73807 63.852512 23.841608 63.852512 C 24.941232 63.852512 25.833454 64.744734 25.833454 65.844359 Z M 22.432837 64.435587 L 25.250379 67.25313 M 22.432837 67.25313 L 25.250379 64.435587 \" transform=\"matrix(0.99821,0,0,-0.99821,35.779188,147.878856)\"/>\n",
       "<path style=\"fill-rule:nonzero;fill:rgb(59.999084%,39.99939%,19.999695%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(44.999695%,29.998779%,14.99939%);stroke-opacity:1;stroke-miterlimit:10;\" d=\"M 82.48563 127.45854 C 82.48563 128.562078 81.593408 129.4543 80.489871 129.4543 C 79.390246 129.4543 78.498024 128.562078 78.498024 127.45854 C 78.498024 126.358916 79.390246 125.466694 80.489871 125.466694 C 81.593408 125.466694 82.48563 126.358916 82.48563 127.45854 Z M 79.081099 126.049769 L 81.902555 128.871225 M 79.081099 128.871225 L 81.902555 126.049769 \" transform=\"matrix(0.99821,0,0,-0.99821,35.779188,147.878856)\"/>\n",
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       "<path style=\"fill-rule:nonzero;fill:rgb(59.999084%,39.99939%,19.999695%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(44.999695%,29.998779%,14.99939%);stroke-opacity:1;stroke-miterlimit:10;\" d=\"M 1.993912 49.295208 C 1.993912 50.394832 1.10169 51.287054 -0.00184763 51.287054 C -1.101472 51.287054 -1.993694 50.394832 -1.993694 49.295208 C -1.993694 48.195584 -1.101472 47.303362 -0.00184763 47.303362 C 1.10169 47.303362 1.993912 48.195584 1.993912 49.295208 Z M -1.410619 47.886437 L 1.410837 50.70398 M -1.410619 50.70398 L 1.410837 47.886437 \" transform=\"matrix(0.99821,0,0,-0.99821,35.779188,147.878856)\"/>\n",
       "<path style=\"fill-rule:nonzero;fill:rgb(59.999084%,39.99939%,19.999695%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(44.999695%,29.998779%,14.99939%);stroke-opacity:1;stroke-miterlimit:10;\" d=\"M 67.490041 10.135277 C 67.490041 11.234901 66.597819 12.127123 65.498195 12.127123 C 64.398571 12.127123 63.506349 11.234901 63.506349 10.135277 C 63.506349 9.035653 64.398571 8.143431 65.498195 8.143431 C 66.597819 8.143431 67.490041 9.035653 67.490041 10.135277 Z M 64.089424 8.726506 L 66.906966 11.544048 M 64.089424 11.544048 L 66.906966 8.726506 \" transform=\"matrix(0.99821,0,0,-0.99821,35.779188,147.878856)\"/>\n",
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       "<path style=\"fill-rule:nonzero;fill:rgb(59.999084%,39.99939%,19.999695%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(44.999695%,29.998779%,14.99939%);stroke-opacity:1;stroke-miterlimit:10;\" d=\"M 33.746053 67.530971 C 33.746053 68.634509 32.857745 69.522817 31.754207 69.522817 C 30.654583 69.522817 29.762361 68.634509 29.762361 67.530971 C 29.762361 66.431347 30.654583 65.539125 31.754207 65.539125 C 32.857745 65.539125 33.746053 66.431347 33.746053 67.530971 Z M 30.345436 66.1222 L 33.162979 68.939742 M 30.345436 68.939742 L 33.162979 66.1222 \" transform=\"matrix(0.99821,0,0,-0.99821,35.779188,147.878856)\"/>\n",
       "<path style=\"fill-rule:nonzero;fill:rgb(59.999084%,39.99939%,19.999695%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(44.999695%,29.998779%,14.99939%);stroke-opacity:1;stroke-miterlimit:10;\" d=\"M 90.558673 129.544305 C 90.558673 130.643929 89.666451 131.536151 88.566826 131.536151 C 87.463289 131.536151 86.571067 130.643929 86.571067 129.544305 C 86.571067 128.44468 87.463289 127.552458 88.566826 127.552458 C 89.666451 127.552458 90.558673 128.44468 90.558673 129.544305 Z M 87.158055 128.135533 L 89.975598 130.953076 M 87.158055 130.953076 L 89.975598 128.135533 \" transform=\"matrix(0.99821,0,0,-0.99821,35.779188,147.878856)\"/>\n",
       "</g>\n",
       "</svg>\n",
       "\n"
      ],
      "text/plain": [
       "Axis(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), Any[Plot(false, true, PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(\"only_marks\" => nothing), true), Table(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), TableData([0.8452806343666234 -0.4374246713807611; 0.31782328801765264 -0.35283054570019073; … ; 2.3260727739882325 -0.09982693477217132; -2.348483863011309 -0.2222214394143747], [\"x\", \"y\"], Int64[], true)), Any[]), Plot(false, true, PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(\"only_marks\" => nothing), true), Table(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), TableData([-0.9256362939316316 -0.44555187472635377; -0.6075589591070245 -0.5797257850966302; … ; -0.8944883960293535 -0.5213174128923601; 0.1675201164262458 -0.49363157669947355], [\"x\", \"y\"], Int64[], true)), Any[]), Plot(false, true, PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(\"only_marks\" => nothing), true), Table(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), TableData([-0.02151045942758559 1.7078955605236368; -0.7739103507728556 -1.1957885389730967; … ; -1.604509764900999 0.3550790250064003; 0.21898059772837114 1.8507256949228967], [\"x\", \"y\"], Int64[], true)), Any[])])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## 古典的なPCAでの2次元可視化\n",
    "@pgf Axis(\n",
    "  [\n",
    "    PlotInc(\n",
    "      {only_marks},\n",
    "      Table(\n",
    "        x=(Y*V[:,1:2])[findall(e->e==label, labels),1],\n",
    "        y=(Y*V[:,1:2])[findall(e->e==label, labels),2]\n",
    "      )\n",
    "    )\n",
    "    for label in unique(labels)\n",
    "  ]...\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "∂k∂x (generic function with 1 method)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k(τ,σ,η,x,y,l,m) = l==m ? τ^2*exp(-(norm(x-y)/σ)^2) + η^2 : τ^2*exp(-(norm(x-y)/σ)^2) + η*0.0\n",
    "∂k∂x(n,j,τ,σ,η,x,y,l,m) = l==m ? 0.0 :\n",
    "  l!=m && n==l ? ((τ/σ)^2)*(y[j] - x[j])*exp(-(norm(y-x)/σ)^2) :\n",
    "  l!=m && n==m ? ((τ/σ)^2)*(x[j] - y[j])*exp(-(norm(x-y)/σ)^2) : 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "logq (generic function with 1 method)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function logq(X)\n",
    "  -0.5*sum([norm(X[i,:])^2 for i in 1:N]) - 0.5*N*D*log(2π)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "logp (generic function with 1 method)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function logp(τ,σ,η,Y,X)\n",
    "  local Kₓ = [\n",
    "    k(τ,σ,η,X[l,:],X[m,:],l,m)\n",
    "    for l in 1:N, m in 1:N\n",
    "  ]\n",
    "  local invKₓ = inv(Kₓ)\n",
    "  -0.5*tr(invKₓ*Y*Y')-0.5*D*logdet(Kₓ) - 0.5*N*D*log(2π)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "∂logp∂X (generic function with 1 method)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function ∂logp∂X_col(j,τ,σ,η,Y,X)\n",
    "  local Kₓ = [\n",
    "    k(τ,σ,η,X[l,:],X[m,:],l,m)\n",
    "    for l in 1:N, m in 1:N\n",
    "  ]\n",
    "  local invKₓ = inv(Kₓ)\n",
    "  G = 0.5 .* (invKₓ*Y*Y'*invKₓ - D .* invKₓ)\n",
    "  \n",
    "  [\n",
    "    sum([\n",
    "      G[n,l] * (X[l,j] - X[n,j]) * exp(-(norm(X[l,:]-X[n,:])/σ)^2)\n",
    "      for l in 1:N\n",
    "    ])\n",
    "    for n in 1:N\n",
    "  ] .* (4.0*(τ/σ)^2)\n",
    "end\n",
    "\n",
    "function ∂logp∂X_row(n,τ,σ,η,Y,X)\n",
    "  local Kₓ = [\n",
    "    k(τ,σ,η,X[l,:],X[m,:],l,m)\n",
    "    for l in 1:N, m in 1:N\n",
    "  ]\n",
    "  local invKₓ = inv(Kₓ)\n",
    "  G = 0.5 .* (invKₓ*Y*Y'*invKₓ - D .* invKₓ)\n",
    "  \n",
    "  [\n",
    "    sum([\n",
    "      G[n,l] * (X[l,j] - X[n,j]) * exp(-(norm(X[l,:]-X[n,:])/σ)^2)\n",
    "      for l in 1:N\n",
    "    ])\n",
    "    for j in 1:K\n",
    "  ] .* (4.0*(τ/σ)^2)\n",
    "end\n",
    "\n",
    "function ∂logp∂X(τ,σ,η,Y,X)\n",
    "  local Kₓ = [\n",
    "    k(τ,σ,η,X[l,:],X[m,:],l,m)\n",
    "    for l in 1:N, m in 1:N\n",
    "  ]\n",
    "  local invKₓ = inv(Kₓ)\n",
    "  G = 0.5 .* (invKₓ*Y*Y'*invKₓ - D .* invKₓ)\n",
    "  \n",
    "  [\n",
    "    sum([\n",
    "      G[n,l]*(X[l,j]-X[n,j])*exp(-(norm(X[l,:]-X[n,:])/σ)^2)\n",
    "      for l in 1:N\n",
    "    ])\n",
    "    for n in 1:N, j in 1:K\n",
    "  ] .* (4.0 * (τ/σ)^2)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "∂logp∂τση (generic function with 1 method)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function ∂logp∂τση(τ,σ,η,Y,X)\n",
    "  local Kₓ = [\n",
    "    k(τ,σ,η,X[l,:],X[m,:],l,m)\n",
    "    for l in 1:N, m in 1:N\n",
    "  ]\n",
    "  local invKₓ = inv(Kₓ)\n",
    "  G = 0.5 .* (invKₓ*Y*Y'*invKₓ - D .* invKₓ)\n",
    "  \n",
    "  local L = [\n",
    "    exp(-(norm(X[l,:]-X[m,:])/σ)^2)\n",
    "    for l in 1:N, m in 1:N\n",
    "  ].*(2τ)\n",
    "  \n",
    "  local H = [\n",
    "    (2.0/σ) * ((τ*norm(X[l,:]-X[m,:])/σ)^2) * exp(-(norm(X[l,:]-X[m,:])/σ)^2)\n",
    "    for l in 1:N, m in 1:N\n",
    "  ]\n",
    "  \n",
    "  [\n",
    "    sum(L.*G)\n",
    "    sum(H.*G)\n",
    "    sum(diag(G))*(2η)\n",
    "  ]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PLL (generic function with 1 method)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# PLL...posterior log likelihood\n",
    "function PLL(τ,σ,η,Y,X)\n",
    "  logq(X) + logp(τ,σ,η,Y,X)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. 各潜在変数ベクトルごと($n=1\\dots N$)に、他変数を固定して逐次更新"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[DONE] loop: 1, logp: -329.76942525946106, (τ,σ,η): (1.0220229522952078, 4.994227231779866, -0.2390030587154211)\n",
      "[DONE] loop: 2, logp: -222.93321325107013, (τ,σ,η): (1.721472455270631, 4.757209447385623, -0.22363029899063636)\n",
      "[DONE] loop: 3, logp: 55.52938272442907, (τ,σ,η): (2.40375817100968, 4.2431983680026235, -0.1774317318237547)\n",
      "[DONE] loop: 4, logp: 354.95741415830844, (τ,σ,η): (2.6733247280946473, 3.8754278698557103, -0.20249240548327233)\n",
      "[DONE] loop: 5, logp: 550.1696127981659, (τ,σ,η): (2.6764748227046375, 3.8698142076736834, -0.16611410379714692)\n",
      "[DONE] loop: 6, logp: 740.8196524521732, (τ,σ,η): (3.1050094223892244, 3.0105843163615518, -0.13738941696273393)\n",
      "[DONE] loop: 7, logp: 963.6889823799129, (τ,σ,η): (3.497058290743304, 1.5572035862205158, -0.12513246997138686)\n",
      "[DONE] loop: 8, logp: 1147.2670180317314, (τ,σ,η): (3.443411939761093, 1.5311371278947583, -0.11778881253077375)\n",
      "[DONE] loop: 9, logp: 1207.4277751701843, (τ,σ,η): (3.4062664757811807, 1.4391186915513354, -0.11216805709701501)\n",
      "[DONE] loop: 10, logp: 1254.5562190213573, (τ,σ,η): (3.217160839505723, 1.3371673040455638, -0.10934650176208804)\n",
      "[DONE] loop: 11, logp: 1281.2445093223846, (τ,σ,η): (3.174348739441772, 1.382181505639216, -0.1090596733527549)\n",
      "[DONE] loop: 12, logp: 1296.049951045909, (τ,σ,η): (3.1470898830649117, 1.3310723259094799, -0.10850948363498447)\n",
      "[DONE] loop: 13, logp: 1312.3189497301005, (τ,σ,η): (3.103764661400465, 1.2840195152708964, -0.10730567138213766)\n",
      "[DONE] loop: 14, logp: 1339.4899390931737, (τ,σ,η): (3.073086352215127, 1.2418113487986293, -0.10535607616324999)\n",
      "[DONE] loop: 15, logp: 1363.0920642908854, (τ,σ,η): (3.0354490270051038, 1.2009850806925757, -0.10383416933622973)\n",
      "[DONE] loop: 16, logp: 1385.6066792662828, (τ,σ,η): (2.998978526425053, 1.1606143406256746, -0.10236415814182827)\n",
      "[DONE] loop: 17, logp: 1412.7148478765894, (τ,σ,η): (2.9674364523607046, 1.1216229404748759, -0.10066714942333792)\n",
      "[DONE] loop: 18, logp: 1445.0405119845013, (τ,σ,η): (2.94114339448924, 1.0848029250086053, -0.09877004032201725)\n",
      "[DONE] loop: 19, logp: 1480.7103943547677, (τ,σ,η): (2.9184932221492823, 1.050726189856799, -0.09674490214059005)\n",
      "[DONE] loop: 20, logp: 1522.4666568207977, (τ,σ,η): (2.902288227873706, 1.0164348200021025, -0.09431099531467553)\n",
      "[DONE] loop: 21, logp: 1564.647752661484, (τ,σ,η): (2.8876738656388534, 0.9821883262474628, -0.0918981238297172)\n",
      "[DONE] loop: 22, logp: 1606.1764504492844, (τ,σ,η): (2.8738021921444057, 0.9474864635825055, -0.08952307735910485)\n",
      "[DONE] loop: 23, logp: 1628.1262603758541, (τ,σ,η): (2.8525880044170737, 0.9195543032370728, -0.08832984176885823)\n",
      "[DONE] loop: 24, logp: 1653.7898068628233, (τ,σ,η): (2.7967657694362615, 0.8824527340433573, -0.08693541348106569)\n",
      "[DONE] loop: 25, logp: 1670.0690180125252, (τ,σ,η): (2.6090424466604856, 0.9181549084749302, -0.08717873040461686)\n",
      "[DONE] loop: 26, logp: 1679.7629029335253, (τ,σ,η): (2.59981999897341, 0.8721639116682075, -0.08636985881643795)\n",
      "[DONE] loop: 27, logp: 1687.6982395156506, (τ,σ,η): (2.581707541693314, 0.8389171640610554, -0.08564016384492706)\n",
      "[DONE] loop: 28, logp: 1698.7734291803722, (τ,σ,η): (2.5621558499731036, 0.7990692080047878, -0.0844508246665251)\n",
      "[DONE] loop: 29, logp: 1800.4806098991953, (τ,σ,η): (2.518503994526969, 0.7708913226225931, -0.07990021942566766)\n",
      "[DONE] loop: 30, logp: 1810.831926583387, (τ,σ,η): (2.4986796327683853, 0.7958922284237372, -0.07930424810891464)\n",
      "[DONE] loop: 31, logp: 1825.588504672773, (τ,σ,η): (2.2873049960104392, 0.757014926171951, -0.07853687084547557)\n",
      "[DONE] loop: 32, logp: 1830.9109271117586, (τ,σ,η): (2.2478108738051965, 0.7790339245716953, -0.07923248852068004)\n",
      "[DONE] loop: 33, logp: 1835.4919580919054, (τ,σ,η): (2.218144712918417, 0.7512578164281765, -0.07885461031124012)\n",
      "[DONE] loop: 34, logp: 1839.839461400291, (τ,σ,η): (2.162722358629101, 0.7741714068588937, -0.07916550229058897)\n",
      "[DONE] loop: 35, logp: 1843.4046218369585, (τ,σ,η): (2.14628895696164, 0.7482921221721774, -0.07873465294198413)\n",
      "[DONE] loop: 36, logp: 1851.9999420098952, (τ,σ,η): (1.505553281113512, 0.7687020195937053, -0.07832588420038016)\n",
      "[DONE] loop: 37, logp: 1880.686208612392, (τ,σ,η): (1.5062063753599735, 0.6965005411519112, -0.07876516684266176)\n",
      "[DONE] loop: 38, logp: 1886.8794181623066, (τ,σ,η): (1.490389512804937, 0.6659860527575514, -0.07828092483312274)\n",
      "[DONE] loop: 39, logp: 1894.8514534054261, (τ,σ,η): (1.3726755052441983, 0.6034748693829513, -0.07773349443223872)\n",
      "[DONE] loop: 40, logp: 1903.6926293898164, (τ,σ,η): (1.3442521775397598, 0.6257528917656312, -0.07766323896100204)\n",
      "[DONE] loop: 41, logp: 1909.6900258145447, (τ,σ,η): (1.3181114141489405, 0.5953658628243179, -0.0772186411472281)\n",
      "[DONE] loop: 42, logp: 1917.0770718017607, (τ,σ,η): (1.2773639678418198, 0.5924225673368058, -0.07671360946382103)\n",
      "[DONE] loop: 43, logp: 1924.1554431284562, (τ,σ,η): (1.2313678524687925, 0.571023068610633, -0.07745866418462755)\n",
      "[DONE] loop: 44, logp: 1948.3881248902076, (τ,σ,η): (0.772284745464354, 0.42413637765571455, -0.07525521827636314)\n",
      "[DONE] loop: 45, logp: 1968.237142512024, (τ,σ,η): (0.7589317660840986, 0.44424168668160285, -0.07510128630157327)\n",
      "[DONE] loop: 46, logp: 1978.3743294281662, (τ,σ,η): (0.7459018852414738, 0.4265037324118765, -0.07441778831918787)\n",
      "[DONE] loop: 47, logp: 1988.3729253357938, (τ,σ,η): (0.7362277331876587, 0.4012513553008697, -0.0731355153291715)\n",
      "[DONE] loop: 48, logp: 2026.057706117122, (τ,σ,η): (0.7360739291074052, 0.3433014242539252, -0.06810002005325207)\n",
      "[DONE] loop: 49, logp: 2127.7602858969744, (τ,σ,η): (0.7327500672439282, 0.30945946651242395, -0.06258695285320798)\n",
      "[DONE] loop: 50, logp: 2227.7722477815, (τ,σ,η): (0.7296083435146268, 0.28174368530515786, -0.057705372547382984)\n",
      "[DONE] loop: 51, logp: 2283.3719631000936, (τ,σ,η): (0.7256851619177651, 0.26726314737331275, -0.05582105613987121)\n",
      "[DONE] loop: 52, logp: 2340.4733517980617, (τ,σ,η): (0.7205561999062157, 0.2585431073069966, -0.05368595191728335)\n",
      "[DONE] loop: 53, logp: 2382.213657136877, (τ,σ,η): (0.6581897270160346, 0.26189079200063703, -0.05293152879964151)\n",
      "[DONE] loop: 54, logp: 2402.263503367714, (τ,σ,η): (0.6574175246069314, 0.25228250160931565, -0.05239329627171181)\n",
      "[DONE] loop: 55, logp: 2417.3990647601563, (τ,σ,η): (0.6486723504106449, 0.24704205799559573, -0.05242686013618994)\n",
      "[DONE] loop: 56, logp: 2428.9359809916355, (τ,σ,η): (0.6423586379362533, 0.2494130814435703, -0.05203287192760472)\n",
      "[DONE] loop: 57, logp: 2437.972300875864, (τ,σ,η): (0.6401296664448826, 0.2460028872144156, -0.05187319530799609)\n",
      "[DONE] loop: 58, logp: 2446.4321037695167, (τ,σ,η): (0.6119454869574898, 0.2374670220221348, -0.051815985599905474)\n",
      "[DONE] loop: 59, logp: 2453.134688561467, (τ,σ,η): (0.6108225896213304, 0.23970958663963343, -0.05146742173275164)\n",
      "[DONE] loop: 60, logp: 2458.62607879491, (τ,σ,η): (0.5898364132950884, 0.23584111147441358, -0.05154401395983738)\n",
      "[DONE] loop: 61, logp: 2463.0643036287333, (τ,σ,η): (0.5898305473589924, 0.23536793197125327, -0.051282772884260995)\n",
      "[DONE] loop: 62, logp: 2466.7906300830577, (τ,σ,η): (0.5894550784124691, 0.23477672275433392, -0.051186836020229456)\n",
      "[DONE] loop: 63, logp: 2470.0076912268137, (τ,σ,η): (0.5885906992388766, 0.23424307750055073, -0.051204584636412885)\n",
      "[DONE] loop: 64, logp: 2472.826034191426, (τ,σ,η): (0.5885266016978344, 0.23364711787947084, -0.05111452188176141)\n",
      "[DONE] loop: 65, logp: 2475.326424544354, (τ,σ,η): (0.5885111067527835, 0.23314597130738784, -0.05108158866792695)\n",
      "[DONE] loop: 66, logp: 2477.5622280668827, (τ,σ,η): (0.5885596445234518, 0.23270400210597073, -0.05105556987258028)\n",
      "[DONE] loop: 67, logp: 2479.577060334878, (τ,σ,η): (0.5886215882573961, 0.23228971675706298, -0.05102941079875496)\n",
      "[DONE] loop: 68, logp: 2481.404609972988, (τ,σ,η): (0.5886907780180145, 0.23190311394583266, -0.05100505541192333)\n",
      "[DONE] loop: 69, logp: 2483.071515735955, (τ,σ,η): (0.5887691147202084, 0.23154479151016807, -0.05098259983799506)\n",
      "[DONE] loop: 70, logp: 2484.5995771286885, (τ,σ,η): (0.5888719601872646, 0.23121443761841293, -0.05096075906271263)\n",
      "[DONE] loop: 71, logp: 2486.0074493058232, (τ,σ,η): (0.5896264389551872, 0.23098936336459597, -0.05093086590746503)\n",
      "[DONE] loop: 72, logp: 2487.309640983602, (τ,σ,η): (0.5897107001907732, 0.23074837944315882, -0.05093074872465779)\n",
      "[DONE] loop: 73, logp: 2488.518702046415, (τ,σ,η): (0.5909136399249019, 0.2307040653712751, -0.05092798107302832)\n",
      "[DONE] loop: 74, logp: 2489.644927917035, (τ,σ,η): (0.5909737334709235, 0.23045679402511746, -0.05091134362877886)\n",
      "[DONE] loop: 75, logp: 2490.698141128503, (τ,σ,η): (0.5913145449813146, 0.23025874978766186, -0.050890190846312036)\n",
      "[DONE] loop: 76, logp: 2491.68517804091, (τ,σ,η): (0.5913912426219992, 0.23009052993709656, -0.05088994330353379)\n",
      "[DONE] loop: 77, logp: 2492.6127580164425, (τ,σ,η): (0.5926072890765429, 0.23012067811220502, -0.05088632603356229)\n",
      "[DONE] loop: 78, logp: 2493.4857155625746, (τ,σ,η): (0.5930958730553468, 0.23001502645515431, -0.05088009855395339)\n",
      "[DONE] loop: 79, logp: 2494.3096815827353, (τ,σ,η): (0.5934949009008395, 0.2299153231905589, -0.05087336541490457)\n",
      "[DONE] loop: 80, logp: 2495.0882829542493, (τ,σ,η): (0.5938974541861313, 0.22985459697610575, -0.0508708703590839)\n",
      "[DONE] loop: 81, logp: 2495.8248331155323, (τ,σ,η): (0.594049562672969, 0.22972454799429864, -0.050861247126201596)\n",
      "[DONE] loop: 82, logp: 2496.522985258019, (τ,σ,η): (0.5941058510955537, 0.22962424197106965, -0.05085841808379628)\n",
      "[DONE] loop: 83, logp: 2497.1851041164896, (τ,σ,η): (0.5944458214302564, 0.22959120408176825, -0.050846983648553376)\n",
      "[DONE] loop: 84, logp: 2497.813639473717, (τ,σ,η): (0.5945048263895917, 0.22947332344133917, -0.05085077705863182)\n",
      "[DONE] loop: 85, logp: 2498.411528247058, (τ,σ,η): (0.5948189059934803, 0.2294465488862706, -0.05083731156955443)\n",
      "[DONE] loop: 86, logp: 2498.979973471976, (τ,σ,η): (0.594912016248988, 0.22934874768929828, -0.05084069738774673)\n",
      "[DONE] loop: 87, logp: 2499.521330333286, (τ,σ,η): (0.59505034366062, 0.22928007090271973, -0.05083411893940149)\n",
      "[DONE] loop: 88, logp: 2500.0370677739606, (τ,σ,η): (0.5952569532779982, 0.22922534611078943, -0.05082720552414216)\n",
      "[DONE] loop: 89, logp: 2500.5288005527705, (τ,σ,η): (0.5955707028045016, 0.22919456562390086, -0.05082015445190956)\n",
      "[DONE] loop: 90, logp: 2500.9978688082424, (τ,σ,η): (0.5959433714865874, 0.22918008190190614, -0.050815916882798205)\n",
      "[DONE] loop: 91, logp: 2501.4454757452263, (τ,σ,η): (0.5963081210905934, 0.22916999298162957, -0.050813733699735956)\n",
      "[DONE] loop: 92, logp: 2501.872786548725, (τ,σ,η): (0.5966540152213201, 0.22916094160981065, -0.05081167178062483)\n",
      "[DONE] loop: 93, logp: 2502.280931227609, (τ,σ,η): (0.596984146359275, 0.22915232692159573, -0.050809325946122474)\n",
      "[DONE] loop: 94, logp: 2502.6709690122484, (τ,σ,η): (0.5973028913261603, 0.22914429842541925, -0.05080666919889216)\n",
      "[DONE] loop: 95, logp: 2503.043907441624, (τ,σ,η): (0.5976130802982598, 0.22913701894176747, -0.05080373612583172)\n",
      "[DONE] loop: 96, logp: 2503.4007025763744, (τ,σ,η): (0.5979151485338247, 0.2291302971302758, -0.05080056359169611)\n",
      "[DONE] loop: 97, logp: 2503.742283216024, (τ,σ,η): (0.5982086075700902, 0.22912377889634805, -0.050797132765924145)\n",
      "[DONE] loop: 98, logp: 2504.069560286796, (τ,σ,η): (0.5984922075056532, 0.22911693095725968, -0.050793407907806364)\n",
      "[DONE] loop: 99, logp: 2504.383439679684, (τ,σ,η): (0.5987642714322274, 0.2291090810522016, -0.05078933181342891)\n",
      "[DONE] loop: 100, logp: 2504.6848350589858, (τ,σ,η): (0.5990227341345246, 0.2290994112488946, -0.05078483335640297)\n"
     ]
    }
   ],
   "source": [
    "# GPLVMの最適化 各データ点毎更新 loop n=1...N\n",
    "X = Y*V[:,1:2]\n",
    "τ = 1.0\n",
    "σ = 5.0\n",
    "η = 1.0\n",
    "\n",
    "for loop in 1:100\n",
    "for n in 1:N\n",
    "  xₛ = SCG(\n",
    "    X[n,:],\n",
    "    x -> -PLL(\n",
    "      τ,σ,η,Y,\n",
    "      X.*(ones(N,K) - Matrix(1.0I,N,N)[:,n]*ones(1,K)) + (Matrix(1.0I,N,N)[:,n]*x')\n",
    "    ),\n",
    "    x -> -∂logp∂X_row(\n",
    "        n,τ,σ,η,Y,\n",
    "        X.*(ones(N,K) - Matrix(1.0I,N,N)[:,n]*ones(1,K)) + (Matrix(1.0I,N,N)[:,n]*x')\n",
    "      ) + x,\n",
    "    MaxLoop=3\n",
    "  )\n",
    "  X = X.*(ones(N,K) - Matrix(1.0I,N,N)[:,n]*ones(1,K)) + (Matrix(1.0I,N,N)[:,n]*xₛ')\n",
    "end\n",
    "  θₛ = SCG(\n",
    "    [τ,σ,η],\n",
    "    θ -> -logp(θ...,Y,X),\n",
    "    θ -> -∂logp∂τση(θ...,Y,X),\n",
    "    MaxLoop=3\n",
    "  )\n",
    "  τ = θₛ[1]\n",
    "  σ = θₛ[2]\n",
    "  η = θₛ[3]\n",
    "  \n",
    "  println(\"[DONE] loop: $(loop), logp: $(logp(τ,σ,η,Y,X)), (τ,σ,η): $((τ,σ,η))\")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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       "<path style=\"fill-rule:nonzero;fill:rgb(59.999084%,39.99939%,19.999695%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(44.999695%,29.998779%,14.99939%);stroke-opacity:1;stroke-miterlimit:10;\" d=\"M 68.072801 134.147371 C 68.072801 135.246989 67.180584 136.139206 66.080966 136.139206 C 64.977435 136.139206 64.085218 135.246989 64.085218 134.147371 C 64.085218 133.047753 64.977435 132.155536 66.080966 132.155536 C 67.180584 132.155536 68.072801 133.047753 68.072801 134.147371 Z M 64.672203 132.738607 L 67.48973 135.556134 M 64.672203 135.556134 L 67.48973 132.738607 \" transform=\"matrix(0.998216,0,0,-0.998216,35.825991,147.880696)\"/>\n",
       "<path style=\"fill-rule:nonzero;fill:rgb(59.999084%,39.99939%,19.999695%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(44.999695%,29.998779%,14.99939%);stroke-opacity:1;stroke-miterlimit:10;\" d=\"M 66.546641 132.374677 C 66.546641 133.474295 65.654424 134.366512 64.554806 134.366512 C 63.455188 134.366512 62.562971 133.474295 62.562971 132.374677 C 62.562971 131.275059 63.455188 130.382842 64.554806 130.382842 C 65.654424 130.382842 66.546641 131.275059 66.546641 132.374677 Z M 63.146043 130.965913 L 65.963569 133.78344 M 63.146043 133.78344 L 65.963569 130.965913 \" transform=\"matrix(0.998216,0,0,-0.998216,35.825991,147.880696)\"/>\n",
       "<path style=\"fill-rule:nonzero;fill:rgb(59.999084%,39.99939%,19.999695%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(44.999695%,29.998779%,14.99939%);stroke-opacity:1;stroke-miterlimit:10;\" d=\"M 68.072801 134.495648 C 68.072801 135.595266 67.180584 136.487483 66.077053 136.487483 C 64.977435 136.487483 64.085218 135.595266 64.085218 134.495648 C 64.085218 133.39603 64.977435 132.503813 66.077053 132.503813 C 67.180584 132.503813 68.072801 133.39603 68.072801 134.495648 Z M 64.66829 133.086885 L 67.485816 135.904412 M 64.66829 135.904412 L 67.485816 133.086885 \" transform=\"matrix(0.998216,0,0,-0.998216,35.825991,147.880696)\"/>\n",
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       "<path style=\"fill-rule:nonzero;fill:rgb(59.999084%,39.99939%,19.999695%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(44.999695%,29.998779%,14.99939%);stroke-opacity:1;stroke-miterlimit:10;\" d=\"M 66.350979 131.498113 C 66.350979 132.597731 65.458762 133.489948 64.359144 133.489948 C 63.259526 133.489948 62.36731 132.597731 62.36731 131.498113 C 62.36731 130.398495 63.259526 129.506278 64.359144 129.506278 C 65.458762 129.506278 66.350979 130.398495 66.350979 131.498113 Z M 62.950381 130.08935 L 65.767908 132.906876 M 62.950381 132.906876 L 65.767908 130.08935 \" transform=\"matrix(0.998216,0,0,-0.998216,35.825991,147.880696)\"/>\n",
       "</g>\n",
       "</svg>\n",
       "\n"
      ],
      "text/plain": [
       "Axis(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), Any[Plot(false, true, PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(\"only_marks\" => nothing), true), Table(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), TableData([0.40833208019082473 -0.3558003411188564; 0.3965136210726314 -0.3129027744849499; … ; 0.5292612256561161 -0.3201660675318003; -0.41129434531978054 -0.2878297160470624], [\"x\", \"y\"], Int64[], true)), Any[]), Plot(false, true, PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(\"only_marks\" => nothing), true), Table(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), TableData([-0.39584927010697535 -0.6914406723042504; -0.2835594556726163 -0.4603785153808626; … ; -0.3066124036020477 -0.4483961730121771; 0.11346112042755896 0.16548094945044511], [\"x\", \"y\"], Int64[], true)), Any[]), Plot(false, true, PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(\"only_marks\" => nothing), true), Table(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), TableData([-0.03632881837001716 1.0184332245101355; -0.6022171939326656 -1.3084273770697943; … ; -1.2347918848219928 0.4642032436872349; -0.06643634182177122 1.010963544472276], [\"x\", \"y\"], Int64[], true)), Any[])])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@pgf Axis(\n",
    "  [\n",
    "    PlotInc(\n",
    "      {only_marks},\n",
    "      Table(\n",
    "        x=X[findall(e->e==label, labels),1],\n",
    "        y=X[findall(e->e==label, labels),2]\n",
    "      )\n",
    "    )\n",
    "    for label in unique(labels)\n",
    "  ]...\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. 潜在変数ベクトルの各要素ごと($j=1\\dots L$)に、他変数を固定して逐次更新"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[DONE] loop: 1, logp: -550.7526810512466, (τ,σ,η): (1.419704968403417, 4.903887571140026, -0.26815890902049905)\n",
      "[DONE] loop: 2, logp: -153.74028329268776, (τ,σ,η): (1.6071497472123126, 4.814204028407499, -0.25043894451744486)\n",
      "[DONE] loop: 3, logp: 173.97231450316576, (τ,σ,η): (1.6115719715894437, 4.810974612745392, -0.19907306968998562)\n",
      "[DONE] loop: 4, logp: 473.0219387442189, (τ,σ,η): (1.6998502756815947, 4.745946537699605, -0.1839573519664241)\n",
      "[DONE] loop: 5, logp: 625.8995837881744, (τ,σ,η): (1.8577900304316435, 4.616986250010838, -0.17485932870285154)\n",
      "[DONE] loop: 6, logp: 720.2448346166798, (τ,σ,η): (2.131950459563166, 4.342865293217436, -0.16978084171427807)\n",
      "[DONE] loop: 7, logp: 866.2851368675733, (τ,σ,η): (2.1366468713394178, 4.335865995362045, -0.14602822044166852)\n",
      "[DONE] loop: 8, logp: 1074.0283766003286, (τ,σ,η): (2.6583991241200327, 3.5411775934670793, -0.1372949080441395)\n",
      "[DONE] loop: 9, logp: 1128.6192639893002, (τ,σ,η): (2.779934175376376, 2.918267295031082, -0.13145564793629363)\n",
      "[DONE] loop: 10, logp: 1200.6867711739856, (τ,σ,η): (2.812964207049082, 2.2376196195595286, -0.125296630850861)\n",
      "[DONE] loop: 11, logp: 1310.7698584633504, (τ,σ,η): (2.8134535082560888, 2.198001647228261, -0.1146497852545648)\n",
      "[DONE] loop: 12, logp: 1403.3699267891607, (τ,σ,η): (2.8075021198691674, 1.9873062940512207, -0.10863425190264216)\n",
      "[DONE] loop: 13, logp: 1433.6260280569923, (τ,σ,η): (2.75100569394755, 1.850878320586589, -0.10364355242877382)\n",
      "[DONE] loop: 14, logp: 1454.5686497364936, (τ,σ,η): (2.5962210686581337, 1.6984576490884908, -0.10141544893405097)\n",
      "[DONE] loop: 15, logp: 1486.3687580171486, (τ,σ,η): (1.4127977730257588, 1.4843228166898492, -0.08808927933284179)\n",
      "[DONE] loop: 16, logp: 1576.6866766937796, (τ,σ,η): (1.3961560543912386, 1.344556488302233, -0.09555675950631687)\n",
      "[DONE] loop: 17, logp: 1652.4269194275762, (τ,σ,η): (1.3432720477276394, 1.1495876704507642, -0.09208203440778813)\n",
      "[DONE] loop: 18, logp: 1756.85700403392, (τ,σ,η): (1.319607110372401, 0.9013018997676848, -0.08046977986634529)\n",
      "[DONE] loop: 19, logp: 1899.6541074984739, (τ,σ,η): (1.296372548755079, 0.7752375278454121, -0.07304405299971528)\n",
      "[DONE] loop: 20, logp: 2062.8726801326325, (τ,σ,η): (1.2812813948782162, 0.7245885760775091, -0.06723941758590868)\n",
      "[DONE] loop: 21, logp: 2146.0849692521756, (τ,σ,η): (1.2592451601996915, 0.6841554478488313, -0.06306830630431647)\n",
      "[DONE] loop: 22, logp: 2222.876223298372, (τ,σ,η): (1.2261004455366675, 0.6416079285205708, -0.05985464326776848)\n",
      "[DONE] loop: 23, logp: 2276.9034183790714, (τ,σ,η): (1.2075528141304177, 0.6082111152667549, -0.05764013221308538)\n",
      "[DONE] loop: 24, logp: 2330.148848348584, (τ,σ,η): (1.1852845266189638, 0.5774852385988957, -0.05517977832603938)\n",
      "[DONE] loop: 25, logp: 2369.6658331972826, (τ,σ,η): (1.1607710056625606, 0.5508459442124611, -0.053624257938917244)\n",
      "[DONE] loop: 26, logp: 2403.068705303834, (τ,σ,η): (1.0122388406987335, 0.5681086346351695, -0.053137220870461944)\n",
      "[DONE] loop: 27, logp: 2430.418352655492, (τ,σ,η): (1.0007840618143105, 0.5437818983172675, -0.05274539430442399)\n",
      "[DONE] loop: 28, logp: 2450.321280357231, (τ,σ,η): (0.9878193745425243, 0.5243837396726317, -0.05186005684556297)\n",
      "[DONE] loop: 29, logp: 2475.7593561396293, (τ,σ,η): (0.8234759159154051, 0.5326077056676559, -0.05122815426294178)\n",
      "[DONE] loop: 30, logp: 2497.8978518604813, (τ,σ,η): (0.8193425672952089, 0.5093633057188309, -0.05119889883580439)\n",
      "[DONE] loop: 31, logp: 2510.2862106096914, (τ,σ,η): (0.8099510196580454, 0.4947777416040929, -0.05071024350395896)\n",
      "[DONE] loop: 32, logp: 2524.942487812135, (τ,σ,η): (0.6891844684508155, 0.4925958906585578, -0.050342253005071884)\n",
      "[DONE] loop: 33, logp: 2537.4393160899576, (τ,σ,η): (0.6883599910773536, 0.47829126037528175, -0.05021042598375264)\n",
      "[DONE] loop: 34, logp: 2545.0646447143185, (τ,σ,η): (0.6848351180386308, 0.47075990723888606, -0.04993345220757351)\n",
      "[DONE] loop: 35, logp: 2554.285219263447, (τ,σ,η): (0.6375668448274148, 0.4532629174329379, -0.04949562107096353)\n",
      "[DONE] loop: 36, logp: 2562.192999273209, (τ,σ,η): (0.6347187569509264, 0.4548779564784246, -0.0492654890303105)\n",
      "[DONE] loop: 37, logp: 2568.8773120360324, (τ,σ,η): (0.6220871970665662, 0.45213546540788685, -0.049035123179583424)\n",
      "[DONE] loop: 38, logp: 2573.7785368791824, (τ,σ,η): (0.6222729463345736, 0.45011124446634854, -0.048835764293731404)\n",
      "[DONE] loop: 39, logp: 2577.3909119387795, (τ,σ,η): (0.6211083237088113, 0.44950431550964093, -0.04871834818148304)\n",
      "[DONE] loop: 40, logp: 2580.253192688069, (τ,σ,η): (0.6209493244204866, 0.4490780219372436, -0.04863671208496014)\n",
      "[DONE] loop: 41, logp: 2582.812018004973, (τ,σ,η): (0.6210591194892746, 0.44833880388507596, -0.04856619753510931)\n",
      "[DONE] loop: 42, logp: 2585.2171360038205, (τ,σ,η): (0.6210163262326691, 0.4483916895332206, -0.04850173201345495)\n",
      "[DONE] loop: 43, logp: 2587.5400755350106, (τ,σ,η): (0.6210490997842626, 0.44798124876767764, -0.04842243442338044)\n",
      "[DONE] loop: 44, logp: 2589.425919149851, (τ,σ,η): (0.6210696261625168, 0.44775945571235376, -0.048356335204978555)\n",
      "[DONE] loop: 45, logp: 2590.9768794222996, (τ,σ,η): (0.6210719057285323, 0.4479988043514143, -0.04832039839757454)\n",
      "[DONE] loop: 46, logp: 2592.1245037136773, (τ,σ,η): (0.6211228329612868, 0.44785482252299497, -0.0482764156221569)\n",
      "[DONE] loop: 47, logp: 2593.222115568185, (τ,σ,η): (0.6210800405813045, 0.44837266288440686, -0.04826341323446695)\n",
      "[DONE] loop: 48, logp: 2594.147199740983, (τ,σ,η): (0.6211110429402849, 0.4484476957565902, -0.04823667812502703)\n",
      "[DONE] loop: 49, logp: 2594.836536862395, (τ,σ,η): (0.6210954342400485, 0.44873580345982383, -0.04823419558818441)\n",
      "[DONE] loop: 50, logp: 2595.4818910075496, (τ,σ,η): (0.6210789826376374, 0.4487476913275047, -0.04821883345781692)\n",
      "[DONE] loop: 51, logp: 2596.0317134165957, (τ,σ,η): (0.6210353150422171, 0.4489956467217782, -0.04821805273322185)\n",
      "[DONE] loop: 52, logp: 2596.572049408977, (τ,σ,η): (0.6209907273023393, 0.4491008731546691, -0.04820780685537491)\n",
      "[DONE] loop: 53, logp: 2597.064223001245, (τ,σ,η): (0.6209419975601937, 0.4492421182721965, -0.048206008380805326)\n",
      "[DONE] loop: 54, logp: 2597.5429169128433, (τ,σ,η): (0.6208621228375617, 0.4494173712756145, -0.04820096382285567)\n",
      "[DONE] loop: 55, logp: 2597.9869781432794, (τ,σ,η): (0.6207937319063881, 0.4495519865036767, -0.04819948907217899)\n",
      "[DONE] loop: 56, logp: 2598.421857753005, (τ,σ,η): (0.6206939125765616, 0.4497316257046924, -0.04819599556800352)\n",
      "[DONE] loop: 57, logp: 2598.827016124968, (τ,σ,η): (0.6202106136048116, 0.44976888666265236, -0.04818739997572365)\n",
      "[DONE] loop: 58, logp: 2599.23314807838, (τ,σ,η): (0.6201196413263015, 0.44995091945543825, -0.048194132083551264)\n",
      "[DONE] loop: 59, logp: 2599.611580643131, (τ,σ,η): (0.6194394906543733, 0.4498687105991926, -0.04819513379531915)\n",
      "[DONE] loop: 60, logp: 2599.9884877730215, (τ,σ,η): (0.6193654876696882, 0.4500582432296906, -0.04819327144847579)\n",
      "[DONE] loop: 61, logp: 2600.347553328051, (τ,σ,η): (0.6189511617249858, 0.45004101850502437, -0.04819236228694314)\n",
      "[DONE] loop: 62, logp: 2600.7025667257653, (τ,σ,η): (0.6188874083248395, 0.4501748938224683, -0.04819177844135631)\n",
      "[DONE] loop: 63, logp: 2601.0519918861532, (τ,σ,η): (0.6188415012364117, 0.45022649920175317, -0.048192437982115956)\n",
      "[DONE] loop: 64, logp: 2601.3936910001535, (τ,σ,η): (0.6187523838533583, 0.4503083006785088, -0.048189845944914295)\n",
      "[DONE] loop: 65, logp: 2601.731764295398, (τ,σ,η): (0.6184971355661772, 0.4503127201640264, -0.04818978467574746)\n",
      "[DONE] loop: 66, logp: 2602.0577984695688, (τ,σ,η): (0.6183355803811068, 0.450178494532414, -0.048186740025307595)\n",
      "[DONE] loop: 67, logp: 2602.374044023956, (τ,σ,η): (0.6182908579340127, 0.450232567876352, -0.04819138192807189)\n",
      "[DONE] loop: 68, logp: 2602.6795251430153, (τ,σ,η): (0.6180709982506739, 0.45008055484263515, -0.04818274651962278)\n",
      "[DONE] loop: 69, logp: 2602.97728568916, (τ,σ,η): (0.6180399387994142, 0.45015673157528263, -0.04819322897758608)\n",
      "[DONE] loop: 70, logp: 2603.2701828986114, (τ,σ,η): (0.617929446581661, 0.45005369896192, -0.04818872651179026)\n",
      "[DONE] loop: 71, logp: 2603.556894408933, (τ,σ,η): (0.6179058835433262, 0.4501366538533091, -0.04819612374574394)\n",
      "[DONE] loop: 72, logp: 2603.844242237617, (τ,σ,η): (0.6177721238157837, 0.450045064332454, -0.04819298179322186)\n",
      "[DONE] loop: 73, logp: 2604.1250354671133, (τ,σ,η): (0.617758128369627, 0.45012934832053614, -0.04819949974408751)\n",
      "[DONE] loop: 74, logp: 2604.408275985695, (τ,σ,η): (0.6176620352108746, 0.4501288820828622, -0.04819919526604633)\n",
      "[DONE] loop: 75, logp: 2604.6864331578704, (τ,σ,η): (0.6176738517245193, 0.45016802486607554, -0.04820338019561548)\n",
      "[DONE] loop: 76, logp: 2604.9666934630072, (τ,σ,η): (0.6176767800633494, 0.45016643700211706, -0.04820513046964469)\n",
      "[DONE] loop: 77, logp: 2605.245546257716, (τ,σ,η): (0.6176982190439678, 0.4502134662015662, -0.048208240060638584)\n",
      "[DONE] loop: 78, logp: 2605.5266891361457, (τ,σ,η): (0.6177267463917261, 0.45024126412890914, -0.04821038447320706)\n",
      "[DONE] loop: 79, logp: 2605.810996398049, (τ,σ,η): (0.6178038161300867, 0.450305577771367, -0.04821341015703484)\n",
      "[DONE] loop: 80, logp: 2606.0974264135452, (τ,σ,η): (0.6180007440657096, 0.45032300164745154, -0.048216582287948055)\n",
      "[DONE] loop: 81, logp: 2606.3891683985344, (τ,σ,η): (0.6180273029944462, 0.4503813403558441, -0.04822175852470345)\n",
      "[DONE] loop: 82, logp: 2606.683388604785, (τ,σ,η): (0.6181542375510365, 0.4504593555276097, -0.04822303799403031)\n",
      "[DONE] loop: 83, logp: 2606.9872148984864, (τ,σ,η): (0.6185559626642048, 0.450529797647993, -0.04823038452572157)\n",
      "[DONE] loop: 84, logp: 2607.2959491915913, (τ,σ,η): (0.6185739717196022, 0.45057367518388414, -0.04823273769335103)\n",
      "[DONE] loop: 85, logp: 2607.6186619365058, (τ,σ,η): (0.6186667247521673, 0.4506454172164063, -0.04823672001565814)\n",
      "[DONE] loop: 86, logp: 2607.9490641139323, (τ,σ,η): (0.6190043970257461, 0.4506762432917319, -0.04823875289588544)\n",
      "[DONE] loop: 87, logp: 2608.297168791432, (τ,σ,η): (0.6190368038596114, 0.4507410473527283, -0.04824541783140046)\n",
      "[DONE] loop: 88, logp: 2608.6569881106793, (τ,σ,η): (0.6193224623358347, 0.45088503920869305, -0.04824687084986346)\n",
      "[DONE] loop: 89, logp: 2609.040598533363, (τ,σ,η): (0.6194095573715933, 0.4508459469581278, -0.048251718844814204)\n",
      "[DONE] loop: 90, logp: 2609.4417665970664, (τ,σ,η): (0.6199531480301845, 0.45098160290426675, -0.048255588857536724)\n",
      "[DONE] loop: 91, logp: 2609.875052870218, (τ,σ,η): (0.6201838572628077, 0.45109107806488796, -0.0482589105214507)\n",
      "[DONE] loop: 92, logp: 2610.337092725685, (τ,σ,η): (0.6202165324127636, 0.4510404418071411, -0.048260150342968336)\n",
      "[DONE] loop: 93, logp: 2610.8447060356443, (τ,σ,η): (0.6203982042278382, 0.45102513138289385, -0.04825898224151871)\n",
      "[DONE] loop: 94, logp: 2611.401958049572, (τ,σ,η): (0.6204589231706392, 0.4509977967583849, -0.048258370567639965)\n",
      "[DONE] loop: 95, logp: 2612.0322281286003, (τ,σ,η): (0.620844167393342, 0.4510282396728835, -0.04825768959324842)\n",
      "[DONE] loop: 96, logp: 2612.7528778798946, (τ,σ,η): (0.6208641772958684, 0.4509807287360682, -0.0482518537269527)\n",
      "[DONE] loop: 97, logp: 2613.6091959444725, (τ,σ,η): (0.620896250700725, 0.4509282349391801, -0.04824306748408385)\n",
      "[DONE] loop: 98, logp: 2614.657321233683, (τ,σ,η): (0.6209279042173359, 0.45075314577195374, -0.04822344177448691)\n",
      "[DONE] loop: 99, logp: 2616.015169066582, (τ,σ,η): (0.6209556370407645, 0.45055337890494146, -0.04819391890705613)\n",
      "[DONE] loop: 100, logp: 2617.8114848286464, (τ,σ,η): (0.6209683244024089, 0.4501530707440033, -0.048140019041248254)\n"
     ]
    }
   ],
   "source": [
    "# GPLVMの最適化 各潜在変数毎更新 loop coefId=1,2\n",
    "X = Y*V[:,1:2]\n",
    "τ = 1.0\n",
    "σ = 5.0\n",
    "η = 1.0\n",
    "\n",
    "for loop in 1:100\n",
    "for coefId in [1,2]\n",
    "  xₛ = SCG(\n",
    "    X[:,coefId],\n",
    "    x -> -PLL(\n",
    "      τ,σ,η,Y,\n",
    "      X.*(ones(N,K) - ones(N,1)*Matrix(1.0I,K,K)[:,coefId]') + (x*Matrix(1.0I,K,K)[:,coefId]')\n",
    "    ),\n",
    "    x -> -∂logp∂X_col(\n",
    "        coefId,τ,σ,η,Y,\n",
    "        X.*(ones(N,K) - ones(N,1)*Matrix(1.0I,K,K)[:,coefId]') + (x*Matrix(1.0I,K,K)[:,coefId]')\n",
    "      ) + x,\n",
    "    MaxLoop=3\n",
    "  )\n",
    "  X = X.*(ones(N,K) - ones(N,1)*Matrix(1.0I,K,K)[:,coefId]') + (xₛ*Matrix(1.0I,K,K)[:,coefId]')\n",
    "end\n",
    "  θₛ = SCG(\n",
    "    [τ,σ,η],\n",
    "    θ -> -logp(θ...,Y,X),\n",
    "    θ -> -∂logp∂τση(θ...,Y,X),\n",
    "    MaxLoop=3\n",
    "  )\n",
    "  τ = θₛ[1]\n",
    "  σ = θₛ[2]\n",
    "  η = θₛ[3]\n",
    "  \n",
    "  println(\"[DONE] loop: $(loop), logp: $(logp(τ,σ,η,Y,X)), (τ,σ,η): $((τ,σ,η))\")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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       "</g>\n",
       "</svg>\n",
       "\n"
      ],
      "text/plain": [
       "Axis(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), Any[Plot(false, true, PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(\"only_marks\" => nothing), true), Table(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), TableData([0.4078307968573494 -0.6713292006292365; 0.3948033187662138 -0.5967410810673403; … ; 0.6145889318007605 -0.5882331805978366; 0.1804969611543545 0.04426524767862792], [\"x\", \"y\"], Int64[], true)), Any[]), Plot(false, true, PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(\"only_marks\" => nothing), true), Table(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), TableData([-0.574475918410366 -0.49705887101880236; -0.46001302476225037 -0.4974298851923337; … ; -0.47275422916666104 -0.4378255151821505; 0.7585679631166025 -0.16411074002753945], [\"x\", \"y\"], Int64[], true)), Any[]), Plot(false, true, PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(\"only_marks\" => nothing), true), Table(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), TableData([-0.5769149347144166 1.7519773238889518; -1.7753164228346867 -0.8107815454330769; … ; -1.0605642277593053 1.1367467478859516; -0.6337721067583919 1.7463840565746604], [\"x\", \"y\"], Int64[], true)), Any[])])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@pgf Axis(\n",
    "  [\n",
    "    PlotInc(\n",
    "      {only_marks},\n",
    "      Table(\n",
    "        x=X[findall(e->e==label, labels),1],\n",
    "        y=X[findall(e->e==label, labels),2]\n",
    "      )\n",
    "    )\n",
    "    for label in unique(labels)\n",
    "  ]...\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### すべての潜在変数の更新と、ハイパーパラメタの更新を反復"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[DONE] loop: 1, logp: -335.88333548833566, (τ,σ,η): (1.0669582091227587, 4.982292091272072, -0.26649379344136037)\n",
      "[DONE] loop: 2, logp: 613.2131778833013, (τ,σ,η): (1.0872737921838354, 4.97122060785486, 0.14543549186759003)\n",
      "[DONE] loop: 3, logp: 1115.9385259829, (τ,σ,η): (1.8216044212097602, 4.403994319501933, 0.1260401677487533)\n",
      "[DONE] loop: 4, logp: 1203.88218665645, (τ,σ,η): (2.2834621084054216, 3.662087739178965, 0.12307696607563899)\n",
      "[DONE] loop: 5, logp: 1219.483854785451, (τ,σ,η): (2.4150268574492295, 3.190366844007198, 0.12196959374997096)\n",
      "[DONE] loop: 6, logp: 1295.9699467802943, (τ,σ,η): (2.565602300476355, 2.561833168096101, 0.1155050656230831)\n",
      "[DONE] loop: 7, logp: 1430.9604081320417, (τ,σ,η): (2.582541381703858, 2.075408403314972, 0.10719122839483726)\n",
      "[DONE] loop: 8, logp: 1594.3208012268278, (τ,σ,η): (2.588592939893565, 1.9381970181478314, 0.09507877747389164)\n",
      "[DONE] loop: 9, logp: 1801.5572697935636, (τ,σ,η): (2.608504859156734, 1.5562843136798188, 0.08196434808178474)\n",
      "[DONE] loop: 10, logp: 2029.6595610148192, (τ,σ,η): (2.6091563003740785, 1.4840044473851648, 0.07160659242996112)\n",
      "[DONE] loop: 11, logp: 2173.271678251384, (τ,σ,η): (2.552012378383837, 1.3146641762897917, 0.0676464648004223)\n",
      "[DONE] loop: 12, logp: 2277.097546424516, (τ,σ,η): (2.490474471992281, 1.2118177107713564, 0.06102067159734655)\n",
      "[DONE] loop: 13, logp: 2336.6333546033616, (τ,σ,η): (2.416797177102357, 1.2047303441673496, 0.06058548838918558)\n",
      "[DONE] loop: 14, logp: 2365.1846678307243, (τ,σ,η): (2.258522100687153, 1.196732222912771, 0.06005740009727959)\n",
      "[DONE] loop: 15, logp: 2380.1017736523295, (τ,σ,η): (2.1330273073012402, 1.187899829327431, 0.06009786607187744)\n",
      "[DONE] loop: 16, logp: 2395.554456283356, (τ,σ,η): (1.8290158228106586, 1.1690975672943469, 0.06000940240121627)\n",
      "[DONE] loop: 17, logp: 2407.0718049411803, (τ,σ,η): (1.8203151877513863, 1.1144743683773464, 0.059822730756100555)\n",
      "[DONE] loop: 18, logp: 2418.972703716687, (τ,σ,η): (1.6474475347954223, 1.09849387657268, 0.05943227105507639)\n",
      "[DONE] loop: 19, logp: 2428.5035324993974, (τ,σ,η): (1.5320426108119127, 1.0841133593764243, 0.0595564717545995)\n",
      "[DONE] loop: 20, logp: 2437.717321778909, (τ,σ,η): (1.5250340610812154, 1.0256707081678311, 0.058759544145243814)\n",
      "[DONE] loop: 21, logp: 2451.578173272346, (τ,σ,η): (1.3734068645276858, 1.0047032708929522, 0.058322970766619436)\n",
      "[DONE] loop: 22, logp: 2466.1531255064597, (τ,σ,η): (1.249597080013985, 0.9810049493871581, 0.05819528488127429)\n",
      "[DONE] loop: 23, logp: 2482.978573493861, (τ,σ,η): (1.0390329659745905, 0.9380149437445956, 0.05740620267857683)\n",
      "[DONE] loop: 24, logp: 2498.426741183555, (τ,σ,η): (0.8904979574782617, 0.8945057024237772, 0.05732745693687286)\n",
      "[DONE] loop: 25, logp: 2513.9841359905454, (τ,σ,η): (0.6349612910555582, 0.7891149281375199, 0.05564368242376242)\n",
      "[DONE] loop: 26, logp: 2544.586236033277, (τ,σ,η): (0.6486044577069716, 0.760119784874616, 0.05498474460791778)\n",
      "[DONE] loop: 27, logp: 2552.7304672393734, (τ,σ,η): (0.6590721776565914, 0.7455647569354947, 0.05452795356301678)\n",
      "[DONE] loop: 28, logp: 2557.103981587417, (τ,σ,η): (0.6564378637296484, 0.7148466535174448, 0.053970546501705366)\n",
      "[DONE] loop: 29, logp: 2629.655879992873, (τ,σ,η): (0.6521486707439249, 0.6892559252144985, 0.05106213725220483)\n",
      "[DONE] loop: 30, logp: 2645.6163991043654, (τ,σ,η): (0.6443235387729335, 0.6782288470324924, 0.050359381063643856)\n",
      "[DONE] loop: 31, logp: 2667.649658384887, (τ,σ,η): (0.6492862045712388, 0.6576678898866506, 0.04911985750297335)\n",
      "[DONE] loop: 32, logp: 2684.276671332989, (τ,σ,η): (0.6515180743601969, 0.6597596078036199, 0.048822353668361365)\n",
      "[DONE] loop: 33, logp: 2689.349458310852, (τ,σ,η): (0.6484308186688079, 0.6529519981339271, 0.04866248071020032)\n",
      "[DONE] loop: 34, logp: 2693.804286636268, (τ,σ,η): (0.6491680804335196, 0.6498283699415607, 0.04857322133352421)\n",
      "[DONE] loop: 35, logp: 2698.9703008303563, (τ,σ,η): (0.6465875002713765, 0.6432473567041234, 0.04850961485308037)\n",
      "[DONE] loop: 36, logp: 2704.1610791074595, (τ,σ,η): (0.6507772304810375, 0.6421577786789343, 0.048440325184916325)\n",
      "[DONE] loop: 37, logp: 2706.774272493641, (τ,σ,η): (0.6553006157280523, 0.6412181558842527, 0.04848532395937196)\n",
      "[DONE] loop: 38, logp: 2708.9971589536867, (τ,σ,η): (0.6586519008100501, 0.641043227838754, 0.0484390827871803)\n",
      "[DONE] loop: 39, logp: 2710.5610302159107, (τ,σ,η): (0.6607617126468445, 0.6413160361354199, 0.048479494509571334)\n",
      "[DONE] loop: 40, logp: 2712.6190305188707, (τ,σ,η): (0.6634680329221471, 0.6411166276621222, 0.048426531348453615)\n",
      "[DONE] loop: 41, logp: 2713.9623131316807, (τ,σ,η): (0.667053563341828, 0.6424872835755139, 0.04846328610885089)\n",
      "[DONE] loop: 42, logp: 2715.8868776611766, (τ,σ,η): (0.6679310802465734, 0.6418660170660119, 0.048413993034112576)\n",
      "[DONE] loop: 43, logp: 2717.2446923224184, (τ,σ,η): (0.6694415227423035, 0.6430000606645168, 0.04845249748654982)\n",
      "[DONE] loop: 44, logp: 2719.2152839199675, (τ,σ,η): (0.6701501846087329, 0.6430304048415414, 0.04841167835341897)\n",
      "[DONE] loop: 45, logp: 2720.6504527812135, (τ,σ,η): (0.6719855701298487, 0.6443344689625085, 0.04844815700014506)\n",
      "[DONE] loop: 46, logp: 2722.461723074273, (τ,σ,η): (0.6729995241007163, 0.644368565493393, 0.04841808564216638)\n",
      "[DONE] loop: 47, logp: 2723.4703864044536, (τ,σ,η): (0.6769571199748105, 0.6458288267515855, 0.04844605669179431)\n",
      "[DONE] loop: 48, logp: 2724.409005190812, (τ,σ,η): (0.6777427881006756, 0.6448514630636656, 0.04842644696932392)\n",
      "[DONE] loop: 49, logp: 2724.7297198153187, (τ,σ,η): (0.6798597083538132, 0.6449286264047503, 0.0484500278754888)\n",
      "[DONE] loop: 50, logp: 2725.3558509485515, (τ,σ,η): (0.6798597015157152, 0.643563108509366, 0.048428654522176325)\n",
      "[DONE] loop: 51, logp: 2725.569911590433, (τ,σ,η): (0.681947931971721, 0.6430870967108792, 0.04844192017275048)\n",
      "[DONE] loop: 52, logp: 2726.143563972049, (τ,σ,η): (0.6806891811799138, 0.64166897856427, 0.04842893296689733)\n",
      "[DONE] loop: 53, logp: 2726.346221588073, (τ,σ,η): (0.6819042639019633, 0.6407700139408345, 0.048436656711897993)\n",
      "[DONE] loop: 54, logp: 2726.9010531052913, (τ,σ,η): (0.6804806718250807, 0.6392577061973435, 0.048427218512951425)\n",
      "[DONE] loop: 55, logp: 2727.1101297441487, (τ,σ,η): (0.681298976225542, 0.6381329273586331, 0.04843293163748971)\n",
      "[DONE] loop: 56, logp: 2727.6625502019656, (τ,σ,η): (0.6799704711219092, 0.6365761012023649, 0.04842298236541281)\n",
      "[DONE] loop: 57, logp: 2727.8949408699486, (τ,σ,η): (0.6805421567582595, 0.6352501400046074, 0.048429073542489084)\n",
      "[DONE] loop: 58, logp: 2728.4455543250765, (τ,σ,η): (0.6789241686193086, 0.6331535270001557, 0.04841783879047425)\n",
      "[DONE] loop: 59, logp: 2728.77951751525, (τ,σ,η): (0.6797994013151328, 0.6317750380128234, 0.04842100461990211)\n",
      "[DONE] loop: 60, logp: 2729.3581726563966, (τ,σ,η): (0.6790423748910692, 0.6302947600662137, 0.048415905848609685)\n",
      "[DONE] loop: 61, logp: 2729.7837758097244, (τ,σ,η): (0.6792958236814338, 0.6285901155398255, 0.04841764603319762)\n",
      "[DONE] loop: 62, logp: 2730.477606863354, (τ,σ,η): (0.6781069216829958, 0.62690063089106, 0.04841277876912345)\n",
      "[DONE] loop: 63, logp: 2731.094125645856, (τ,σ,η): (0.6783497032219767, 0.6250906365830378, 0.04841469256040099)\n",
      "[DONE] loop: 64, logp: 2732.111811995295, (τ,σ,η): (0.6769357177061935, 0.6232161266653027, 0.04840969014001307)\n",
      "[DONE] loop: 65, logp: 2733.2773964271805, (τ,σ,η): (0.6774638455576866, 0.6214926507430663, 0.04841480644125188)\n",
      "[DONE] loop: 66, logp: 2735.312317674275, (τ,σ,η): (0.6746425897357148, 0.6187485458628997, 0.04841003834566028)\n",
      "[DONE] loop: 67, logp: 2739.1580162574405, (τ,σ,η): (0.6776838783304503, 0.6182425651073157, 0.04839545561463926)\n",
      "[DONE] loop: 68, logp: 2746.4779170184897, (τ,σ,η): (0.6797275155287892, 0.617865947590896, 0.048334041466919574)\n",
      "[DONE] loop: 69, logp: 2748.7419195696016, (τ,σ,η): (0.6840301015048734, 0.6181893211026351, 0.048318793738716136)\n",
      "[DONE] loop: 70, logp: 2749.2328086703033, (τ,σ,η): (0.6906067889271675, 0.6161791908422538, 0.04830771256176177)\n",
      "[DONE] loop: 71, logp: 2749.8100048143656, (τ,σ,η): (0.6946416088985733, 0.6153727197658116, 0.048303848680237606)\n",
      "[DONE] loop: 72, logp: 2749.9718802875173, (τ,σ,η): (0.694775942063169, 0.6126902985579877, 0.04830074658415594)\n",
      "[DONE] loop: 73, logp: 2750.376656508722, (τ,σ,η): (0.6962483878406545, 0.6114919230025817, 0.04829458521937813)\n",
      "[DONE] loop: 74, logp: 2750.4579487591923, (τ,σ,η): (0.695027109081395, 0.6091898997843174, 0.04830169693672101)\n",
      "[DONE] loop: 75, logp: 2750.785963285693, (τ,σ,η): (0.6967933160399162, 0.6081676199600071, 0.04829636914054866)\n",
      "[DONE] loop: 76, logp: 2750.83100786408, (τ,σ,η): (0.6951465050315511, 0.6057463542084538, 0.0483023638433963)\n",
      "[DONE] loop: 77, logp: 2751.1131625698395, (τ,σ,η): (0.6966499498388522, 0.6046396823871922, 0.04829670810302248)\n",
      "[DONE] loop: 78, logp: 2751.13917384547, (τ,σ,η): (0.6950090481036866, 0.6022351985310892, 0.04830206214285517)\n",
      "[DONE] loop: 79, logp: 2751.386654899959, (τ,σ,η): (0.6961474580736797, 0.6008453724100823, 0.0482950560599886)\n",
      "[DONE] loop: 80, logp: 2751.404029595797, (τ,σ,η): (0.6947962305618502, 0.5985851095152602, 0.04829981997946795)\n",
      "[DONE] loop: 81, logp: 2751.6227420541722, (τ,σ,η): (0.6960740039685607, 0.5974502281894101, 0.04829637392777711)\n",
      "[DONE] loop: 82, logp: 2751.639725073924, (τ,σ,η): (0.6945530596544125, 0.5951887759270681, 0.04830080468454794)\n",
      "[DONE] loop: 83, logp: 2751.833182033243, (τ,σ,η): (0.6955808531774328, 0.5939476026637817, 0.048296405832225074)\n",
      "[DONE] loop: 84, logp: 2751.856965130048, (τ,σ,η): (0.69421015522498, 0.591782266578418, 0.04830012787766533)\n",
      "[DONE] loop: 85, logp: 2752.0241648324886, (τ,σ,η): (0.6951005981986755, 0.5905109123137016, 0.04829630811972246)\n",
      "[DONE] loop: 86, logp: 2752.060821117431, (τ,σ,η): (0.6938378197696793, 0.5884681631484823, 0.04829935507783352)\n",
      "[DONE] loop: 87, logp: 2752.1991046155085, (τ,σ,η): (0.6946611403684582, 0.5872002619258654, 0.04829660575780171)\n",
      "[DONE] loop: 88, logp: 2752.2455968079644, (τ,σ,η): (0.6934635210616782, 0.5852435532149649, 0.048299037697612006)\n",
      "[DONE] loop: 89, logp: 2752.3633494435694, (τ,σ,η): (0.6942203315715707, 0.583966658195485, 0.04829703698562806)\n",
      "[DONE] loop: 90, logp: 2752.420021114463, (τ,σ,η): (0.6930905518825754, 0.582090501399597, 0.048298779215695496)\n",
      "[DONE] loop: 91, logp: 2752.519913852058, (τ,σ,η): (0.6937909539645848, 0.580808405019551, 0.04829731563947161)\n",
      "[DONE] loop: 92, logp: 2752.5858305352263, (τ,σ,η): (0.6927237933641577, 0.5790034502772106, 0.04829850989488938)\n",
      "[DONE] loop: 93, logp: 2752.6695807713336, (τ,σ,η): (0.6933847662964281, 0.5777208707489007, 0.048297673922484616)\n",
      "[DONE] loop: 94, logp: 2752.7432109219285, (τ,σ,η): (0.6923786264395195, 0.5759736906690369, 0.048298293770634146)\n",
      "[DONE] loop: 95, logp: 2752.813782787063, (τ,σ,η): (0.6929986965328117, 0.5746878142515391, 0.048298063407643685)\n",
      "[DONE] loop: 96, logp: 2752.8943444484216, (τ,σ,η): (0.6920535979828983, 0.5729910929874653, 0.04829812061294898)\n",
      "[DONE] loop: 97, logp: 2752.9532372021135, (τ,σ,η): (0.6926297330605637, 0.571699548662754, 0.048298460636759966)\n",
      "[DONE] loop: 98, logp: 2753.0394204969857, (τ,σ,η): (0.691748044231026, 0.570047183203772, 0.04829797988793132)\n",
      "[DONE] loop: 99, logp: 2753.0881466559617, (τ,σ,η): (0.6922779339267181, 0.5687483469643759, 0.04829881790189226)\n",
      "[DONE] loop: 100, logp: 2753.1779422857085, (τ,σ,η): (0.6914635930727779, 0.5671358635238304, 0.04829785104314805)\n"
     ]
    }
   ],
   "source": [
    "# GPLVMの最適化 すべての潜在変数を同時更新\n",
    "X = Y*V[:,1:2]\n",
    "τ = 1.0\n",
    "σ = 5.0\n",
    "η = 1.0\n",
    "\n",
    "for loop in 1:100\n",
    "  xₛ = SCG(\n",
    "    vec(X),\n",
    "    x -> -PLL(\n",
    "      τ,σ,η,Y,\n",
    "      reshape(x, N, K)\n",
    "    ),\n",
    "    x -> -vec(∂logp∂X(\n",
    "        τ,σ,η,Y,\n",
    "        reshape(x, N, K)\n",
    "      )) + x,\n",
    "    MaxLoop=10\n",
    "  )\n",
    "  X = reshape(xₛ, N, K)\n",
    "\n",
    "  θₛ = SCG(\n",
    "    [τ,σ,η],\n",
    "    θ -> -logp(θ...,Y,X),\n",
    "    θ -> -∂logp∂τση(θ...,Y,X),\n",
    "    MaxLoop=5\n",
    "  )\n",
    "  τ = θₛ[1]\n",
    "  σ = θₛ[2]\n",
    "  η = θₛ[3]\n",
    "  \n",
    "  println(\"[DONE] loop: $(loop), logp: $(logp(τ,σ,η,Y,X)), (τ,σ,η): $((τ,σ,η))\")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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       "</g>\n",
       "</svg>\n",
       "\n"
      ],
      "text/plain": [
       "Axis(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), Any[Plot(false, true, PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(\"only_marks\" => nothing), true), Table(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), TableData([0.39878536099777834 -0.2056806018319026; 0.31846884389932467 -0.1670001028002906; … ; 0.41003591414425655 0.006653462622129282; -0.798643212469387 0.027955972108163425], [\"x\", \"y\"], Int64[], true)), Any[]), Plot(false, true, PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(\"only_marks\" => nothing), true), Table(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), TableData([-0.18022831348540894 -0.7997021509551027; -0.14171061658261636 -0.8622440946226049; … ; -0.09270175647270315 -0.8234815617098855; -0.11742297070618332 0.34099746629520744], [\"x\", \"y\"], Int64[], true)), Any[]), Plot(false, true, PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(\"only_marks\" => nothing), true), Table(PGFPlotsX.Options(OrderedCollections.OrderedDict{Any,Any}(), false), TableData([0.05041130628027627 1.2646201237610024; -0.6326755733736491 -1.6313040274174793; … ; -1.1940070859213947 0.7247113842445886; -0.012981622135295162 1.2549722693956171], [\"x\", \"y\"], Int64[], true)), Any[])])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@pgf Axis(\n",
    "  [\n",
    "    PlotInc(\n",
    "      {only_marks},\n",
    "      Table(\n",
    "        x=X[findall(e->e==label, labels),1],\n",
    "        y=X[findall(e->e==label, labels),2]\n",
    "      )\n",
    "    )\n",
    "    for label in unique(labels)\n",
    "  ]...\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## まとめ\n",
    "\n",
    "ハイパーパラメタの初期値によって結果が変わってきたりするので、安定して同じ解を得ることは難しそうです。観測データの潜在表現獲得という意味でGPLVMはとても面白い手法ですが、実際にどのように使えばいいかは把握していないため、そのあたりの情報も集めつつ更新していきたいと思っています。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "mimetype": "application/julia",
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