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Julia_Tips.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 前準備"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"using Pkg, LinearAlgebra, LaTeXStrings, Mamba, Random;\n",
"Random.seed!(0);\n",
"\n",
"# subplot, subplot_pgf 両方が要請するパッケージ\n",
"using Statistics;\n",
"# subplotが要請するパッケージ\n",
"using Gadfly;\n",
"# subplot_pgfが要請するパッケージ\n",
"using PGFPlotsX, KernelDensity;"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Julia Version 1.2.0\n",
"Commit c6da87ff4b (2019-08-20 00:03 UTC)\n",
"Platform Info:\n",
" OS: Linux (x86_64-pc-linux-gnu)\n",
" CPU: Intel(R) Core(TM) i5-4300U CPU @ 1.90GHz\n",
" WORD_SIZE: 64\n",
" LIBM: libopenlibm\n",
" LLVM: libLLVM-6.0.1 (ORCJIT, haswell)\n",
"Environment:\n",
" JULIA_CMDSTAN_HOME = /home/nobuta05/src/cmdstan-2.21.0\n",
" JULIA_NUM_THREADS = 4\n"
]
}
],
"source": [
"versioninfo()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[32m\u001b[1m Status\u001b[22m\u001b[39m `~/.julia/environments/v1.2/Project.toml`\n",
" \u001b[90m [c91e804a]\u001b[39m\u001b[37m Gadfly v1.0.1\u001b[39m\n",
" \u001b[90m [5ab0869b]\u001b[39m\u001b[37m KernelDensity v0.5.1\u001b[39m\n",
" \u001b[90m [b964fa9f]\u001b[39m\u001b[37m LaTeXStrings v1.0.3\u001b[39m\n",
" \u001b[90m [5424a776]\u001b[39m\u001b[37m Mamba v0.12.2\u001b[39m\n",
" \u001b[90m [8314cec4]\u001b[39m\u001b[37m PGFPlotsX v1.1.0\u001b[39m\n"
]
}
],
"source": [
"Pkg.status([\"PGFPlotsX\", \"LaTeXStrings\", \"Mamba\", \"Gadfly\", \"KernelDensity\"])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Mambaのサンプリング結果において，描画する変数を指定した描画\n",
"\n",
"Mambaでは`mcmc`関数の結果を`plot`関数へ渡すことで，デフォルトではtraceplotとdensityplotが得られます．しかし特定の変数のみを指定して描画することができません．したがって変数の数が多いモデルを実行した際，ちょっとした確認が難しいです．\n",
"\n",
"Mambaライブラリの中身をほとんど真似た関数ではありますが，描画する変数の指定が可能な関数`subplot, subplot_pgf`を作成しました．前者はGadfly.Plot配列を返すのに対して，後者はPGFPlotsXのGroupPlotを返します．基本的に`subplot`のみで十分ですが，私のJuno環境下ではPlot数が増加すると，Plot output枠に描画されなくなるという現象が生じているため，一時的な対策として`subplot_pgf`を作成しました．\n",
"\n",
"現状，traceplotとdensityplot以外は対応していません．また`subplot_pgf`関数内の`*1`について，unicodeの`β`などが変数名として設定されている場合，表示されない場合があります．これを防ぐためにプリアンブルに`\\usepackage{luatexja}`を追加しています．しかし下付き文字`β₁, z₂`があると，\"glyphsがない\"というコンパイルエラーが生じます．私はこれの解決策を現状把握していません．「一部文字が表示されなくても良いからグラフを生成してほしい」場合には，**プリアンブルの`\\usepackage{luatexja}`を取り除いてください．**"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"subplot_pgf (generic function with 3 methods)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function subplot_pgf(\n",
" m::AbstractChains,\n",
" syms::Vector{Symbol},\n",
" ptype::Vector{Symbol}=[:trace, :density],\n",
" preambles::Vector{String} = [raw\"\\usepackage{luatexja}\"]\n",
")\n",
" #----- (START *1)\n",
" for preamble in preambles\n",
" if !(preamble in PGFPlotsX.CUSTOM_PREAMBLE)\n",
" push!(PGFPlotsX.CUSTOM_PREAMBLE, preamble);\n",
" end\n",
" end\n",
" #----- (END, *1)\n",
" \n",
" (nrows, nvars, nchains) = size(m.value);\n",
" c = length(ptype);\n",
" ids = [\n",
" findfirst(isequal(String(sym)), sim.names)\n",
" for sym in syms\n",
" if !isnothing(findfirst(isequal(String(sym)), sim.names))\n",
" ];\n",
" r = length(ids);\n",
"\n",
" @pgf GroupPlot(\n",
" {\n",
" group_style = {\n",
" columns = c,\n",
" rows = r,\n",
" vertical_sep = \"5em\",\n",
" horizontal_sep = \"5em\",\n",
" }\n",
" },\n",
" [[\n",
" [\n",
" typ == :trace ? Axis(\n",
" {\n",
" grid = \"both\",\n",
" legend_style = {\n",
" legend_pos = \"outer north east\"\n",
" },\n",
" xlabel = \"Iteration\",\n",
" ylabel = \"Value\",\n",
" title = sim.names[id]\n",
" },\n",
" [\n",
" PlotInc(\n",
" {\n",
" no_marks,\n",
" opacity = 0.5,\n",
" line_width = 1\n",
" },\n",
" Table(\n",
" x = m.range,\n",
" y = m.value[:,id,c]\n",
" )\n",
" )\n",
" for c in 1:nchains\n",
" ]...,\n",
" typid == length(ptype) ?\n",
" [\n",
" LegendEntry(\"Chn $c\")\n",
" for c in 1:nchains\n",
" ] : []\n",
" ) :\n",
" typ == :density ? Axis(\n",
" {\n",
" grid =\"both\",\n",
" legend_style = {\n",
" legend_pos = \"outer north east\"\n",
" },\n",
" title = sim.names[id],\n",
" xlabel = \"Value\",\n",
" ylabel = \"Density\"\n",
" },\n",
" [\n",
" begin\n",
" qs = Statistics.quantile(sim.value[:,id,c], [0.025, 0.975]);\n",
" vals = sim.value[qs[1].<=sim.value[:,id,c].<=qs[2],id,c];\n",
" minval = minimum(vals);\n",
" maxval = maximum(vals);\n",
" rng = range(minval-(maxval-minval)/10, maxval+(maxval-minval)/10, length=500);\n",
" \n",
" PlotInc(\n",
" {\n",
" no_marks,\n",
" opacity = 0.5,\n",
" line_width = 1\n",
" },\n",
" Table(\n",
" x = rng,\n",
" y = map(x->pdf(kde(vals),x), rng)\n",
" )\n",
" )\n",
" end\n",
" for c in 1:nchains\n",
" ]...,\n",
" typid == length(ptype) ? [\n",
" LegendEntry(\"Chn $c\")\n",
" for c in 1:nchains\n",
" ] : []\n",
" ) :\n",
" throw(ArgumentError(\"unsupported type $(type)\"))\n",
" for (typid, typ) in enumerate(ptype)\n",
" ]\n",
" for id in ids\n",
" ]...;]...\n",
" )\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"subplot (generic function with 1 method)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function subplot(\n",
" m::AbstractChains,\n",
" syms::Vector{Symbol};\n",
" ptype::Vector{Symbol}=[:trace, :density]\n",
")\n",
" (nrows, nvars, nchains) = size(m.value);\n",
" N = length(ptype);\n",
" ids = [\n",
" findfirst(isequal(String(s)), m.names)\n",
" for s in syms\n",
" if !isnothing(findfirst(isequal(String(s)), m.names))\n",
" ];\n",
" plots = Array{Gadfly.Plot}(undef, N, length(ids));\n",
" \n",
" for (i, id) in enumerate(ids)\n",
" for n in 1:N\n",
" plots[n, i] =\n",
" ptype[n] == :trace ? plot(\n",
" x = repeat(m.range|>collect, outer=nchains),\n",
" y = [[\n",
" m.value[:,id,c]\n",
" for c in 1:nchains\n",
" ]...;],\n",
" Geom.line(),\n",
" color = repeat(m.chains, inner=length(m.range)),\n",
" Scale.color_discrete(),\n",
" Guide.colorkey(title=\"Chain\"),\n",
" Guide.xlabel(\"Iteration\", orientation=:horizontal),\n",
" Guide.ylabel(\"Value\", orientation=:vertical),\n",
" Guide.title(m.names[id]),\n",
" Theme(line_width=0.1mm)\n",
" ) :\n",
" ptype[n] == :density ? plot(\n",
" x = [[\n",
" begin\n",
" qs = Statistics.quantile(m.value[:,id,c], [0.025, 0.975]);\n",
" m.value[qs[1].<=m.value[:,id,c].<=qs[2],id,c]\n",
" end\n",
" for c in 1:nchains\n",
" ]...;],\n",
" Geom.density(),\n",
" color = repeat(m.chains, inner=length(m.range)),\n",
" Scale.color_discrete(),\n",
" Guide.colorkey(title=\"Chain\"),\n",
" Guide.xlabel(\"Value\", orientation=:horizontal),\n",
" Guide.ylabel(\"Density\", orientation=:vertical),\n",
" Guide.title(m.names[id]),\n",
" Theme(line_width=0.3mm)\n",
" ) :\n",
" throw(ArgumentError(\"unsupported plot type $(ptype[n])\"));\n",
" end\n",
" end\n",
"\n",
" plots\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"次の簡単なモデルで，上記の`subplot`関数を確認する．"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"model = Model(\n",
" y = Stochastic(1,\n",
" (X, β, σ²) -> MvNormal(X*β, I.*σ²),\n",
" false\n",
" ),\n",
" β = Stochastic(1,\n",
" () -> MvNormal(zeros(2), I.*1000)\n",
" ),\n",
" σ² = Stochastic(\n",
" () -> Uniform(0, 1000)\n",
" )\n",
");\n",
"scheme = [NUTS([:β, :σ²])];\n",
"\n",
"\n",
"N = 10;\n",
"true_β = rand(MvNormal(zeros(2), I));\n",
"true_σ² = rand(Gamma(1,1));\n",
"X = [ones(N) rand(Uniform(-10,10),N)|>sort];\n",
"y = rand(MvNormal(X*true_β, I.*true_σ²));\n",
"\n",
"inputs = Dict{Symbol,Any}(\n",
" :X => X\n",
");\n",
"inits = [\n",
" Dict{Symbol,Any}(\n",
" :y => y,\n",
" :β => rand(MvNormal(zeros(2), I.*100)),\n",
" :σ² => rand(Gamma(1,1))\n",
" )\n",
" for _ in 1:3\n",
"];"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"MCMC Simulation of 10000 Iterations x 3 Chains...\n",
"\n",
"Chain 1: 0% [0:35:37 of 0:35:39 remaining]\n",
"Chain 1: 10% [0:00:26 of 0:00:28 remaining]\n",
"Chain 1: 20% [0:00:13 of 0:00:16 remaining]\n",
"Chain 1: 30% [0:00:09 of 0:00:12 remaining]\n",
"Chain 1: 40% [0:00:06 of 0:00:10 remaining]\n",
"Chain 1: 50% [0:00:05 of 0:00:09 remaining]\n",
"Chain 1: 60% [0:00:03 of 0:00:09 remaining]\n",
"Chain 1: 70% [0:00:02 of 0:00:08 remaining]\n",
"Chain 1: 80% [0:00:01 of 0:00:07 remaining]\n",
"Chain 1: 90% [0:00:01 of 0:00:07 remaining]\n",
"Chain 1: 100% [0:00:00 of 0:00:07 remaining]\n",
"\n",
"Chain 2: 0% [0:00:03 of 0:00:03 remaining]\n",
"Chain 2: 10% [0:00:06 of 0:00:06 remaining]\n",
"Chain 2: 20% [0:00:04 of 0:00:05 remaining]\n",
"Chain 2: 30% [0:00:03 of 0:00:05 remaining]\n",
"Chain 2: 40% [0:00:03 of 0:00:05 remaining]\n",
"Chain 2: 50% [0:00:02 of 0:00:04 remaining]\n",
"Chain 2: 60% [0:00:02 of 0:00:04 remaining]\n",
"Chain 2: 70% [0:00:01 of 0:00:04 remaining]\n",
"Chain 2: 80% [0:00:01 of 0:00:04 remaining]\n",
"Chain 2: 90% [0:00:00 of 0:00:04 remaining]\n",
"Chain 2: 100% [0:00:00 of 0:00:04 remaining]\n",
"\n",
"Chain 3: 0% [0:01:12 of 0:01:12 remaining]\n",
"Chain 3: 10% [0:00:05 of 0:00:05 remaining]\n",
"Chain 3: 20% [0:00:04 of 0:00:04 remaining]\n",
"Chain 3: 30% [0:00:03 of 0:00:04 remaining]\n",
"Chain 3: 40% [0:00:03 of 0:00:04 remaining]\n",
"Chain 3: 50% [0:00:02 of 0:00:04 remaining]\n",
"Chain 3: 60% [0:00:02 of 0:00:04 remaining]\n",
"Chain 3: 70% [0:00:01 of 0:00:04 remaining]\n",
"Chain 3: 80% [0:00:01 of 0:00:04 remaining]\n",
"Chain 3: 90% [0:00:00 of 0:00:04 remaining]\n",
"Chain 3: 100% [0:00:00 of 0:00:04 remaining]\n",
"\n"
]
}
],
"source": [
"setsamplers!(model, scheme);\n",
"sim = mcmc(model, inputs, inits, 10000, burnin=5000, thin=2, chains=3);"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
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"<svg xmlns=\"http://www.w3.org/2000/svg\"\n",
" xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
" xmlns:gadfly=\"http://www.gadflyjl.org/ns\"\n",
" version=\"1.2\"\n",
" width=\"203.2mm\" height=\"203.2mm\" viewBox=\"0 0 203.2 203.2\"\n",
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" <g transform=\"translate(158.88,191.59)\">\n",
" <g class=\"primitive\">\n",
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" </g>\n",
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