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Created July 22, 2020 23:36
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PyStanによるレプリカ交換モンテカルロの実装例。基本的に@hankagosa さんの<http://statmodeling.hatenablog.com/entry/stan-parallel-tempering>をベースに実装。
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replica-exchange.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# PyStanによるレプリカ交換モンテカルロ実装\n",
"- PyStanを用いてレプリカ交換モンテカルロ法の実装を試行した。\n",
" - @hankagosa さんの実装例<http://statmodeling.hatenablog.com/entry/stan-parallel-tempering>をベースとした。\n",
" - 変更点はPython化と、ベクトル値の引数に対応したことくらい。\n",
"- GMM型の分布を設定し、そこから妥当なサンプルが得られるか確認した。"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pickle\n",
"\n",
"import matplotlib.pyplot as plt \n",
"import numpy as np \n",
"import pandas as pd \n",
"import seaborn as sns\n",
"\n",
"from matplotlib import cm \n",
"from mpl_toolkits.mplot3d import Axes3D \n",
"from pystan import StanModel \n",
"from scipy.stats import multivariate_normal\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"np.random.seed(1234)\n",
"plt.style.use('seaborn-whitegrid')\n",
"sns.set_palette('hls')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. 準備\n",
"### 1.1. サンプリングする分布の設定"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"data": {
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\n"
},
"metadata": {}
}
],
"source": [
"A1 = 0.9 ## ratio of GMM\n",
"A2 = 0.1 \n",
"\n",
"grid = np.meshgrid(np.arange(-3, 7, 0.005), np.arange(-3, 7, 0.005))\n",
"z = A1*multivariate_normal.pdf(mean=[0, 0], cov=[[0.2, 0], [0, 0.2]], x=np.c_[grid[0].reshape(-1), grid[1].reshape(-1)])\n",
"z += A2*multivariate_normal.pdf(mean=[4, 4], cov=[[0.2, 0], [0, 0.2]], x=np.c_[grid[0].reshape(-1), grid[1].reshape(-1)])\n",
"\n",
"fig = plt.figure()\n",
"ax = Axes3D(fig)\n",
"ax.plot_wireframe(grid[0], grid[1], z.reshape(grid[0].shape), color=\"tab:green\", alpha=0.3)\n",
"ax.contour(grid[0], grid[1], z.reshape(grid[0].shape), zdir=\"z\", offset=0.001, cmap=cm.jet)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- この分布から、MCMCによるサンプリングを試行する。\n",
" - 2つの山の間を超えられるか。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1.2. Stanモデル定義\n",
"- データは入力せず、事前分布からそのままサンプリングを行う。\n",
"- 逆温度をdataブロックで与え、逆温度可変でのサンプリングを可能にする。"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"stancode = \"\"\"\n",
"data {\n",
" real beta;\n",
"}\n",
"\n",
"parameters {\n",
" vector[2] p;\n",
"}\n",
"\n",
"model {\n",
" vector[2] mu1;\n",
" vector[2] mu2;\n",
" matrix[2, 2] cov1;\n",
" matrix[2, 2] cov2;\n",
"\n",
" for (d in 1:2) {\n",
" mu1[d] = 0.0;\n",
" mu2[d] = 4.0;\n",
" }\n",
" cov1[1][1] = 0.2; cov1[1][2] = 0.0; cov1[2][1] = 0.0; cov1[2][2] = 0.2;\n",
" cov2[1][1] = 0.2; cov2[1][2] = 0.0; cov2[2][1] = 0.0; cov2[2][2] = 0.2;\n",
"\n",
" target += beta * log_sum_exp(\n",
" log(0.9) + multi_normal_lpdf(p | mu1, cov1),\n",
" log(0.1) + multi_normal_lpdf(p | mu2, cov2)\n",
" );\n",
"}\n",
"\n",
"\"\"\""
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"filename = \"./model/gmm-posterior-PT.pickle\"\n",
"try:\n",
" with open(filename, mode=\"rb\") as f:\n",
" stanmodel = pickle.load(f)\n",
"except FileNotFoundError:\n",
" stanmodel = StanModel(model_code=stancode)\n",
" with open(filename, mode=\"wb\") as g:\n",
" pickle.dump(stanmodel, g)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. レプリカ交換モンテカルロ実装"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2.1. 関数定義\n",
"- 交換するレプリカの対を指定する関数"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"def idx_ex(n_rep, ee):\n",
" idx = np.arange(0, np.floor(n_rep/2), dtype=np.int64) * 2\n",
" if (ee % 2 == 1):\n",
" return idx[:-1] + 1\n",
" else:\n",
" return idx"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"def cast_staninit(init):\n",
" try:\n",
" return np.asscalar(init)\n",
" except ValueError:\n",
" return init"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- 交換モンテカルロ法を実行する関数"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"def replica_exMCMC(inv_T, n_ex, stanmodel, data, par_list, init, n_iter, warmup):\n",
" par_length = get_par_length(par_list)\n",
"\n",
" n_rep = len(inv_T)\n",
" len_mcmc = n_iter - warmup\n",
" n_param = np.sum(par_length) + 1 # n_parameters includes lp__.\n",
" ms_T1 = np.zeros((len_mcmc*n_ex, n_param)) # <- MCMC samples at inv_T=1.\n",
"\n",
" idx_tbl = np.zeros((n_ex, n_rep), dtype=np.int64) # index table of (exchange time, replica)\n",
" E_tbl = np.zeros((n_ex, n_rep)) # E table\n",
" init_list = [init] * n_rep\n",
"\n",
" for ee in range(n_ex):\n",
" fit_list = []\n",
" for r in range(n_rep):\n",
" data[\"beta\"] = inv_T[r]\n",
" fit_list.append(stanmodel.sampling(data=data, init=init_list[r], iter=n_iter, warmup=warmup, chains=1, seed=r, check_hmc_diagnostics=False))\n",
" ms_T1[ee * len_mcmc : (ee+1) * len_mcmc, :] = fit_list[0].extract(permuted=False, inc_warmup=False)[:,0,:]\n",
"\n",
" ## exchange replicas\n",
" E = [-fit_list[r].extract(permuted=False, pars=\"lp__\")[\"lp__\"][-1] for r in range(n_rep)]\n",
" idx = np.arange(n_rep, dtype=np.int64)\n",
"\n",
" for rr in idx_ex(n_rep, ee):\n",
" w = np.exp(-(inv_T[rr+1] - inv_T[rr]) * (E[rr] - E[rr+1]))\n",
" if (np.random.uniform(0,1,1) < w):\n",
" idx[rr] = rr+1\n",
" idx[rr+1] = rr\n",
" E_tbl[ee, :] = E\n",
" idx_tbl[ee, :] = idx\n",
"\n",
" for rr in range(n_rep):\n",
" ms = fit_list[idx_tbl[ee, rr]].extract(permuted=False)[-1, 0, :np.sum(par_length)]\n",
" init_dict = [dict(zip(par_list, np.split(ms, np.cumsum(par_length))))]\n",
" init_list[rr] = [{k:v for k,v in zip(init_dict[0].keys(), [cast_staninit(init[1]) for init in init_dict[0].items()])}]\n",
"\n",
" return ms_T1, idx_tbl, E_tbl\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"def get_par_length(par_list):\n",
" par_length = []\n",
" for item in par_list.values():\n",
" try:\n",
" par_length += [len(item)]\n",
" except TypeError:\n",
" par_length += [1]\n",
" return np.array(par_length)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2.2. サンプリング"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "CPU times: user 35.9 s, sys: 1.43 s, total: 37.4 s\nWall time: 37.5 s\n"
}
],
"source": [
"%%time\n",
"data = {}\n",
"init = [{\"p\":np.array([0.0, 0.0])}]\n",
"\n",
"N_rep = 30 ## number of replicas\n",
"N_ex = 200 ## number of exchanges\n",
"Inv_T = 0.5 ** np.linspace(0, -np.log(0.2)/np.log(2), num=N_rep)\n",
"\n",
"result = replica_exMCMC(inv_T=Inv_T, n_ex=N_ex, stanmodel=stanmodel, data=data, par_list=dict(p=np.array([0, 0])), init=init, n_iter=70, warmup=50)\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "array([1. , 0.94601405, 0.89494258, 0.84662825, 0.80092222,\n 0.75768368, 0.7167794 , 0.67808338, 0.64147641, 0.60684569,\n 0.57408455, 0.54309205, 0.51377271, 0.4860362 , 0.45979708,\n 0.43497449, 0.41149198, 0.3892772 , 0.3682617 , 0.34838074,\n 0.32957307, 0.31178076, 0.29494898, 0.27902588, 0.2639624 ,\n 0.24971214, 0.23623119, 0.22347802, 0.21141335, 0.2 ])"
},
"metadata": {},
"execution_count": 11
}
],
"source": [
"Inv_T"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3. 結果"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"取得されたサンプルを、正解の分布と重ねて見る。"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"data": {
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