Skip to content

Instantly share code, notes, and snippets.

@tok41
Created September 6, 2021 07:47
Show Gist options
  • Star 0 You must be signed in to star a gist
  • Fork 0 You must be signed in to fork a gist
  • Save tok41/6dc4d7732a896f8f7263f2a390a43cb4 to your computer and use it in GitHub Desktop.
Save tok41/6dc4d7732a896f8f7263f2a390a43cb4 to your computer and use it in GitHub Desktop.
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"id": "4d3c7488-9672-478a-b11a-c14a8e1a0a3c",
"metadata": {},
"source": [
"pythonでGibbs samplingする"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "776c463f-faaa-4ccd-aabb-acd120484f1d",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from tqdm import tqdm"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "5fb0f33e-5de9-4e36-8ec4-7310034296b7",
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"sns.set()\n",
"c_list = sns.color_palette().as_hex()\n",
"color_num = len(c_list)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "b3ac8bdd-1c2e-44b5-a0aa-216a25db83b3",
"metadata": {},
"outputs": [],
"source": [
"np.random.seed(1)"
]
},
{
"cell_type": "markdown",
"id": "78c9f81e-46a5-4c7f-bcca-07c3dbcfe00b",
"metadata": {},
"source": [
"# 線形基底関数モデル(多項式回帰)"
]
},
{
"cell_type": "markdown",
"id": "d1368122-5094-48d0-855b-576db0529169",
"metadata": {},
"source": [
"## トイデータ"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "a01ab95a-37cf-461f-b6d7-9b126e4a164c",
"metadata": {},
"outputs": [],
"source": [
"def polynomial(x, degree):\n",
" return [np.power(x, d) for d in np.arange(0, degree+1)]\n",
"\n",
"def system_model(feature, w):\n",
" y = np.dot(w, feature)\n",
" return y\n",
"\n",
"def observation(x, w, degree=3, var=0.5):\n",
" feature = polynomial(x, degree)\n",
" y = system_model(feature, w)\n",
" z = np.random.normal(loc=y, scale=np.sqrt(var))\n",
" return z"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "acff73e7-b257-4992-aabe-f08b1c77f904",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 720x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"xs = np.linspace(-3, 3, 100)\n",
"w_t = [0., 0.1, -1.5, 0.5]\n",
"y = system_model(polynomial(xs, len(w_t)-1), w_t)\n",
"\n",
"var_y = (1.0)**2\n",
"x_sample = np.random.uniform(low=-2, high=2, size=10)\n",
"z = observation(x=x_sample, w=w_t, degree=len(w_t)-1, var=var_y)\n",
"\n",
"fig = plt.figure(figsize=(10, 4))\n",
"ax = fig.subplots(1, 1)\n",
"ax.plot(xs, y, color=c_list[1], label=\"setting function\")\n",
"ax.scatter(x_sample, z, color=c_list[0], alpha=0.8, label=\"sample\")\n",
"ax.legend()\n",
"ax.set_xlabel(\"x\");\n",
"ax.set_ylabel(\"y\");"
]
},
{
"cell_type": "markdown",
"id": "431de59f-87b9-4edb-ac3d-cb8f54ee01da",
"metadata": {},
"source": [
"## 実装"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "df8ceeb7-3bd9-47b9-b3c3-24f0b55ccde9",
"metadata": {},
"outputs": [],
"source": [
"# wの事前分布のパラメータ\n",
"var_w = 1.0"
]
},
{
"cell_type": "markdown",
"id": "a7193882-2112-4126-aeb9-536550144ab5",
"metadata": {},
"source": [
"### 解析解"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "6fd5a4b2-493d-466f-a15b-004d14f7f838",
"metadata": {},
"outputs": [],
"source": [
"def design_matrix(xs, n_degree):\n",
" return np.array(polynomial(xs, n_degree)).T"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "ef949266-fdfa-4747-8017-131602b71db0",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 15.4 ms, sys: 7.08 ms, total: 22.5 ms\n",
"Wall time: 21.7 ms\n"
]
}
],
"source": [
"%%time\n",
"# 解析解\n",
"Phi = design_matrix(x_sample, 3)\n",
"Sig_hat_inv = var_y * np.dot(Phi.T, Phi) + var_w * np.eye(4)\n",
"Sig_hat = np.linalg.inv(Sig_hat_inv)\n",
"mu_hat = var_y * np.dot(np.dot(Sig_hat, Phi.T), z)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "aab4dae0-775b-4b34-b987-56cef7878b8a",
"metadata": {},
"outputs": [],
"source": [
"n_sample = 1000\n",
"w_post = np.random.multivariate_normal(mu_hat, Sig_hat, n_sample)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "4c57aa0f-4f2e-4d37-867b-c018e62964eb",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 864x864 with 4 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 3*len(mu_hat)))\n",
"ax = fig.subplots(len(mu_hat),1, sharex=True)\n",
"\n",
"for i in range(len(mu_hat)):\n",
" ax[i].hist(w_post[:,i], alpha=0.8, label=f\"dim:{i}\")\n",
" ax[i].vlines(w_t[i], 0, n_sample/10, color=\"red\", label=\"setting\")\n",
" ax[i].legend()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "cf59996c-587e-4de0-abe8-bfb910986484",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 720x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"w = mu_hat\n",
"y = system_model(polynomial(xs, len(w)-1), w)\n",
"y_set = system_model(polynomial(xs, len(w_t)-1), w_t)\n",
"\n",
"fig = plt.figure(figsize=(10, 4))\n",
"ax = fig.subplots(1, 1)\n",
"ax.plot(xs, y, color=c_list[0], label=\"mean\")\n",
"for i in range(100):\n",
" w_tmp = w_post[i,:]\n",
" y_tmp = system_model(polynomial(xs, len(w_tmp)-1), w_tmp)\n",
" ax.plot(xs, y_tmp, color=\"gray\", alpha=0.2)\n",
"\n",
"ax.scatter(x_sample, z, color=\"blue\", alpha=0.8, label=\"data\")\n",
"ax.plot(xs, y_set, color=c_list[1], label=\"setting function\")\n",
"ax.legend()\n",
"ax.set_xlabel(\"x\");\n",
"ax.set_ylabel(\"y\");"
]
},
{
"cell_type": "markdown",
"id": "9a88c186-9708-4596-9e8c-0dc3d576849b",
"metadata": {},
"source": [
"### Gibbs sampling"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "69760b02-f6e6-4b20-a143-f26368b33126",
"metadata": {},
"outputs": [],
"source": [
"# ギブスサンプリング\n",
"n_degree = 3 # モデルの次数\n",
"\n",
"n_sample = 10000\n",
"n_burn = 500\n",
"w = np.zeros(n_degree+1)\n",
"ws = np.zeros((n_sample+1, n_degree+1))\n",
"ws[0] = w"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "6041eaed-051e-413c-a015-f6a2bd37e2f8",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(10, 4)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"design_mat = design_matrix(xs=x_sample, n_degree=n_degree)\n",
"design_mat.shape"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "f5b92823-d813-4269-b2ec-7f968e26d37e",
"metadata": {},
"outputs": [],
"source": [
"def alpha_i(design_mat, w, idx):\n",
" w_not_i = np.delete(w, idx)\n",
" dm_not_i = np.delete(design_mat, idx, 1)\n",
" return np.dot(w_not_i, dm_not_i.T)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "d4b7cc6b-45b7-4ed9-815a-f4b071d864c5",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 10000/10000 [00:08<00:00, 1129.12it/s]"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 8.99 s, sys: 98.4 ms, total: 9.08 s\n",
"Wall time: 8.94 s\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"%%time\n",
"for i in tqdm(np.arange(n_sample)):\n",
" for idx in range(n_degree+1): # wを一つづつサンプル\n",
" sum_phi_2 = np.dot(design_mat[:,idx], design_mat[:,idx])\n",
" inv_var_hat = (1./var_w) + (1./var_y) * sum_phi_2\n",
" var_hat = 1. / inv_var_hat\n",
" \n",
" sum_y_phi = np.dot(z, design_mat[:, idx])\n",
" alpha = alpha_i(design_mat, w, idx)\n",
" sum_a_phi = np.dot(alpha, design_mat[:, idx])\n",
" m_hat = (sum_y_phi - sum_a_phi) * (1./var_y) * var_hat\n",
" \n",
" w[idx] = np.random.normal(m_hat, np.sqrt(var_hat))\n",
" ws[i+1] = w.copy()"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "9f0a1d81-55df-41b3-bfea-aacc4dd540d3",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(10001, 4)"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ws.shape"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "b2c965d8-61d4-4fd0-85a5-26895562b1be",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x407fb50b80>"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 864x216 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 3))\n",
"ax = fig.subplots(1,1)\n",
"\n",
"for i in np.arange(n_degree+1):\n",
" ax.plot(ws[n_burn:,i], label='{} degree'.format(i))\n",
"ax.legend()"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "5ff2a30c-a804-406f-9aa4-5085b39b3175",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 864x864 with 4 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 3*(n_degree+1)))\n",
"ax = fig.subplots((n_degree+1),1, sharex=True)\n",
"if n_degree < 1:\n",
" ax = [ax]\n",
"\n",
"for i in range(n_degree+1):\n",
" ax[i].hist(ws[n_burn:,i], label=f'{i}-degree')\n",
" ax[i].vlines(w_t[i], 0, n_sample/10, color=\"red\", label=\"setting\")\n",
" ax[i].legend()"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "6a3cf9b9-a0a7-4a7e-a938-996fb7393a46",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x407f68a5b0>]"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 720x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# 事後分布からwをサンプル\n",
"rand_idx = np.random.choice(n_sample-n_burn, 100, replace=False) + n_burn\n",
"sample_post_ws = ws[rand_idx, :]\n",
"\n",
"fig = plt.figure(figsize=(10, 4))\n",
"ax = fig.subplots(1,1)\n",
"\n",
"sample_prior = list(map(lambda x:np.dot(sample_post_ws, polynomial(x=x, degree=n_degree)), xs))\n",
"ax.plot(xs, sample_prior, '-', c='gray', alpha=0.2)\n",
"ax.plot(xs, y, '--', lw=3)\n",
"ax.plot(x_sample, z, 'o')"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ab0ca4e7-54fd-470c-bbc8-c1ce51424d39",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment