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@tok41
Created July 3, 2022 13:53
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{
"cells": [
{
"cell_type": "markdown",
"id": "3bfc56ee-e55e-46d1-b3cf-655c24a8b2a7",
"metadata": {},
"source": [
"# About\n",
"\n",
"勝率をカテゴリ分布(多項分布)のパラメータとして、パラメータを推定する"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "9d5ace60-bd1a-4417-8eac-d15ff6028620",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import collections\n",
"import scipy\n",
"\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"sns.set(font_scale=1.5)\n",
"c_list = sns.color_palette().as_hex()\n",
"color_num = len(c_list)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "d0401a82-bd72-418a-a47f-d8fc33fe3acf",
"metadata": {},
"outputs": [],
"source": [
"dct_player = {\n",
" \"さくま\": \"sakuma\", \"ようきひ\":\"yohkihi\", \"ガキ\": \"gaki\"\n",
"}\n",
"\n",
"s = \"\"\"\n",
"さくま:ガキ:ようきひ\n",
"さくま:ようきひ:ガキ\n",
"ガキ:ようきひ:さくま\n",
"ようきひ:ガキ:さくま\n",
"ようきひ:さくま:ガキ\n",
"ようきひ:ガキ:さくま\n",
"ようきひ:ガキ:さくま\n",
"ようきひ:さくま:ガキ\n",
"ようきひ:さくま:ガキ\n",
"さくま:ガキ:ようきひ\n",
"ガキ:さくま:ようきひ\n",
"ようきひ:さくま:ガキ\n",
"ようきひ:さくま:ガキ\n",
"ようきひ:さくま:ガキ\n",
"さくま:ようきひ:ガキ\n",
"さくま:ガキ:ようきひ\n",
"さくま:ようきひ:ガキ\n",
"さくま:ガキ:ようきひ\n",
"ようきひ:ガキ:さくま\n",
"ようきひ:さくま:ガキ\n",
"ようきひ:さくま:ガキ\n",
"ようきひ:さくま:ガキ\n",
"ようきひ:さくま:ガキ\n",
"ようきひ:さくま:ガキ\n",
"ようきひ:さくま:ガキ\n",
"ようきひ:さくま:ガキ\n",
"ようきひ:さくま:ガキ\n",
"\"\"\""
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "aa2f5cf2-b342-46fc-b730-b476049f4d8b",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>1</th>\n",
" <th>2</th>\n",
" <th>3</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>さくま</td>\n",
" <td>ガキ</td>\n",
" <td>ようきひ</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>さくま</td>\n",
" <td>ようきひ</td>\n",
" <td>ガキ</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>ガキ</td>\n",
" <td>ようきひ</td>\n",
" <td>さくま</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>ようきひ</td>\n",
" <td>ガキ</td>\n",
" <td>さくま</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>ようきひ</td>\n",
" <td>さくま</td>\n",
" <td>ガキ</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" 1 2 3\n",
"0 さくま ガキ ようきひ\n",
"1 さくま ようきひ ガキ\n",
"2 ガキ ようきひ さくま\n",
"3 ようきひ ガキ さくま\n",
"4 ようきひ さくま ガキ"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lst_rank = []\n",
"for t in s.strip().split(\"\\n\"):\n",
" rank = t.split(\":\")\n",
" lst_rank.append({1:rank[0], 2:rank[1], 3:rank[2]})\n",
"df_rank = pd.DataFrame(lst_rank)\n",
"df_rank.head()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "b454d2cd-637d-450f-87b7-b48996b9ac67",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Counter({'さくま': 7, 'ガキ': 2, 'ようきひ': 18})"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cnt_top = collections.Counter(df_rank[1])\n",
"cnt_top"
]
},
{
"cell_type": "markdown",
"id": "7d4f378b-d099-4dd0-88d5-a542c7860718",
"metadata": {},
"source": [
"# パラメータ推定"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "5bd4e2ad-2d9d-4bc4-9a76-b8662900beb9",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[8.0, 19.0, 3.0]"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"targets = [\"さくま\", \"ようきひ\", \"ガキ\"]\n",
"alpha = [cnt_top[k] + 1. for k in targets]\n",
"alpha"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "f34da9b4-78ae-43e3-9250-62c5a51179eb",
"metadata": {},
"outputs": [],
"source": [
"def get_dirichlet_pdf(x, alpha):\n",
" if np.min(x) <= 0:\n",
" return np.nan\n",
" return scipy.stats.dirichlet.pdf(x, alpha)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "f4e04143-1e43-4402-8fbb-f0c8d20f71c1",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x576 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N=100\n",
"x1 = np.linspace(0, 1, N)[1:N-1]\n",
"x2 = np.linspace(0, 1, N)[1:N-1]\n",
"xx1, xx2 = np.meshgrid(x1, x2)\n",
"xx3 = 1.0 - (xx1 + xx2)\n",
"l = len(x1)\n",
"res_xx1 = xx1.reshape(l*l)\n",
"res_xx2 = xx2.reshape(l*l)\n",
"res_xx3 = xx3.reshape(l*l)\n",
"\n",
"fig = plt.figure(figsize=(10, 8))\n",
"ax = fig.subplots(1, 1)\n",
"\n",
"pdfs = np.array(\n",
" [\n",
" get_dirichlet_pdf([s1,s2,s3], alpha) \n",
" for (s1, s2, s3) in zip(res_xx1, res_xx2, res_xx3)\n",
" ]\n",
")\n",
"pdfs = pdfs.reshape(l,l)\n",
"sns.heatmap(np.flipud(pdfs), ax=ax, xticklabels=False, yticklabels=False);\n",
"ax.set_xlabel(dct_player[targets[0]]);\n",
"ax.set_ylabel(dct_player[targets[1]]);"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "673c25d3-4242-4d92-bbfc-0e21f25edef1",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.26666667, 0.63333333, 0.1 ])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"scipy.stats.dirichlet.mean(alpha)"
]
},
{
"cell_type": "markdown",
"id": "2eb79f4b-c35b-43cd-ac95-64538fe33886",
"metadata": {},
"source": [
"周辺分布\n",
"\n",
"周辺分布はベータ分布になる([ref1](https://en.wikipedia.org/wiki/Dirichlet_distribution#Marginal_distributions), [ref2](https://statisticaloddsandends.wordpress.com/2021/04/20/marginal-distributions-of-the-dirichlet-distribution-and-the-aggregation-property/))\n",
"\n",
"証明は[こちら](https://math.stackexchange.com/questions/543764/let-x-y-have-a-dirichlet-distribution-with-paramters-alpha-1-alpha-2-al)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "a99cea1a-7ee7-4493-9ed3-1c85bcb4762e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(10, 5))\n",
"ax = fig.subplots(1, 1)\n",
"\n",
"x = np.linspace(0, 1, 100)\n",
"\n",
"beta_0 = scipy.stats.beta(a=alpha[0], b=sum(alpha)-alpha[0])\n",
"beta_1 = scipy.stats.beta(a=alpha[1], b=sum(alpha)-alpha[1])\n",
"beta_2 = scipy.stats.beta(a=alpha[2], b=sum(alpha)-alpha[2])\n",
"\n",
"ax.plot(x, beta_0.pdf(x=x), color=c_list[0], label=\"sakuma\");\n",
"ax.plot(x, beta_1.pdf(x=x), color=c_list[1], label=\"yohkihi\");\n",
"ax.plot(x, beta_2.pdf(x=x), color=c_list[2], label=\"gaki\");\n",
"ax.legend();\n",
"ax.set_xlabel(\"winning rate (inference)\");\n",
"ax.set_ylabel(\"density\");\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "0299b197-344d-42ca-82b0-fefdd8d5c3e8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(10, 5))\n",
"ax = fig.subplots(1, 1)\n",
"\n",
"x = np.linspace(0, 1, 100)\n",
"\n",
"beta_0 = scipy.stats.beta(a=alpha[0], b=sum(alpha)-alpha[0])\n",
"beta_1 = scipy.stats.beta(a=alpha[1], b=sum(alpha)-alpha[1])\n",
"#beta_2 = scipy.stats.beta(a=alpha[2], b=sum(alpha)-alpha[2])\n",
"\n",
"low_bound_95_0, up_bound_95_0 = beta_0.ppf([0.025, 0.975])\n",
"low_bound_95_1, up_bound_95_1 = beta_1.ppf([0.025, 0.975])\n",
"area_0 = (low_bound_95_0 < x) & (x < up_bound_95_0)\n",
"area_1 = (low_bound_95_1 < x) & (x < up_bound_95_1)\n",
"\n",
"ax.plot(x, beta_0.pdf(x=x), color=c_list[0], label=\"sakuma\");\n",
"ax.plot(x, beta_1.pdf(x=x), color=c_list[1], label=\"yohkihi\");\n",
"ax1, ax2, ay1, ay2 = ax.axis()\n",
"ax.vlines(low_bound_95_0, 0, ay2, color=c_list[0])\n",
"ax.vlines(up_bound_95_0, 0, ay2, color=c_list[0])\n",
"ax.vlines(low_bound_95_1, 0, ay2, color=c_list[1])\n",
"ax.vlines(up_bound_95_1, 0, ay2, color=c_list[1])\n",
"\n",
"ax.fill_between(x[area_0], beta_0.pdf(x=x)[area_0], color=c_list[0], alpha=0.3)\n",
"ax.fill_between(x[area_1], beta_1.pdf(x=x)[area_1], color=c_list[1], alpha=0.3)\n",
"\n",
"ax.legend();\n",
"ax.set_xlabel(\"winning rate (inference)\");\n",
"ax.set_ylabel(\"density\");"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "51661f10-ebc7-4a8b-8b1a-abd0d8e5d185",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.98547\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(10, 5))\n",
"ax = fig.subplots(1, 1)\n",
"\n",
"rs = scipy.stats.dirichlet(alpha).rvs(100000)\n",
"rate = rs[:,1] / rs[:, 0]\n",
"\n",
"b = np.linspace(0.001, 6., 30)\n",
"hst = ax.hist(rate, bins=b, color=c_list[0], density=True);\n",
"ax1, ax2, ay1, ay2 = ax.axis()\n",
"ax.vlines(1.0, 0.0, ay2, color=c_list[1], lw=3);\n",
"\n",
"print(np.mean((rate) > 1))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9d7e22da-7eb0-40fe-8010-85583c3b387b",
"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",
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}
},
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}
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