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@akelleh
Created August 20, 2015 15:12
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{
"cells": [
{
"cell_type": "code",
"execution_count": 80,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as pp"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Build Some Toy Data, X1 -> X2"
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>x1</th>\n",
" <th>x2</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>2.173585</td>\n",
" <td>2.623847</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1.573401</td>\n",
" <td>1.659568</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>-0.665749</td>\n",
" <td>-0.816180</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>-0.676711</td>\n",
" <td>1.008868</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>-0.365540</td>\n",
" <td>-2.415795</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" x1 x2\n",
"0 2.173585 2.623847\n",
"1 1.573401 1.659568\n",
"2 -0.665749 -0.816180\n",
"3 -0.676711 1.008868\n",
"4 -0.365540 -2.415795"
]
},
"execution_count": 82,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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KuOMvbyCqxrZsvxYR5xj+8Ls9JEd4LEXcLw95rufwQ9yaHk4p1RFI9mIhYb5i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\nDEOFW1EUJcP4/wG0KH/1dKwAHgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x114e79510>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x1 = np.random.normal(size=1000)\n",
"x2 = np.random.normal(x1)\n",
"X = pd.DataFrame({'x1' : x1, 'x2' : x2})\n",
"X.to_csv('toy_data.csv', index=False) # it doesnt like indexes -- bug!\n",
"X.plot(x='x1',y='x2', style='bo', xlim=(-5,5))\n",
"X.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# (see tetrad)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Build some more toy data: X1; X2; (X1, X2) -> X3; X3 -> X4"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x1 = np.random.normal(size=1000)\n",
"x2 = np.random.normal(size=1000)\n",
"x3 = np.random.normal(x1 + x2)\n",
"x4 = np.random.normal(x3)\n",
"X = pd.DataFrame({'x1' : x1, 'x2' : x2, 'x3' : x3, 'x4' : x4})\n",
"X.to_csv('toy_data.csv', index=False) "
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>x1</th>\n",
" <th>x2</th>\n",
" <th>x3</th>\n",
" <th>x4</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>-0.332813</td>\n",
" <td>-0.043417</td>\n",
" <td>-1.156068</td>\n",
" <td>0.200340</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1.071049</td>\n",
" <td>0.837356</td>\n",
" <td>0.571666</td>\n",
" <td>1.315886</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.093297</td>\n",
" <td>-0.433966</td>\n",
" <td>-0.188383</td>\n",
" <td>-1.969194</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>-0.125888</td>\n",
" <td>-0.892061</td>\n",
" <td>-1.495235</td>\n",
" <td>0.080824</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.412368</td>\n",
" <td>-1.043631</td>\n",
" <td>-2.444322</td>\n",
" <td>-2.938931</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" x1 x2 x3 x4\n",
"0 -0.332813 -0.043417 -1.156068 0.200340\n",
"1 1.071049 0.837356 0.571666 1.315886\n",
"2 0.093297 -0.433966 -0.188383 -1.969194\n",
"3 -0.125888 -0.892061 -1.495235 0.080824\n",
"4 0.412368 -1.043631 -2.444322 -2.938931"
]
},
"execution_count": 84,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X.head()"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x11504a250>"
]
},
"execution_count": 85,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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tTu5eN/sd3TAMA6WU4feZ9rjHCUzvG8yaGN4vYFradB577BqHt9XYOJkan4xu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\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1150d97d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X.plot(x='x1',y='x2', style='bo', xlim=(-5,5))"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x115066090>"
]
},
"execution_count": 86,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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GccklE9iwYaEjW5XFNAGk/tmJSZOW0Nb2LGZ/SdNNb/bsZn73u+22401O2mzWUGLb/xAw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\niW6NkFWK1wv4ipDNcx9OPF8vrCpMc/8bE1n3vb7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g+fK5vPTSxButc+d+kvHxj2bWYdar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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11506b3d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X.plot(x='x1',y='x3', style='bo', xlim=(-5,5))"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x11507d890>"
]
},
"execution_count": 87,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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pWzVQGkmzuNTJk6W8+WbtBdNVx6NeGZHw41AS9UJx3ApDAG+O+0EHt1kl4CGR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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1153fa390>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X.plot(x='x3',y='x4', style='bo', xlim=(-5,5))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Let's Measure the Conditionals!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from statsmodels.nonparametric.kernel_density import KDEMultivariateConditional, KDEMultivariate\n",
"from statsmodels.nonparametric.kde import KDEUnivariate"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"var_types = { 'x1' : 'c', 'x2' : 'c', 'x3' : 'c', 'x4' : 'c' } # specify continuous, ordered, or unordered: c, o, u\n",
"bw = 'normal_reference' # how to decide the kernel bandwidth\n",
"\n",
"endog = ['x3'] # node\n",
"exog = ['x1','x2'] # parents\n",
"dep_type = [var_types[var] for var in endog] # node type (continuous = 'c')\n",
"indep_type = [var_types[var] for var in exog] # parent types\n",
"\n",
"x3_density = KDEMultivariateConditional(X[endog], X[exog], ''.join(dep_type), ''.join(indep_type), bw)"
]
},
{
"cell_type": "code",
"execution_count": 89,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"endog = ['x4']\n",
"exog = ['x3']\n",
"dep_type = [var_types[var] for var in endog] # node type (continuous = 'c')\n",
"indep_type = [var_types[var] for var in exog] # parent types\n",
"\n",
"x4_density = KDEMultivariateConditional(X[endog], X[exog], ''.join(dep_type), ''.join(indep_type), bw)"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x1_density = KDEMultivariate(X['x1'], var_type='c', bw=bw)"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x2_density = KDEMultivariate(X['x2'], var_type='c', bw=bw)"
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[<matplotlib.axes._subplots.AxesSubplot object at 0x11512df10>]], dtype=object)"
]
},
"execution_count": 93,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x11541fd90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X.hist('x2')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# What do they look like?"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x1150d9dd0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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YZWXl1z+Xl5dTXl7e/OSSE8uWwZNPwuLFsZNIrmy3HfziF6EF8cILunKpUKRS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\nB/YxOx45JtoAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11356ba90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"xmin = -5\n",
"xmax = 5\n",
"step = 0.01\n",
"pp.plot(np.arange(xmin, xmax, step), x1_density.pdf(np.arange(xmin, xmax, step)) ); pp.xlabel('x1'); pp.ylabel('density'); pp.show()\n",
"pp.plot(np.arange(xmin, xmax, step), x2_density.pdf(np.arange(xmin, xmax, step)) ); pp.xlabel('x2'); pp.ylabel('density'); pp.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.36064622, 0.22690031, 0.37083545, 0.36752322, 0.33030804,\n",
" 0.14391812, 0.32721756, 0.22715694, 0.33288873, 0.24578569])"
]
},
"execution_count": 95,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x1_density.pdf(X['x1'])[:10]"
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.37482433, 0.2840571 , 0.33979886, 0.28313592, 0.25392792,\n",
" 0.00310194, 0.33573431, 0.36488728, 0.16825916, 0.19423033])"
]
},
"execution_count": 96,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x2_density.pdf(X['x2'])[:10]"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.25170398, 0.21505744, 0.31212285, 0.27293907, 0.09585589,\n",
" 0.52303677, 0.05030287, 0.28048304, 0.28995415, 0.29221256])"
]
},
"execution_count": 97,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x3_density.pdf(X['x3'], X[['x1','x2']])[:10]"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.1880622 , 0.25325459, 0.11889284, 0.16214686, 0.24666503,\n",
" 0.28516412, 0.28058522, 0.22104826, 0.30552735, 0.24224658])"
]
},
"execution_count": 98,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x4_density.pdf(X['x4'], X[['x3']])[:10]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Let's measure the probability density of the data!"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"joint = x1_density.pdf(X['x1'])*x2_density.pdf(X['x2'])*x3_density.pdf(X['x3'], X[['x1','x2']])*x4_density.pdf(X['x4'], X[['x3']])"
]
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"-5733.6259989922792"
]
},
"execution_count": 101,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sum([ np.log(xi) for xi in joint])"
]
},
{
"cell_type": "code",
"execution_count": 100,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 6.39883291e-03, 3.51036720e-03, 4.67610711e-03,\n",
" 4.60525831e-03, 1.98315204e-03, 6.65848436e-05,\n",
" 1.55056456e-03, 5.13899793e-03, 4.96200526e-03,\n",
" 3.37932691e-03])"
]
},
"execution_count": 100,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"joint[:10]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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