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{
"metadata": {
"name": "",
"signature": "sha256:4546c842a966e540020e2626b019a53eeef72a80bedb27aced68db94017f3b00"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"!date\n",
"import numpy as np, pandas as pd, pymc as pm, matplotlib.pyplot as plt, seaborn as sns\n",
"%matplotlib inline\n",
"sns.set_context('paper')\n",
"sns.set_style('darkgrid')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Sun May 3 20:21:15 PDT 2015\r\n"
]
}
],
"prompt_number": 47
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"> Each data entry has following information: Deputy name, date, bill number, vote. The vote field can be yes, no, didn't vote (treated as no) and not present.\n",
"\n",
"Simulation of data extracted from this format:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"np.random.seed(12345) # set random seed for reproducibility\n",
"\n",
"#### simulate votes\n",
"n = 450 # number of voters\n",
"p = 30 # number of votes\n",
"\n",
"# latent variables for how and how often voters vote\n",
"position = np.random.normal(size=n)\n",
"activity = np.random.normal(size=n)\n",
"\n",
"# simulate complete data of how voters vote\n",
"# and observed data of how/whether they vote\n",
"complete_votes = np.empty((n,p))\n",
"observed_votes = np.empty((n,p))\n",
"for i in range(n):\n",
" for j in range(p):\n",
" if np.random.rand() < np.exp(position[i]) / (1 + np.exp(position[i])):\n",
" complete_votes[i,j] = 0\n",
" else:\n",
" complete_votes[i,j] = 1\n",
" \n",
" if np.random.rand() < np.exp(activity[i]) / (1 + np.exp(activity[i])):\n",
" observed_votes[i,j] = 9\n",
" else:\n",
" observed_votes[i,j] = complete_votes[i,j]\n",
" \n",
" \n",
"\n",
"print observed_votes[:10,:10]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[[ 1. 9. 1. 9. 9. 1. 1. 1. 1. 0.]\n",
" [ 9. 1. 9. 9. 9. 9. 9. 1. 9. 9.]\n",
" [ 9. 1. 9. 9. 9. 9. 0. 1. 0. 9.]\n",
" [ 0. 9. 0. 1. 9. 1. 9. 9. 9. 9.]\n",
" [ 9. 9. 9. 0. 0. 0. 9. 0. 9. 0.]\n",
" [ 1. 9. 0. 9. 9. 9. 9. 9. 9. 0.]\n",
" [ 1. 9. 0. 9. 1. 0. 1. 9. 9. 9.]\n",
" [ 9. 9. 9. 9. 0. 9. 9. 1. 9. 9.]\n",
" [ 0. 0. 1. 9. 0. 0. 0. 1. 1. 0.]\n",
" [ 0. 0. 0. 9. 9. 0. 0. 0. 0. 9.]]\n"
]
}
],
"prompt_number": 48
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the parlance of missing data, I would call what you are dealing with \"informative missingness\". The scikits-learn solution is simple: use an encoding that shows what is missing. For example, if you have prepared your data with rows for voters and columns for votes, and encoded yes, no, and missing as 1, 0, 9, you can use `sklearn.preprocessing.OneHotEncoder` to map this into a feature space with columns for yes, no, and missing:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import sklearn.preprocessing\n",
"X = sklearn.preprocessing.OneHotEncoder().fit_transform(observed_votes)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 49
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can use this transformed data in svd, mds, clustering, or whatever you like."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import sklearn.decomposition"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 50
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"X_2d = sklearn.decomposition.PCA(n_components=2).fit_transform(X.toarray())"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 51
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(X_2d[:,0], activity, 'o')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 52,
"text": [
"[<matplotlib.lines.Line2D at 0x7fe267387590>]"
]
},
{
"metadata": {},
"output_type": "display_data",
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Ca6HpD9+9bfzZPOls3udgHpWUouNX/z7pdAr7+joZbMqMQYGqijUAAHBMffjt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\n",
"text": [
"<matplotlib.figure.Figure at 0x7fe2673feb10>"
]
}
],
"prompt_number": 52
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(X_2d[:,1], position, 'o')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 53,
"text": [
"[<matplotlib.lines.Line2D at 0x7fe2672c7c90>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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e61nyg45m4gaVAkkck0kIgDaE1S23wd7+0yn43XYUYXwbujyEycodYye4G5PT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\nYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x7fe26739d690>"
]
}
],
"prompt_number": 53
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(X_2d[:,0], X_2d[:,1], 'o')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 54,
"text": [
"[<matplotlib.lines.Line2D at 0x7fe26720f7d0>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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vDURzQqNASoXO5ZRkpF+UgGtSo+c1btc/mMFzL5zSNs0L+q1Nw9iM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\n",
"text": [
"<matplotlib.figure.Figure at 0x7fe2672ebd50>"
]
}
],
"prompt_number": 54
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 54
}
],
"metadata": {}
}
]
}
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