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@aflaxman
Created July 30, 2014 22:50
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{
"metadata": {
"name": "",
"signature": "sha256:ea0abb0a418c259c6dad0633abc68018d9b728c0c338a7c18b4fe288cbcb80a3"
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"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import pymc as pm, numpy as np, matplotlib.pyplot as plt, seaborn as sns\n",
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# PyMC for Linear Programming\n",
"\n",
"Stack Overflow http://stats.stackexchange.com/questions/105557/stochastic-programming-e-g-lp-with-mcmc\n",
"\n",
"> While I understand that there are far superior methods for solving LP problems (e.g. interior point algorithms), can MCMC be used to solve a stochastic LP problem?\n",
"\n",
"PyMC2 can be combined with the LP solver of your choice to solve stochastic LP problems like this one. Here is code to do it for this very simple case. I've left a note on how I would change this for a more complex LP."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"c1 = pm.Normal('c1', mu=2, tau=.5**-2)\n",
"c2 = -3\n",
"b1 = pm.Normal('b1', mu=0, tau=3.**-2)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"@pm.deterministic\n",
"def x(c1=c1, c2=c2, b1=b1):\n",
" # use an LP solver here for a complex problem\n",
" arg_min = np.empty(2)\n",
" min_val = np.inf\n",
" for x1,x2 in [[0,0], [0, b1], [-b1, 0]]: # there are only three possible extreme points,\n",
" if -x1 + x2 <= b1 and x1 >= 0 and x2 >= 0: # so check obj value at each valid one\n",
" val = c1*x1 + c2*x2\n",
" if val < min_val:\n",
" min_val = val\n",
" arg_min = [x1,x2]\n",
" \n",
" return np.array(arg_min, dtype=float)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"m = pm.MCMC(dict(c1=c1, c2=c2, b1=b1, x=x))\n",
"m.sample(20000, 10000, 10)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------80%---------- ] 16154 of 20000 complete in 0.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------100%-----------------] 20000 of 20000 complete in 0.6 sec"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pm.Matplot.plot(m)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plotting b1\n",
"Plotting"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" c1\n",
"Plotting"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" x_0\n",
"Plotting"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" x_1\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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dXT2+LAmUyTnWbY5JpI7Zv37Ldkcv4gLb7EtAsa2jC+sSLKSKn95ftin5AWHz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\nRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x3483da0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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WXV0a9fr+8OjsABWVJVH7/8dLy/ni6+1MGT8o6j2lpYUMGhR/bKW8vNDgeC02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\njV1GVlNdXsQiXWv/xnhMuwB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cYpJhiAlq4hzrmjOmsbUhejoXt2/a2Zob5NTu4wfxnX16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\nV0KIXFCklLqa0FAM8r1lQnJqhBWpH96SLykhRC6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Mw70LV5IkabDVnbk6HzgmMzdHxBnA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\n",
"text": [
"<matplotlib.figure.Figure at 0x1aa1ae80>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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kHy/bxY79Tdz42+OieHVvZmu0RZOP5hNyGilCrLMjmuV6/O5ujG4AKrocKDvU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\ngg==\n",
"text": [
"<matplotlib.figure.Figure at 0x1af6a7b8>"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Look at the weird joint distribution for $(x_1, x_2)$:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sns.jointplot(m.x.trace()[:,0], m.x.trace()[:,1], stat_func=None)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 6,
"text": [
"<seaborn.axisgrid.JointGrid at 0x1bc11908>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
"<matplotlib.figure.Figure at 0x1bc119e8>"
]
}
],
"prompt_number": 6
}
],
"metadata": {}
}
]
}
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