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{
"metadata": {
"name": "",
"signature": "sha256:4911b90af9bf83478ccb23dc20c106cb57f01b0c1602cf34ec05ca53b130e6ed"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"!date"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Sat Aug 2 07:13:32 PDT 2014\r\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From http://stackoverflow.com/questions/25076711/stochastic-optimization-in-python :\n",
"\n",
"> I am trying to combine cvxopt (an optimization solver) and PyMC (a sampler) to solve convex stochastic optimization problems.\n",
"\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Testing that cvxopt works\n",
"import cvxopt as co\n",
"\n",
"# Example from http://cvxopt.org/userguide/coneprog.html#linear-programming\n",
"\n",
"c = co.matrix([-4., -5.])\n",
"G = co.matrix([[2., 1., -1., 0.], [1., 2., 0., -1.]])\n",
"h = co.matrix([3., 3., 0., 0.])\n",
"sol = co.solvers.lp(c, G, h)\n",
"\n",
"# The solution sol['x'] is correct: (1,1)\n",
"list(sol['x'])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" pcost dcost gap pres dres k/t\n",
" 0: -8.1000e+00 -1.8300e+01 4e+00 0e+00 8e-01 1e+00\n",
" 1: -8.8055e+00 -9.4357e+00 2e-01 1e-16 4e-02 3e-02\n",
" 2: -8.9981e+00 -9.0049e+00 2e-03 1e-16 5e-04 4e-04\n",
" 3: -9.0000e+00 -9.0000e+00 2e-05 1e-16 5e-06 4e-06\n",
" 4: -9.0000e+00 -9.0000e+00 2e-07 1e-16 5e-08 4e-08\n",
"Optimal solution found.\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 2,
"text": [
"[0.9999999397665257, 1.0000000104681235]"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"> PyMC allows you to sample from any function of your choice. In this particular case, the function from which we sample is one that maps an LP problem to a solution. We are sampling from this function because our LP problem contains stochastic coefficients, so one cannot just apply an LP solver off-the-shelf.\n",
"\n",
"> More specifically in this case, a single PyMC output sample is simply a solution to the LP problem. As parameters of the LP problem vary (according to distributions of your choice), the output samples from PyMC would be different, and the hope is to get a posterior distribution.\n",
"\n",
"> The solution above is inspired by [this answer](http://stats.stackexchange.com/a/110063/30802), the only difference is that I am hoping to use a true general solver (in this case `cvxopt`)\n",
"\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np, pymc as pm, cvxopt as co\n",
"\n",
"# suppress cvxopt solver output, since it will be inside MCMC loop\n",
"co.solvers.options['show_progress'] = False\n",
"\n",
"c1 = pm.Normal('c1', mu=-4, tau=4.**-2)\n",
"\n",
"@pm.deterministic\n",
"def x(c1=c1):\n",
" c = co.matrix([float(c1), -5.])\n",
" G = co.matrix([[2., 1., -1., 0.], [1., 2., 0., -1.]])\n",
" h = co.matrix([3., 3., 0., 0.])\n",
" sol = co.solvers.lp(c, G, h)\n",
" solution = np.array(sol['x'],dtype=float).flatten()\n",
" return solution\n",
"\n",
"m = pm.MCMC(dict(c1=c1, x=x))\n",
"m.sample(20000, 10000, 10)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------55%- ] 11172 of 20000 complete in 0.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------73%------- ] 14702 of 20000 complete in 1.0 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------91%-------------- ] 18202 of 20000 complete in 1.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------100%-----------------] 20000 of 20000 complete in 1.8 sec"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import matplotlib.pyplot as plt, seaborn as sns\n",
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pm.Matplot.plot(m)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plotting 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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RlZWF7OxsREVFYceOHViyhH9VwrvrjjpUf2FhOeprjPux5eeX4c6dKrP3eix/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\nwsv/F7X1eb84j7ert0VtffGEDRcREalucN6OyJeUtCgxaSK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"text": [
"<matplotlib.figure.Figure at 0x7f247baee950>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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ojBQhnsVqY6S4EnLGxMSgoKAASqUSd+/eRWhoqJnhGqauQAX4m5bZ3J2zeJtL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\nEISJkCNFEARBEARhIv8/zqlVf1qtBIsAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x7f247b602050>"
]
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sns.jointplot(x.trace()[:,0], x.trace()[:,1], stat_func=None)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 8,
"text": [
"<seaborn.axisgrid.JointGrid at 0x7f247b2a6590>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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se2BgQF6vd9qYRYsWTftNdaYx2cwjST09PWppaVF7e7vmzZuXsyxnz57Vli1b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\n",
"text": [
"<matplotlib.figure.Figure at 0x7f247b2a6ad0>"
]
}
],
"prompt_number": 8
}
],
"metadata": {}
}
]
}
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