Created
April 10, 2012 16:46
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An iPython notebook containing a short PyMC tutorial on Gaussian Processes. Requires PyMC and iPython (>=0.12) to be installed.
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{ | |
"metadata": { | |
"name": "GP Tutorial" | |
}, | |
"nbformat": 3, | |
"worksheets": [ | |
{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"collapsed": true, | |
"input": [ | |
"from pymc.gp import *" | |
], | |
"language": "python", | |
"outputs": [], | |
"prompt_number": 23 | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"## Mean function", | |
"", | |
"The mean function of a GP can be interpreted as a \"prior guess\" at the form of the true function." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"# Generate mean", | |
"def quadfun(x, a, b, c):", | |
" return (a*x**2 + b*x + c)", | |
"", | |
"M = Mean(quadfun, a=1., b=0.5, c=2.)" | |
], | |
"language": "python", | |
"outputs": [], | |
"prompt_number": 24 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"from pylab import *", | |
"x = arange(-1,1,0.1)", | |
"plot(x, M(x), 'k-')" | |
], | |
"language": "python", | |
"outputs": [ | |
{ | |
"output_type": "pyout", | |
"prompt_number": 25, | |
"text": [ | |
"[<matplotlib.lines.Line2D at 0x111c94a90>]" | |
] | |
}, | |
{ | |
"output_type": "display_data", | |
"png": 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DB9HU1GTvMp1GTzeVWvJ72ecRzTvvvGO4k7WzBQsWYPLkyT1+f0NDA7y9vQ2P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\nIiKJYsATEUkUA56ISKL+D4/fGuInIGK/AAAAAElFTkSuQmCC\n" | |
} | |
], | |
"prompt_number": 25 | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"## Covariance function", | |
"", | |
"The behavior of individual realizations from the GP is governed by the covariance function. The Matèrn class of functions is a flexible choice." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"from pymc.gp.cov_funs import matern", | |
"import numpy as np", | |
"C = Covariance(eval_fun=matern.euclidean, diff_degree=1.4, amp=0.4, scale=1, rank_limit=1000)", | |
"", | |
"subplot(1,2,2)", | |
"contourf(x, x, C(x,x).view(ndarray), origin='lower', extent=(-1,1,-1,1), cmap=cm.bone)", | |
"colorbar()", | |
"", | |
"subplot(1,2,1)", | |
"plot(x, C(x,0).view(ndarray), 'k-')", | |
"ylabel('C(x,0)')" | |
], | |
"language": "python", | |
"outputs": [ | |
{ | |
"output_type": "pyout", | |
"prompt_number": 34, | |
"text": [ | |
"<matplotlib.text.Text at 0x112713290>" | |
] | |
}, | |
{ | |
"output_type": "display_data", | |
"png": 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enp6YNGmSVjsiEvVMYULpWFDVwz6tks/bb7+NF198EUVFRdiyZQt++uknvP/+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\nqh6ptFLzQQJDyWcEHR0dOH3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ff/zxiMcdPnyY0TgUCoVCLpcrUlJSFHfv3lUoFArFhx9+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\nAAAASUVORK5CYII=\n" | |
} | |
], | |
"prompt_number": 34 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"# Returns the diagnonal", | |
"C(x)" | |
], | |
"language": "python", | |
"outputs": [ | |
{ | |
"output_type": "pyout", | |
"prompt_number": 38, | |
"text": [ | |
"array([ 0.16, 0.16, 0.16, 0.16, 0.16, 0.16, 0.16, 0.16, 0.16,", | |
" 0.16, 0.16, 0.16, 0.16, 0.16, 0.16, 0.16, 0.16, 0.16,", | |
" 0.16, 0.16])" | |
] | |
} | |
], | |
"prompt_number": 38 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"diag(C(x,x))" | |
], | |
"language": "python", | |
"outputs": [ | |
{ | |
"output_type": "pyout", | |
"prompt_number": 39, | |
"text": [ | |
"array([ 0.16, 0.16, 0.16, 0.16, 0.16, 0.16, 0.16, 0.16, 0.16,", | |
" 0.16, 0.16, 0.16, 0.16, 0.16, 0.16, 0.16, 0.16, 0.16,", | |
" 0.16, 0.16])" | |
] | |
} | |
], | |
"prompt_number": 39 | |
}, | |
{ | |
"cell_type": "heading", | |
"level": 2, | |
"source": [ | |
"Drawing realizations from a GP" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"# Generate realizations", | |
"f_list = [Realization(M, C) for i in range(3)]", | |
"", | |
"# Plot mean and covariance", | |
"x = arange(-1,1,0.01)", | |
"plot_envelope(M, C, x)", | |
"", | |
"# Add realizations", | |
"for f in f_list:", | |
" plot(x, f(x))" | |
], | |
"language": "python", | |
"outputs": [ | |
{ | |
"output_type": "display_data", | |
"png": 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RkUFRURFerzckjRME4cQhyzJNTU0UFRX1Of9+NNfXu1CanUQumN/vc/h8Pm677bZjrmRt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\n" | |
} | |
], | |
"prompt_number": 44 | |
}, | |
{ | |
"cell_type": "heading", | |
"level": 2, | |
"source": [ | |
"Non-parametric Regression" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"Under a GP prior for an unknown function `f`, when the observation error is normally distributed, the posterior us another GP with new mean and covariance functions." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"M = Mean(quadfun, a=1., b=0.5, c=2.)", | |
"C = Covariance(eval_fun=matern.euclidean, diff_degree=1.4, amp=0.4, scale=1, rank_limit=1000)", | |
"", | |
"obs_x = np.array([-.5, .5])", | |
"V = np.array([0.002, 0.002])", | |
"data = np.array([3.1, 2.9])", | |
"", | |
"observe(M=M, C=C, obs_mesh=obs_x, obs_V=V, obs_vals=data)", | |
"", | |
"# Generate realizations from posterior", | |
"f_list = [Realization(M,C) for i in range(3)]" | |
], | |
"language": "python", | |
"outputs": [], | |
"prompt_number": 68 | |
}, | |
{ | |
"cell_type": "markdown", | |
"source": [ | |
"The function `observe` informs the mean and covariance functions that values on `obs_mesh` with observation variance `V`. Making observations with no error is called `conditioning`. This is useful when, for example, forcing a rate function to be zero when a population's size is zero." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"plot_envelope(M, C, mesh=x)", | |
"for f in f_list:", | |
" plot(x, f(x))" | |
], | |
"language": "python", | |
"outputs": [ | |
{ | |
"output_type": "display_data", | |
"png": 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0/beiG52GpDp5hzqNUuKW0XpePtBCatBxMpLjCQwM7HQLF/fjudR9t5sjy55j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\nwA/AcLwvdevWrVs3Ug30er1s3LiR4uJiVFXFZrMRFxdHRUUFv/jFL1i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| |
} | |
], | |
"prompt_number": 69 | |
}, | |
{ | |
"cell_type": "heading", | |
"level": 2, | |
"source": [ | |
"Salmon Example" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": true, | |
"input": [ | |
"class salmon:", | |
" \"\"\"", | |
" Reads and organizes data from csv files,", | |
" acts as a container for mean and covariance objects,", | |
" makes plots.", | |
" \"\"\"", | |
" def __init__(self, name, data):", | |
"", | |
" # Read in data", | |
"", | |
" self.name = name", | |
"", | |
" self.abundance = data[:,0].ravel()", | |
" self.frye = data[:,1].ravel()", | |
"", | |
" # Specify priors", | |
"", | |
" # Function for prior mean", | |
" def line(x, slope):", | |
" return slope * x", | |
"", | |
" self.M = Mean(line, slope = mean(self.frye / self.abundance))", | |
"", | |
" self.C = Covariance( matern.euclidean,", | |
" diff_degree = 1.4,", | |
" scale = 100. * self.abundance.max(),", | |
" amp = 200. * self.frye.max())", | |
"", | |
" observe(self.M,self.C,obs_mesh = 0, obs_vals = 0, obs_V = 0)", | |
"", | |
" self.xplot = linspace(0,1.25 * self.abundance.max(),100)", | |
"", | |
"", | |
"", | |
" def plot(self):", | |
" \"\"\"", | |
" Plot posterior from simple nonstochetric regression.", | |
" \"\"\"", | |
" figure()", | |
" plot_envelope(self.M, self.C, self.xplot)", | |
" for i in range(3):", | |
" f = Realization(self.M, self.C)", | |
" plot(self.xplot,f(self.xplot))", | |
"", | |
" plot(self.abundance, self.frye, 'k.', markersize=4)", | |
" xlabel('Female abundance')", | |
" ylabel('Frye density')", | |
" title(self.name)", | |
" axis('tight')" | |
], | |
"language": "python", | |
"outputs": [], | |
"prompt_number": 78 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"sockeye_data = np.reshape([2986,9,", | |
"3424,12.39,", | |
"1631,4.5,", | |
"784,2.56,", | |
"9671,32.62,", | |
"2519,8.19,", | |
"1520,4.51,", | |
"6418,15.21,", | |
"10857,35.05,", | |
"15044,36.85,", | |
"10287,25.68,", | |
"16525,52.75,", | |
"19172,19.52,", | |
"17527,40.98,", | |
"11424,26.67,", | |
"24043,52.6,", | |
"10244,21.62,", | |
"30983,56.05,", | |
"12037,29.31,", | |
"25098,45.4,", | |
"11362,18.88,", | |
"24375,19.14,", | |
"18281,33.77,", | |
"14192,20.44,", | |
"7527,21.66,", | |
"6061,18.22,", | |
"15536,42.9,", | |
"18080,46.09,", | |
"17354,38.82,", | |
"17301,42.22,", | |
"11486,21.96,", | |
"20120,45.05,", | |
"10700,13.7,", | |
"12867,27.71,], (34,2))" | |
], | |
"language": "python", | |
"outputs": [], | |
"prompt_number": 79 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"# Instantiate salmon object with sockeye abundance", | |
"sockeye = salmon('sockeye', sockeye_data)", | |
"", | |
"# Observe some data", | |
"observe(sockeye.M, sockeye.C, obs_mesh = sockeye.abundance, obs_vals = sockeye.frye, obs_V = .25*sockeye.frye)" | |
], | |
"language": "python", | |
"outputs": [], | |
"prompt_number": 81 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"sockeye.plot()" | |
], | |
"language": "python", | |
"outputs": [ | |
{ | |
"output_type": "display_data", | |
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Hhy+yGtlR7uKSRCOT+hhQW2nyyc/PJyYmptUmoY7mdHiO+3nPL1FCCNFDHFniuaSkBI+m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\nen6zbCKe3q4d7gte6ZYSomuQBPAzKKXIeieGc5s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APPDAA9qa9E2aFhS7+rxN5W9aYwca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\nTkSuQmCC\n" | |
} | |
], | |
"prompt_number": 82 | |
} | |
] | |
} | |
] | |
} |
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