File:Gaussianprocess posteriorMeanNoise.svg
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Original file (SVG file, nominally 360 × 180 pixels, file size: 27 KB)
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This is a file from the Wikimedia Commons |
Summary
| Description |
English: Posterior gaussian process with input noise visualized with posterior mean and confidence interval |
| Date | |
| Source | Own work |
| Author | Physikinger |
| SVG development |  This plot was created with Matplotlib. |
| Source code | Python code#This source code is public domain
#Author: Christian Schirm
import numpy, scipy.spatial
import matplotlib.pyplot as plt
def covMat(x1, x2, covFunc, noise=0): # Covariance matrix
cov = covFunc(scipy.spatial.distance_matrix(numpy.atleast_2d(x1).T, numpy.atleast_2d(x2).T))
if noise: cov += numpy.diag(numpy.ones(len(cov))*noise)
return cov
def interpol(x_known, y_known, x_unknown, covFunc, noise=0, sigmaPrior=1):
Ckk = covMat(x_known, x_known, covFunc)
Cuk = covMat(x_unknown, x_known, covFunc, noise=0)
y_unknown = numpy.dot(Cuk, numpy.dot(numpy.linalg.inv(Ckk), y_known))
CkkInv = numpy.linalg.inv(Ckk)
sigma_unknown = numpy.sqrt(sigmaPrior * sigmaPrior - numpy.diag(numpy.dot(Cuk, numpy.dot(CkkInv, Cuk.T))))
return y_unknown, sigma_unknown
covFunc = lambda d: numpy.exp(-(d**1.9/8.)) # Covariance function
x_known = numpy.array([2,3,7])
y_known = numpy.array([-1,0,1])
x_unknown = numpy.linspace(0, 10, 300)
y_unknown, sigma_unknown = interpol(x_known, y_known, x_unknown, covFunc)
Ckk = covMat(x_known, x_known, covFunc, noise=0.1)
Cuu = covMat(x_unknown, x_unknown, covFunc, noise=0.00)
CkkInv = numpy.linalg.inv(Ckk)
Cuk = covMat(x_unknown, x_known, covFunc, noise=0.0)
m = 0 #numpy.mean(y)
covPost = Cuu - numpy.dot(numpy.dot(Cuk,CkkInv),Cuk.T)
y_unknown = numpy.dot(numpy.dot(Cuk,CkkInv),y_known)
fig = plt.figure(figsize=(4.0,2))
plt.plot(x_unknown, y_unknown, label=u'Prediction')
sigma = numpy.sqrt(numpy.diag(covPost))
plt.plot(x_known, y_known,'ko')
plt.fill_between(x_unknown.ravel(), y_unknown - sigma, y_unknown + sigma, color = '0.85')
plt.axis([0,10,-3,3])
plt.savefig('Gaussianprocess_posteriorMeanNoise.svg')
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Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 21:56, 21 August 2017 | | 360 × 180 (27 KB) | Physikinger | User created page with UploadWizard |
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