File:Gaussianprocess TrendSnowboard.svg
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Captions
Captions
Extrapolation with Gaussian process
Summary
[edit]| Description |
English: Extrapolation with a Gaussian process of the Google Trend for the search word "snowboard |
| 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
# Data source: https://www.google.de/trends/explore?date=all&q=Snowboard
x = numpy.array([ 2004.08, 2004.17, 2004.25, 2004.33, 2004.42, 2004.50, 2004.58,
2004.67, 2004.75, 2004.83, 2004.92, 2005.00, 2005.08, 2005.17, 2005.25,
2005.33, 2005.42, 2005.50, 2005.58, 2005.67, 2005.75, 2005.83, 2005.92,
2006.00, 2006.08, 2006.17, 2006.25, 2006.33, 2006.42, 2006.50, 2006.58,
2006.67, 2006.75, 2006.83, 2006.92, 2007.00, 2007.08, 2007.17, 2007.25,
2007.33, 2007.42, 2007.50, 2007.58, 2007.67, 2007.75, 2007.83, 2007.92,
2008.00, 2008.08, 2008.17, 2008.25, 2008.33, 2008.42, 2008.50, 2008.58,
2008.67, 2008.75, 2008.83, 2008.92, 2009.00, 2009.08, 2009.17, 2009.25,
2009.33, 2009.42, 2009.50, 2009.58, 2009.67, 2009.75, 2009.83, 2009.92,
2010.00, 2010.08, 2010.17, 2010.25, 2010.33, 2010.42, 2010.50, 2010.58,
2010.67, 2010.75, 2010.83, 2010.92, 2011.00, 2011.08, 2011.17, 2011.25,
2011.33, 2011.42, 2011.50, 2011.58, 2011.67, 2011.75, 2011.83, 2011.92,
2012.00, 2012.08, 2012.17, 2012.25, 2012.33, 2012.42, 2012.50, 2012.58,
2012.67, 2012.75, 2012.83, 2012.92, 2013.00, 2013.08, 2013.17, 2013.25,
2013.33, 2013.42, 2013.50, 2013.58, 2013.67, 2013.75, 2013.83, 2013.92,
2014.00, 2014.08, 2014.17, 2014.25, 2014.33, 2014.42, 2014.50, 2014.58,
2014.67, 2014.75, 2014.83, 2014.92, 2015.00, 2015.08, 2015.17, 2015.25,
2015.33, 2015.42, 2015.50, 2015.58, 2015.67, 2015.75, 2015.83, 2015.92,
2016.00, 2016.08, 2016.17, 2016.25, 2016.33, 2016.42, 2016.50, 2016.58])
y = numpy.array([ 100., 75., 44., 24., 18., 17., 19., 26., 37.,
57., 77., 95., 84., 70., 43., 21., 16., 15.,
18., 24., 33., 50., 70., 94., 78., 80., 43.,
21., 14., 13., 15., 22., 31., 46., 61., 72.,
60., 49., 28., 15., 11., 11., 13., 17., 23.,
33., 50., 68., 58., 44., 27., 14., 10., 10.,
12., 16., 22., 31., 46., 66., 61., 44., 26.,
13., 10., 11., 12., 16., 21., 31., 39., 56.,
56., 65., 28., 13., 10., 9., 10., 13., 17.,
24., 37., 57., 44., 30., 19., 10., 7., 8.,
9., 11., 14., 20., 29., 37., 36., 30., 15.,
10., 10., 8., 8., 9., 12., 16., 23., 34.,
34., 26., 15., 7., 5., 5., 6., 7., 10.,
14., 22., 31., 28., 42., 14., 6., 5., 4.,
5., 7., 8., 11., 18., 25., 27., 21., 11.,
5., 4., 4., 5., 6., 7., 10., 16., 21.,
27., 18., 10., 6., 4., 4., 4.])
x_known = x
y_known = numpy.log(y)
x_unknown = numpy.arange(2016.5,2023,1/12.)
def covFunc(d):
return 0.8*numpy.exp(-numpy.abs(numpy.sin(numpy.pi*d))/0.5 -numpy.abs(d/25.)**2 - 2.5) + \
(0.2-0.01)*numpy.exp(-(numpy.abs(numpy.sin(numpy.pi*d/4))/0.2)) + 0.01*numpy.exp(-numpy.abs(d/45.))
def covMat(x1, x2, covFunc, noise=0):
cov = covFunc(scipy.spatial.distance_matrix(numpy.atleast_2d(x1).T, numpy.atleast_2d(x2).T))
if noise: numpy.fill_diagonal(cov, numpy.diag(cov) + noise)
return cov
Ckk = covMat(x_known, x_known, covFunc, noise=0.02)
Cuu = covMat(x_unknown, x_unknown, covFunc, noise=0.00)
CkkInv = numpy.linalg.inv(Ckk)
Cuk = covMat(x_unknown, x_known, covFunc, noise=0)
m = numpy.mean(y_known)
y_unknown = m + numpy.dot(numpy.dot(Cuk,CkkInv), y_known - m)
sigmaPrior = numpy.sqrt(numpy.mean(numpy.square(y_known)))
sigma = sigmaPrior*numpy.sqrt(numpy.diag(Cuu - numpy.dot(numpy.dot(Cuk,CkkInv),Cuk.T)))
fig = plt.figure(figsize=(6,3), dpi=100)
plt.plot(x,y,'-')
plt.plot(x_unknown,numpy.exp(y_unknown),'r-')
plt.fill_between(x_unknown, numpy.exp(y_unknown - sigma), numpy.exp(y_unknown + sigma), color = '0.85')
plt.xlim(2004,2022.5)
plt.xticks(numpy.arange(2004,2023,2))
plt.ylim(0,100)
plt.vlines([2016.5], 0, 100,'0.6','--')
plt.title('Google trend for the search term "Snowboard"')
plt.ylabel('Searches per montht (%)')
plt.savefig('Gaussianprocess_TrendSnowboard.svg')
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Licensing
[edit]
I, the copyright holder of this work, hereby publish it under the following license:
 
|
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 | 20:52, 21 March 2023 | | 540 × 270 (38 KB) | Physikinger (talk | contribs) | Uploaded own work with UploadWizard |
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