Package: psyneulink-fastkde
Software OverviewfastKDE calculates a kernel density estimate of arbitrarily dimensioned
data; it does so rapidly and robustly using recently developed KDE
techniques. It does so with statistical skill that is as good as
state-of-the-science ‘R’ KDE packages, and it does so 10,000 times
faster for bivariate data (even better improvements for higher
dimensionality).Please cite the following papers when using this method:O’Brien, T. A., Kashinath, K., Cavanaugh, N. R., Collins, W. D. & O’Brien, J. P. A fast and objective multidimensional kernel density estimation method: fastKDE. Comput. Stat. Data Anal. 101, 148–160 (2016).O’Brien, T. A., Collins, W. D., Rauscher, S. A. & Ringler, T. D. Reducing the computational cost of the ECF using a nuFFT: A fast and objective probability density estimation method. Comput. Stat. Data Anal. 79, 222–234 (2014).Example usage:For a standard PDF#!python

import numpy as np
from fastkde import fastKDE
import pylab as PP

#Generate two random variables dataset (representing 100000 pairs of datapoints)
N = 2e5
var1 = 50*np.random.normal(size=N) + 0.1
var2 = 0.01*np.random.normal(size=N) - 300

#Do the self-consistent density estimate
myPDF,axes = fastKDE.pdf(var1,var2)

#Extract the axes from the axis list
v1,v2 = axes

#Plot contours of the PDF should be a set of concentric ellipsoids centered on
#(0.1, -300) Comparitively, the y axis range should be tiny and the x axis range
#should be large
PP.contour(v1,v2,myPDF)
PP.show()For a conditional PDFThe following code generates samples from a non-trivial joint
distributionfromfastkdeimportfastKDEimportpylabasPPimportnumpyasnp#***************************# Generate random samples#***************************# Stochastically sample from the function underlyingFunction() (a sigmoid):# sample the absicissa values from a gamma distribution# relate the ordinate values to the sample absicissa values and add# noise from a normal distribution#Set the number of samplesnumSamples=int(1e6)#Define a sigmoid functiondefunderlyingFunction(x,x0=305,y0=200,yrange=4):return(yrange/2)*np.tanh(x-x0)+y0xp1,xp2,xmid=5,2,305#Set gamma distribution parametersyp1,yp2=0,12#Set normal distribution parameters (mean and std)#Generate random samples of X from the gamma distributionx=-(np.random.gamma(xp1,xp2,int(numSamples))-xp1*xp2)+xmid#Generate random samples of y from x and add normally distributed noisey=underlyingFunction(x)+np.random.normal(loc=yp1,scale=yp2,size=numSamples)Now that we have the x,y samples, the following code calcuates the
conditional#***************************# Calculate the conditional#***************************pOfYGivenX,axes=fastKDE.conditional(y,x)The following plot shows the results:#***************************# Plot the conditional#***************************fig,axs=PP.subplots(1,2,figsize=(10,5))#Plot a scatter plot of the incoming dataaxs[0].plot(x,y,'k.',alpha=0.1)axs[0].set_title('Original (x,y) data')#Set axis labelsforiin(0,1):axs[i].set_xlabel('x')axs[i].set_ylabel('y')#Draw a contour plot of the conditionalaxs[1].contourf(axes[0],axes[1],pOfYGivenX,64)#Overplot the original underlying relationshipaxs[1].plot(axes[0],underlyingFunction(axes[0]),linewidth=3,linestyle='--',alpha=0.5)axs[1].set_title('P(y|x)')#Set axis limits to be the samexlim=[np.amin(axes[0]),np.amax(axes[0])]ylim=[np.amin(axes[1]),np.amax(axes[1])]axs[1].set_xlim(xlim)axs[1].set_ylim(ylim)axs[0].set_xlim(xlim)axs[0].set_ylim(ylim)fig.tight_layout()PP.savefig('conditional_demo.png')PP.show()Conditional PDFHow do I get set up?A standard python build:python setup.py installorpip install fastkdeDownload the sourcePlease contact Travis A. O’BrienTAOBrien@lbl.govto obtain the latest
version of the source.Install pre-requisitesThis code requires the following software:Python >= 2.7.3Numpy >= 1.7scipycythonCopyright InformationLAWRENCE BERKELEY NATIONAL LABORATORY
RESEARCH & DEVELOPMENT, NON-COMMERCIAL USE ONLY, LICENSE

Copyright (c) 2015, The Regents of the University of California, through
Lawrence Berkeley National Laboratory (subject to receipt of any required
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Redistribution and use in source and binary forms, with or without
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without specific prior written permission.

(4) Use of the software, in source or binary form is FOR RESEARCH
& DEVELOPMENT, NON-COMMERCIAL USE, PURPOSES ONLY. All commercial use rights
for the software are hereby reserved. A separate commercial use license is
available from Lawrence Berkeley National Laboratory.

(5) In the event you create any bug fixes, patches, upgrades, updates,
modifications, derivative works or enhancements to the source code or
binary code of the software ("Enhancements") you hereby grant The Regents of
the University of California and the U.S. Government a paid-up,
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SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.  *** Copyright Notice *** FastKDE v1.0,
Copyright (c) 2015, The Regents of the University of California, through
Lawrence Berkeley National Laboratory (subject to receipt of any required
approvals from the U.S. Dept. of Energy).  All rights reserved.
If you have questions about your rights to use or distribute this software,
please contact Berkeley Lab's Innovation & Partnerships Office at
IPO@lbl.gov.
NOTICE.  This software was developed under funding from the U.S. Department of Energy.  As such,
the U.S. Government has been granted for itself and others acting on its
behalf a paid-up, nonexclusive, irrevocable, worldwide license in the
Software to reproduce, prepare derivative works, and perform publicly and
display publicly.  Beginning five (5) years after the date permission to
assert copyright is obtained from the U.S. Department of Energy, and
subject to any subsequent five (5) year renewals, the U.S. Government is
granted for itself and others acting on its behalf a paid-up, nonexclusive,
irrevocable, worldwide license in the Software to reproduce, prepare
derivative works, distribute copies to the public, perform publicly and
display publicly, and to permit others to do so.
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