fastKDE 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:
Example usage:
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()The following code generates samples from a non-trivial joint distribution
from fastkde import fastKDE
import pylab as PP
import numpy as np
#***************************
# 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 samples
numSamples = int(1e6)
#Define a sigmoid function
def underlyingFunction(x,x0=305,y0=200,yrange=4):
return (yrange/2)*np.tanh(x-x0) + y0
xp1,xp2,xmid = 5,2,305 #Set gamma distribution parameters
yp1,yp2 = 0,12 #Set normal distribution parameters (mean and std)
#Generate random samples of X from the gamma distribution
x = -(np.random.gamma(xp1,xp2,int(numSamples))-xp1*xp2) + xmid
#Generate random samples of y from x and add normally distributed noise
y = underlyingFunction(x) + np.random.normal(loc=yp1,scale=yp2,size=numSamples)Now that we have the x,y samples, the following code calculates 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 data
axs[0].plot(x,y,'k.',alpha=0.1)
axs[0].set_title('Original (x,y) data')
#Set axis labels
for i in (0,1):
axs[i].set_xlabel('x')
axs[i].set_ylabel('y')
#Draw a contour plot of the conditional
axs[1].contourf(axes[0],axes[1],pOfYGivenX,64)
#Overplot the original underlying relationship
axs[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 same
xlim = [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 PDF
To see the KDE values at specified points (not necessarily those that were used to generate the KDE):
import numpy as np
from fastkde import fastKDE
train_x = 50*np.random.normal(size=100) + 0.1
train_y = 0.01*np.random.normal(size=100) - 300
test_x = 50*np.random.normal(size=100) + 0.1
test_y = 0.01*np.random.normal(size=100) - 300
test_points = list(zip(test_x, test_y))
test_point_pdf_values = fastKDE.pdf_at_points(train_x, train_y, list_of_points = test_points)Note that this method can be significantly slower than calls to fastkde.pdf() since it does not benefit from using a fast Fourier transform during the final stage in which the PDF estimate is transformed from spectral space into data space, whereas fastkde.pdf() does.
A standard python build: python setup.py install
or
pip install fastkde
Please contact Travis A. O'Brien TAOBrien@lbl.gov to obtain the latest version of the source.
This code requires the following software:
- Python >= 2.7.3
- Numpy >= 1.7
- scipy
- cython
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