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I want to construct and 1D plot a uni-variate Gaussian Mixture with say three components in Python where I already have its parameters including mu,sigma,mix coefficients.

What I am after has an equivalent in MATLAB i.e. gmdistribution(mu,sigma,p)

I think the code should look sth like this:

from numpy import *
from matplotlib.pylab import *
from sklearn import mixture

gmm = mixture.GMM(n_components=3)
gmm.means_ = np.array([[-1], [0], [3]])
gmm.covars_ = np.array([[1.5], [1], [0.5]]) ** 2
gmm.weights_ = np.array([0.3, 0.5, 0.2])
fig = plt.figure(figsize=(5, 1.7))

ax = fig.add_subplot(131)
#ax.plot(gmm, '-k')

Wondering how to do it...

Cheers

user3278640
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1 Answers1

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Assuming the Gaussian's are independent, and you want to plot the pdf, you can just combine the underlying Gaussian pdfs weighted by the probabilities:

import numpy as np
import scipy.stats as ss
import matplotlib.pyplot as plt

means = -1., 0., 3.
stdevs = 1.5, 1., 0.5
weights = 0.3, 0.5, 0.2

x = np.arange(-5., 5., 0.01)

pdfs = [p * ss.norm.pdf(x, mu, sd) for mu, sd, p in zip(means, stdevs, weights)]

density = np.sum(np.array(pdfs), axis=0)
plt.plot(x, density)

That this is correct requires a little elementary probability theory.

stochasticfish
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  • Excellent! How can I determine the Gaussians are independent? If not, what would happen to the pdf calc? – user3278640 Jul 22 '14 at 04:58
  • If you're fitting this to univariate data then one simply assumes the Gaussians are independent (as the problem is over-determined otherwise). There certainly are state space modelling situations where you might assume a non-zero correlation, but it's not typical. – stochasticfish Jul 22 '14 at 05:03