

In [15]:

    
from matplotlib import pyplot as plt
import numpy as np
from sklearn.mixture import GMM
%matplotlib inline

#------------------------------------------------------------
# Set up the dataset with a GMM to sample data from a mixture of 3 Gaussians.



In [2]:

    
# first argument is number of components M=3
model = GMM(3, n_iter=1)

#  Set the internal means, covariances,
#  and weights by-hand.
model.means_ = np.array([[-1], [0], [3]])
model.covars_ = np.array([[1.5], [1], [0.5]]) ** 2
model.weights_ = np.array([0.3, 0.5, 0.2])

X = model.sample(1000)









    



/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function sample_gaussian is deprecated; The function sample_gaussian is deprecated in 0.18 and will be removed in 0.20. Use numpy.random.multivariate_normal instead.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function sample_gaussian is deprecated; The function sample_gaussian is deprecated in 0.18 and will be removed in 0.20. Use numpy.random.multivariate_normal instead.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function sample_gaussian is deprecated; The function sample_gaussian is deprecated in 0.18 and will be removed in 0.20. Use numpy.random.multivariate_normal instead.
  warnings.warn(msg, category=DeprecationWarning)

Fit X in the gmm model for 1, 2, ... 10 components. Hint: You should create 10 instances of a GMM model, e.g. GMM(?).fit(X) would be one instance of a GMM model with ? components.



In [8]:

    
gmms = [GMM(i).fit(X) for i in range(1,10)]









    



/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class GMM is deprecated; The class GMM is deprecated in 0.18 and will be  removed in 0.20. Use class GaussianMixture instead.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function distribute_covar_matrix_to_match_covariance_type is deprecated; The functon distribute_covar_matrix_to_match_covariance_typeis deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)

Calculate the AIC and BIC for each of these 10 models, and find the best model.



In [11]:

    
aics = [g.aic(X) for g in gmms]
bics = [g.bic(X) for g in gmms]









    



/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)
/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)

Plot the AIC and BIC



In [16]:

    
plt.plot(aics)
plt.plot(bics)









    Out[16]:





[<matplotlib.lines.Line2D at 0x10ef3c690>]

Define your PDF by evenly distributing 1000 points in some range. Look up what the eval method of the model instance does, and evaluate on your 1000 data points x. You should be able to extract a pdf, and the individual responsibilities for each of the components.



In [20]:

    
# Data x_i
x = np.linspace(-6,6,1000)
pdf = gmms[2].score_samples(x.reshape(-1,1))









    



/usr/local/lib/python2.7/site-packages/sklearn/utils/deprecation.py:70: DeprecationWarning: Function log_multivariate_normal_density is deprecated; The function log_multivariate_normal_density is deprecated in 0.18 and will be removed in 0.20.
  warnings.warn(msg, category=DeprecationWarning)

Plot x as a histogram, and the PDF values over your x_i values.



In [51]:

    
plt.plot(np.linspace(-6,6,1000),np.exp(pdf[0]))
plt.hist(X,bins='auto',normed=True)









    Out[51]:





(array([ 0.00692436,  0.00230812,  0.00923248,  0.00923248,  0.01846495,
         0.03462178,  0.04154614,  0.07616793,  0.10617347,  0.11540595,
         0.20542259,  0.25850932,  0.30697982,  0.24927685,  0.1823414 ,
         0.10848159,  0.07847604,  0.06001109,  0.09924912,  0.16387645,
         0.13156278,  0.03231367,  0.01154059]),
 array([-5.48397263, -5.0507194 , -4.61746617, -4.18421294, -3.7509597 ,
        -3.31770647, -2.88445324, -2.45120001, -2.01794678, -1.58469355,
        -1.15144032, -0.71818709, -0.28493386,  0.14831937,  0.5815726 ,
         1.01482583,  1.44807907,  1.8813323 ,  2.31458553,  2.74783876,
         3.18109199,  3.61434522,  4.04759845,  4.48085168]),
 <a list of 23 Patch objects>)



In [ ]: