In [2]:

    

%matplotlib inline
%config InlineBackend.figure_formats = {'png', 'retina'}

import scipy.stats
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
from sklearn.naive_bayes import GaussianNB


    

In [3]:

    

# norm(x, y) x : mean, y : distribution
# X0 mean : -2, distribution 1 , shape : (40,1), category 0
# X1 mean : 2, distribution 1 , shape : (60,1), category 1
X0 = scipy.stats.norm(-2, 1).rvs(40)
X1 = scipy.stats.norm(2, 1).rvs(60)

# [:, np.newaxis] : change shape (ex) (60,) -> (60,1) : we need for stack two matrix
X = np.hstack([X0, X1])[:, np.newaxis] 

# two category : 0 and 1
y0 = np.zeros(40)
y1 = np.ones(60)
y = np.hstack([y0, y1])

X.shape, y.shape


    

    
Out[3]:





((100, 1), (100,))

In [4]:

    

sns.distplot(X0, rug=True, kde=False, norm_hist=True, label="class 0")
sns.distplot(X1, rug=True, kde=False, norm_hist=True, label="class 1")
plt.legend()


    

    
Out[4]:





<matplotlib.legend.Legend at 0x109615b00>






    

In [5]:

    

clf_norm = GaussianNB().fit(X, y)


    

In [6]:

    

# the number of categories(y)
clf_norm.classes_


    

    
Out[6]:





array([ 0.,  1.])

In [7]:

    

# the number of (X0, X1) samples
clf_norm.class_count_


    

    
Out[7]:





array([ 40.,  60.])

In [8]:

    

# the rate of (X0, X1) samples 
clf_norm.class_prior_


    

    
Out[8]:





array([ 0.4,  0.6])

In [9]:

    

# mean of (X0, X1)
clf_norm.theta_


    

    
Out[9]:





array([[-1.75176994],
       [ 2.08589069]])

In [10]:

    

# distribution of (X0, X1)
clf_norm.sigma_


    

    
Out[10]:





array([[ 0.66957309],
       [ 0.68820588]])

In [76]:

    

# predict classification of -1
x_new = -1
clf_norm.predict_proba([[x_new]])

# the rate of category 0 is 0.97..


    

    
Out[76]:





array([[ 0.97633995,  0.02366005]])

In [81]:

    

# likelihood
px = sp.stats.norm(clf_norm.theta_, np.sqrt(clf_norm.sigma_)).pdf(x_new)
px


    

    
Out[81]:





array([[ 0.30085478],
       [ 0.00486049]])

In [78]:

    

p = px.flatten() * clf_norm.class_prior_
p


    

    
Out[78]:





array([ 0.12034191,  0.0029163 ])

In [79]:

    

p / p.sum()


    

    
Out[79]:





array([ 0.97633995,  0.02366005])