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Thomas Bayes

The man behind the Bayes' Theorem is Thomas Bayes. He was born in 1701 or 1702 and died on the 7th of April 1761. The picture on the top of this page might be a portrait of him, but it is not sure. He has published two important works in his lifetime:

1. Divine Benevolence, or an Attempt to Prove That the Principal End of the Divine Providence and Government is the Happiness of His Creatures (1731)
2. An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of The Analyst (published anonymously in 1736)

He is most well known for the work he did in his later years, in which he took a deep interest in probability.

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Naive Bayes Classifier with Scikit

We have written Naive Bayes Classifiers from scratch in our previous chapter of our tutorial. In this part of the tutorial on Machine Learning with Python, we want to show you how to use ready-made classifiers. The module Scikit provides naive Bayes classifiers "off the rack".

Our first example uses the "iris dataset" contained in the model to train and test the classifier

# Gaussian Naive Bayes
from sklearn import datasets
from sklearn import metrics
from sklearn.naive_bayes import GaussianNB
# load the iris datasets
dataset = datasets.load_iris()
# fit a Naive Bayes model to the data
model = GaussianNB()
model.fit(dataset.data, dataset.target)
print(model)
# make predictions
expected = dataset.target
predicted = model.predict(dataset.data)
# summarize the fit of the model
print(metrics.classification_report(expected, predicted))
print(metrics.confusion_matrix(expected, predicted))

GaussianNB()
             precision    recall  f1-score   support
          0       1.00      1.00      1.00        50
          1       0.94      0.94      0.94        50
          2       0.94      0.94      0.94        50
avg / total       0.96      0.96      0.96       150
[[50  0  0]
 [ 0 47  3]
 [ 0  3 47]]

We use our person data from the previous chapter of our tutorial to train another classifier in the next example:

import numpy as np
def prepare_person_dataset(fname):
    genders = ["male", "female"]
    persons = []
    with open(fname) as fh:
        for line in fh:
            persons.append(line.strip().split())
    firstnames = []
    dataset = []  # weight and height
    for person in persons:
        firstnames.append( (person[0], person[4]) )
        height_weight = (float(person[2]), float(person[3]))
        dataset.append( (height_weight, person[4]))
    return dataset
learnset = prepare_person_dataset("data/person_data.txt")
testset = prepare_person_dataset("data/person_data_testset.txt")
print(learnset)

[((184.0, 73.0), 'male'), ((149.0, 52.0), 'female'), ((174.0, 63.0), 'female'), ((175.0, 67.0), 'male'), ((183.0, 81.0), 'female'), ((187.0, 60.0), 'male'), ((192.0, 96.0), 'male'), ((204.0, 91.0), 'male'), ((180.0, 66.0), 'male'), ((184.0, 52.0), 'male'), ((174.0, 53.0), 'male'), ((177.0, 91.0), 'male'), ((138.0, 37.0), 'female'), ((200.0, 82.0), 'male'), ((193.0, 79.0), 'male'), ((189.0, 79.0), 'male'), ((145.0, 59.0), 'female'), ((188.0, 53.0), 'male'), ((187.0, 81.0), 'male'), ((187.0, 99.0), 'male'), ((190.0, 81.0), 'male'), ((161.0, 48.0), 'female'), ((179.0, 75.0), 'female'), ((180.0, 67.0), 'male'), ((155.0, 48.0), 'male'), ((201.0, 122.0), 'male'), ((162.0, 62.0), 'female'), ((148.0, 49.0), 'female'), ((171.0, 50.0), 'male'), ((196.0, 86.0), 'female'), ((163.0, 46.0), 'female'), ((159.0, 37.0), 'female'), ((163.0, 53.0), 'male'), ((150.0, 39.0), 'female'), ((170.0, 56.0), 'female'), ((191.0, 55.0), 'male'), ((175.0, 37.0), 'male'), ((169.0, 78.0), 'female'), ((167.0, 59.0), 'female'), ((170.0, 78.0), 'male'), ((178.0, 79.0), 'male'), ((168.0, 71.0), 'female'), ((170.0, 37.0), 'female'), ((167.0, 58.0), 'female'), ((152.0, 43.0), 'female'), ((191.0, 81.0), 'male'), ((155.0, 48.0), 'female'), ((176.0, 61.0), 'male'), ((151.0, 41.0), 'female'), ((166.0, 59.0), 'female'), ((168.0, 46.0), 'male'), ((165.0, 65.0), 'female'), ((169.0, 67.0), 'male'), ((158.0, 43.0), 'female'), ((173.0, 61.0), 'male'), ((180.0, 74.0), 'male'), ((212.0, 59.0), 'male'), ((152.0, 62.0), 'female'), ((189.0, 67.0), 'male'), ((159.0, 56.0), 'female'), ((163.0, 58.0), 'female'), ((174.0, 45.0), 'female'), ((174.0, 69.0), 'male'), ((167.0, 47.0), 'male'), ((131.0, 37.0), 'female'), ((154.0, 74.0), 'female'), ((159.0, 59.0), 'female'), ((159.0, 58.0), 'female'), ((177.0, 83.0), 'female'), ((193.0, 96.0), 'male'), ((180.0, 83.0), 'female'), ((164.0, 54.0), 'male'), ((164.0, 64.0), 'female'), ((171.0, 52.0), 'male'), ((163.0, 41.0), 'female'), ((165.0, 30.0), 'male'), ((161.0, 61.0), 'female'), ((198.0, 75.0), 'male'), ((183.0, 70.0), 'female'), ((185.0, 71.0), 'male'), ((175.0, 58.0), 'male'), ((195.0, 89.0), 'male'), ((170.0, 66.0), 'female'), ((167.0, 61.0), 'female'), ((166.0, 65.0), 'female'), ((180.0, 88.0), 'female'), ((164.0, 55.0), 'male'), ((161.0, 53.0), 'female'), ((187.0, 76.0), 'male'), ((170.0, 63.0), 'female'), ((192.0, 101.0), 'male'), ((175.0, 56.0), 'male'), ((190.0, 100.0), 'male'), ((164.0, 63.0), 'male'), ((172.0, 61.0), 'female'), ((168.0, 69.0), 'female'), ((156.0, 51.0), 'female'), ((167.0, 40.0), 'female'), ((161.0, 18.0), 'male'), ((167.0, 56.0), 'female')]

# Gaussian Naive Bayes
from sklearn import datasets
from sklearn import metrics
from sklearn.naive_bayes import GaussianNB
model = GaussianNB()
#print(dataset.data, dataset.target)
w, l = zip(*learnset)
w = np.array(w)
l = np.array(l)
model.fit(w, l)
print(model)
w, l = zip(*testset)
w = np.array(w)
l = np.array(l)
predicted = model.predict(w)
print(predicted)
print(l)
# summarize the fit of the model
print(metrics.classification_report(l, predicted))
print(metrics.confusion_matrix(l, predicted))

GaussianNB()
['female' 'male' 'male' 'female' 'female' 'male' 'female' 'female' 'female'
 'female' 'female' 'female' 'female' 'female' 'male' 'female' 'male'
 'female' 'female' 'female' 'male' 'female' 'female' 'male' 'male' 'female'
 'female' 'male' 'male' 'male' 'female' 'female' 'male' 'male' 'male'
 'female' 'female' 'male' 'female' 'male' 'male' 'female' 'female' 'male'
 'female' 'male' 'male' 'female' 'male' 'female' 'female' 'female' 'male'
 'female' 'female' 'male' 'female' 'female' 'male' 'female' 'female' 'male'
 'female' 'female' 'female' 'female' 'male' 'female' 'female' 'female'
 'female' 'female' 'male' 'male' 'female' 'female' 'male' 'male' 'female'
 'female' 'male' 'male' 'female' 'male' 'male' 'male' 'female' 'male'
 'female' 'female' 'male' 'male' 'female' 'male' 'female' 'female' 'female'
 'male' 'female' 'male']
['female' 'male' 'male' 'female' 'female' 'male' 'male' 'male' 'female'
 'female' 'female' 'female' 'female' 'female' 'male' 'male' 'male' 'female'
 'female' 'female' 'male' 'female' 'female' 'male' 'male' 'female' 'male'
 'female' 'male' 'female' 'male' 'male' 'male' 'male' 'female' 'female'
 'female' 'male' 'male' 'female' 'male' 'female' 'male' 'male' 'female'
 'male' 'female' 'male' 'female' 'female' 'female' 'male' 'male' 'male'
 'male' 'male' 'female' 'male' 'male' 'female' 'female' 'female' 'male'
 'female' 'male' 'female' 'male' 'female' 'male' 'female' 'female' 'female'
 'male' 'male' 'male' 'female' 'male' 'male' 'female' 'female' 'male'
 'male' 'female' 'female' 'male' 'male' 'female' 'male' 'female' 'male'
 'male' 'female' 'female' 'male' 'male' 'female' 'female' 'male' 'female'
 'female']
             precision    recall  f1-score   support
     female       0.68      0.80      0.73        50
       male       0.76      0.62      0.68        50
avg / total       0.72      0.71      0.71       100
[[40 10]
 [19 31]]

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