Creating Simple and Non-simple Naive Bayesian Networks in Python



Simple Naive Bayesian Network

In this we will work with simple weather dataset as per below data records which is given in screenshot:

















# Naive Bayesian Network for the nominal weather dataset

# using smoothed probabilities given in the data mining book


# Note: pomegranate requires that networkx, joblib,

# and pyyaml be installed

from pomegranate import * 

# Table for Play is discrete (isn't conditional on any other nodes)

P = DiscreteDistribution({'yes': 0.633, 'no': 0.367}) 

# Table for Outlook is conditional on Play

# Columns in the table correspond to Play, Outlook prob's

O = ConditionalProbabilityTable(
 [['yes', 'sunny', 0.238],
 ['yes', 'overcast', 0.429],
 ['yes', 'rainy', 0.333],
 ['no', 'sunny', 0.538],
 ['no', 'overcast', 0.077],
 ['no', 'rainy', 0.385]],
 [P])

# Table for Windy is conditional on Play

# Columns in the table correspond to Play, Windy prob's

W = ConditionalProbabilityTable(
 [['yes', 'false', 0.350],
 ['yes', 'true', 0.650],
 ['no', 'false', 0.583],
 ['no', 'true', 0.417]],
 [P])

# Table for Temperature is conditional on Play

# Columns in the table correspond to Play, Temperature prob's

T = ConditionalProbabilityTable(
 [['yes', 'hot', 0.238],
 ['yes', 'mild', 0.429],
 ['yes', 'cool', 0.333],
 ['no', 'hot', 0.385],
 ['no', 'mild', 0.385],
 ['no', 'cool', 0.231]],
 [P])


# Table for Humidity is conditional on Play

# Columns in the table correspond to Play, Humidity prob's

H = ConditionalProbabilityTable(
 [['yes', 'high', 0.350],
 ['yes', 'normal', 0.650],
 ['no', 'high', 0.750],
 ['no', 'normal', 0.250]],
 [P])

# Create nodes with their probability tables

s1 = Node(P, name="Play")
s2 = Node(O, name="Outlook")
s3 = Node(W, name="Windy")
s4 = Node(T, name="Temperature")
s5 = Node(H, name="Humidity")

Fit into model

model = BayesianNetwork("Weather Bayesian Network")
model.add_states(s1, s2, s3, s4, s5)        # add the nodes
model.add_edge(s1, s2)                      # add the edges
model.add_edge(s1, s3)
model.add_edge(s1, s4)
model.add_edge(s1, s5) 
model.bake()                                # actually create the network


# Can now make predictions
# Order of list is [Play, Outlook, Windy, Temperature, Humidity]
# i.e., same as order nodes were created

instance = ['yes', 'rainy', 'true', 'cool', 'high']
likelihood_yes = model.probability([instance])
instance[0] = 'no'
likelihood_no = model.probability([instance])
prob_yes = (likelihood_yes / (likelihood_yes + likelihood_no))* 100
prob_no = (likelihood_no / (likelihood_yes + likelihood_no))* 100
print(prob_yes, prob_no)

# Here it will predict the None's
print(model.predict([['yes', 'rainy', None, None, None]]))


Non-Simple Naive Bayesian Network











# Note: pomegranate requires that networkx, joblib,

# and pyyaml be installed

from pomegranate import *


# Table for G is discrete (isn't conditional on any other nodes)

G = DiscreteDistribution({'A': 1./3, 'B': 1./3, 'C': 1./3})


# Table for P is discrete (isn't conditional on any other nodes)

P = DiscreteDistribution({'A': 1./3, 'B': 1./3, 'C': 1./3})


# Table for M is conditional on other nodes

# Columns in the table correspond to G, P, M, probability

M = ConditionalProbabilityTable(
 [['A', 'A', 'A', 0.0],
 ['A', 'A', 'B', 0.5],
 ['A', 'A', 'C', 0.5],
 ['A', 'B', 'A', 0.0],
 ['A', 'B', 'B', 0.0],
 ['A', 'B', 'C', 1.0],
 ['A', 'C', 'A', 0.0],
 ['A', 'C', 'B', 1.0],
 ['A', 'C', 'C', 0.0],
 ['B', 'A', 'A', 0.0],
 ['B', 'A', 'B', 0.0],
 ['B', 'A', 'C', 1.0],
 ['B', 'B', 'A', 0.5],
 ['B', 'B', 'B', 0.0],
 ['B', 'B', 'C', 0.5],
 ['B', 'C', 'A', 1.0],
 ['B', 'C', 'B', 0.0],
 ['B', 'C', 'C', 0.0],
 ['C', 'A', 'A', 0.0],
 ['C', 'A', 'B', 1.0],
 ['C', 'A', 'C', 0.0],
 ['C', 'B', 'A', 1.0],
 ['C', 'B', 'B', 0.0],
 ['C', 'B', 'C', 0.0],
 ['C', 'C', 'A', 0.5],
 ['C', 'C', 'B', 0.5],
 ['C', 'C', 'C', 0.0]], [G, P])


# Create nodes with their probability tables

s1 = Node(G, name="G")
s2 = Node(P, name="P")
s3 = Node(M, name="M")


Use Baysian Network Model

model = BayesianNetwork("GPM Bayesian Network")
model.add_states(s1, s2, s3)                # add the nodes
model.add_edge(s1, s3)                      # add the edges
model.add_edge(s2, s3)
model.bake()                                # actually create the network

# Can now make predictions

# For each of these 3 instances, predict the None (which here is

# always the M attribute)

print(model.predict([['A', 'B', None],['A', 'C', None],['C', 'B', None]]))

# For each of these 3 instances, predict the None (which is # the M attribute for the 1st instance, the P attribute for the # 2nd instance, and the G attribute for the 3rd instance)

print(model.predict([['A', 'B', None],['A', None, 'C'],[None, 'B', 'A']]))



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