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']]))Contact Us!
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