Probabilistic Graphical Models with pgmpy

In [1]:

    

!pip install pgmpy


    

    




Collecting pgmpy
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Requirement already satisfied (use --upgrade to upgrade): numpy>=1.7.0 in /opt/conda/lib/python3.5/site-packages (from pgmpy)
Requirement already satisfied (use --upgrade to upgrade): nose>=1.3.0 in /opt/conda/lib/python3.5/site-packages (from pgmpy)
Collecting coveralls>=0.4 (from pgmpy)
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Requirement already satisfied (use --upgrade to upgrade): decorator>=3.4.0 in /opt/conda/lib/python3.5/site-packages (from networkx>=1.8.1->pgmpy)
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Collecting coverage>=3.6 (from coveralls>=0.4->pgmpy)
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Requirement already satisfied (use --upgrade to upgrade): requests>=1.0.0 in /opt/conda/lib/python3.5/site-packages (from coveralls>=0.4->pgmpy)
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Successfully built pgmpy docopt
Installing collected packages: docopt, coverage, coveralls, pgmpy
Successfully installed coverage-4.3.4 coveralls-1.1 docopt-0.6.2 pgmpy-0.1.2
You are using pip version 8.1.2, however version 9.0.1 is available.
You should consider upgrading via the 'pip install --upgrade pip' command.

In [78]:

    

from pgmpy.factors import TabularCPD


    

In [79]:

    

# Declare a CPD 
grade_cpd = TabularCPD(variable="G",
    variable_card=3,
    values=[[0.3, 0.05, 0.9, 0.5],
    [0.4, 0.25, 0.08, 0.3],
    [0.3, 0.7, 0.02, 0.2]],
    evidence=["I", "D"],
    evidence_card=[2, 2])
grade_cpd


    

    
Out[79]:




TabularCPD for G
D
D_0
D_1
I
I_0
I_1
I_0
I_1
G_0
0.3000
0.0500
0.9000
0.5000
G_1
0.4000
0.2500
0.0800
0.3000
G_2
0.3000
0.7000
0.0200
0.2000

In [80]:

    

# Declare the sudent model in pgmpy

from pgmpy.models import BayesianModel
from pgmpy.factors import TabularCPD

# Define nodes and edges
student_model = BayesianModel([("D", "G"),
("I", "G"),
("G", "L"),
("I", "S")])

#Define CPDs

grade_cpd = TabularCPD(
variable="G",
variable_card=3,
values=[[0.3, 0.05, 0.9, 0.5],
[0.4, 0.25, 0.08, 0.3],
[0.3, 0.7, 0.02, 0.2]],
evidence=["I", "D"],
evidence_card=[2, 2])

difficulty_cpd = TabularCPD(
variable="D",
variable_card=2,
values=[[0.6, 0.4]])

intel_cpd = TabularCPD(
variable="I",
variable_card=2,
values=[[0.7, 0.3]])

letter_cpd = TabularCPD(
variable="L",
variable_card=2,
values=[[0.1, 0.4, 0.99],
[0.9, 0.6, 0.01]],
evidence=["G"],
evidence_card=[3])

sat_cpd = TabularCPD(
variable="S",
variable_card=2,
values=[[0.95, 0.2],
[0.05, 0.8]],
evidence=["I"],
evidence_card=[2])


#Add CPDs to nodes and edges
student_model.add_cpds(grade_cpd, difficulty_cpd,
intel_cpd, letter_cpd,
sat_cpd)

grade_cpd


    

    
Out[80]:




TabularCPD for G
D
D_0
D_1
I
I_0
I_1
I_0
I_1
G_0
0.3000
0.0500
0.9000
0.5000
G_1
0.4000
0.2500
0.0800
0.3000
G_2
0.3000
0.7000
0.0200
0.2000

In [81]:

    

student_model.get_cpds('G')


    

    
Out[81]:




TabularCPD for G
D
D_0
D_1
I
I_0
I_1
I_0
I_1
G_0
0.3000
0.0500
0.9000
0.5000
G_1
0.4000
0.2500
0.0800
0.3000
G_2
0.3000
0.7000
0.0200
0.2000

In [85]:

    

student_model.get_parents('G')


    

    
Out[85]:





['D', 'I']

In [56]:

    

from pgmpy.inference import VariableElimination

student_infer = VariableElimination(student_model)

prob_G = student_infer.query(variables='G')

print(prob_G['G'])


    

    




╒═════╤══════════╕
│ G   │   phi(G) │
╞═════╪══════════╡
│ G_0 │   0.4470 │
├─────┼──────────┤
│ G_1 │   0.2714 │
├─────┼──────────┤
│ G_2 │   0.2816 │
╘═════╧══════════╛

In [57]:

    

prob_G = student_infer.query(variables='G', evidence={'I': 1, 'D' : 0})

print(prob_G['G'])


    

    




╒═════╤══════════╕
│ G   │   phi(G) │
╞═════╪══════════╡
│ G_0 │   0.0500 │
├─────┼──────────┤
│ G_1 │   0.2500 │
├─────┼──────────┤
│ G_2 │   0.7000 │
╘═════╧══════════╛

In [58]:

    

prob_G = student_infer.query(variables='G', evidence={'I': 0, 'D' : 1})

print(prob_G['G'])


    

    




╒═════╤══════════╕
│ G   │   phi(G) │
╞═════╪══════════╡
│ G_0 │   0.9000 │
├─────┼──────────┤
│ G_1 │   0.0800 │
├─────┼──────────┤
│ G_2 │   0.0200 │
╘═════╧══════════╛

In [67]:

    

#Train Model from Data

from pgmpy.models import BayesianModel
import pandas as pd
import numpy as np
# Considering that each variable have only 2 states,
# we can generate some random data.

raw_data = np.random.randint(low=0,high=2,size=(1000, 5))


data = pd.DataFrame(raw_data,columns=["D", "I", "G","L", "S"])

print(data[: int(data.shape[0]*0.75)])

data_train = data[: int(data.shape[0] * 0.75)]

student_model = BayesianModel([("D", "G"),("I", "G"),("I", "S"),("G", "L")])
student_model.fit(data_train)
student_model.get_cpds('D')


    

    




     D  I  G  L  S
0    0  1  1  1  1
1    0  0  0  0  1
2    0  1  1  0  0
3    0  0  0  0  1
4    1  1  0  1  1
5    1  0  0  0  0
6    1  1  0  1  1
7    1  0  0  0  1
8    1  1  0  0  1
9    1  0  0  0  0
10   1  1  1  1  0
11   1  1  0  0  0
12   1  1  1  1  0
13   1  0  0  1  1
14   0  1  1  1  1
15   1  0  0  1  1
16   1  1  0  1  1
17   0  0  0  1  0
18   0  0  0  0  0
19   1  1  1  1  1
20   0  0  0  1  1
21   0  0  0  0  0
22   0  0  1  0  0
23   0  0  0  1  0
24   0  0  1  1  1
25   1  0  1  1  1
26   0  1  1  1  0
27   0  1  0  0  1
28   1  1  0  0  1
29   1  0  0  0  0
..  .. .. .. .. ..
720  1  1  1  0  1
721  0  0  1  1  1
722  1  1  1  0  1
723  1  0  0  0  0
724  1  0  0  1  1
725  0  0  1  1  1
726  0  0  1  0  1
727  0  0  1  0  0
728  1  1  1  0  0
729  1  1  0  0  0
730  0  0  0  0  0
731  1  1  1  0  0
732  0  0  1  0  1
733  1  1  0  1  0
734  0  1  0  1  1
735  0  1  1  1  0
736  1  0  1  0  0
737  1  1  1  1  0
738  1  1  1  1  1
739  0  1  1  0  0
740  1  1  1  1  1
741  1  0  1  1  0
742  0  1  1  0  1
743  1  0  1  1  0
744  0  1  1  1  1
745  1  0  0  0  1
746  1  0  0  1  0
747  0  1  1  0  1
748  1  0  0  1  1
749  0  0  1  1  1

[750 rows x 5 columns]






    
Out[67]:




TabularCPD for D
D_0
0.4400
D_1
0.5600

In [60]:

    

student_model.get_cpds('L')


    

    
Out[60]:




TabularCPD for L
G
G_0
G_1
L_0
0.4545
0.5000
L_1
0.5455
0.5000

In [25]:

    

student_model.active_trail_nodes('D')


    

    
Out[25]:





{'D', 'G', 'L'}

In [26]:

    

student_model.local_independencies('G')


    

    
Out[26]:





(G _|_ S | D, I)

In [27]:

    

student_model.get_independencies()


    

    
Out[27]:





(G _|_ L, I, S | D)
(G _|_ L, I, D | S)
(G _|_ I, S, D | L)
(G _|_ L, D | I)
(D _|_ I, S | G)
(D _|_ G, L | S)
(D _|_ G, I, S | L)
(D _|_ G, L | I)
(S _|_ I, D | G)
(S _|_ G, I, L | D)
(S _|_ G, I, D | L)
(L _|_ G, I, S | D)
(L _|_ G, I, D | S)
(L _|_ G, D | I)
(I _|_ D, S | G)
(I _|_ G, S, L | D)
(I _|_ G, L | S)
(I _|_ G, D, S | L)

In [77]:

    

data_test = data[int(0.75 * data.shape[0]) : data.shape[0]]

data_test.drop('G', axis=1, inplace=True)

student_model.predict(data_test)


    

    




/opt/conda/lib/python3.5/site-packages/ipykernel/__main__.py:3: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy
  app.launch_new_instance()






    
Out[77]:






  

    

      

      
G
    
  
  

    

      
750
      
1
    
    

      
751
      
0
    
    

      
752
      
0
    
    

      
753
      
0
    
    

      
754
      
0
    
    

      
755
      
0
    
    

      
756
      
0
    
    

      
757
      
1
    
    

      
758
      
0
    
    

      
759
      
1
    
    

      
760
      
0
    
    

      
761
      
0
    
    

      
762
      
1
    
    

      
763
      
1
    
    

      
764
      
0
    
    

      
765
      
1
    
    

      
766
      
1
    
    

      
767
      
0
    
    

      
768
      
0
    
    

      
769
      
1
    
    

      
770
      
1
    
    

      
771
      
1
    
    

      
772
      
0
    
    

      
773
      
1
    
    

      
774
      
1
    
    

      
775
      
0
    
    

      
776
      
1
    
    

      
777
      
1
    
    

      
778
      
0
    
    

      
779
      
0
    
    

      
...
      
...
    
    

      
970
      
1
    
    

      
971
      
0
    
    

      
972
      
1
    
    

      
973
      
1
    
    

      
974
      
1
    
    

      
975
      
0
    
    

      
976
      
1
    
    

      
977
      
0
    
    

      
978
      
1
    
    

      
979
      
1
    
    

      
980
      
1
    
    

      
981
      
1
    
    

      
982
      
1
    
    

      
983
      
0
    
    

      
984
      
1
    
    

      
985
      
1
    
    

      
986
      
1
    
    

      
987
      
0
    
    

      
988
      
0
    
    

      
989
      
1
    
    

      
990
      
0
    
    

      
991
      
0
    
    

      
992
      
0
    
    

      
993
      
0
    
    

      
994
      
0
    
    

      
995
      
1
    
    

      
996
      
1
    
    

      
997
      
1
    
    

      
998
      
0
    
    

      
999
      
0
    
  

250 rows × 1 columns