asia_pgm.ipynb

Kernel: Python 3

Inference in the "Asia" directed probabilistic graphical model

Based on https://github.com/probml/pmtk3/blob/master/demos/asiaDgm.m and https://github.com/pgmpy/pgmpy/blob/dev/examples/Inference in Bayesian Networks.ipynb

!pip install pgmpy

# https://github.com/pgmpy/pgmpy#installation

Collecting pgmpy
  Downloading pgmpy-0.1.18-py3-none-any.whl (1.9 MB)
     |████████████████████████████████| 1.9 MB 5.0 MB/s 
Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from pgmpy) (4.64.0)
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Installing collected packages: pgmpy
Successfully installed pgmpy-0.1.18

# Fetching the network
!wget http://www.bnlearn.com/bnrepository/asia/asia.bif.gz
!gzip -qd asia.bif.gz
!ls

--2022-04-22 22:02:00--  http://www.bnlearn.com/bnrepository/asia/asia.bif.gz
Resolving www.bnlearn.com (www.bnlearn.com)... 176.58.124.98
Connecting to www.bnlearn.com (www.bnlearn.com)|176.58.124.98|:80... connected.
HTTP request sent, awaiting response... 301 Moved Permanently
Location: https://www.bnlearn.com/bnrepository/asia/asia.bif.gz [following]
--2022-04-22 22:02:00--  https://www.bnlearn.com/bnrepository/asia/asia.bif.gz
Connecting to www.bnlearn.com (www.bnlearn.com)|176.58.124.98|:443... connected.
HTTP request sent, awaiting response... 200 OK
Length: 310 [application/gzip]
Saving to: ‘asia.bif.gz’

asia.bif.gz         100%[===================>]     310  --.-KB/s    in 0s      

2022-04-22 22:02:01 (36.8 MB/s) - ‘asia.bif.gz’ saved [310/310]

asia.bif  sample_data

import numpy as np

from pgmpy.readwrite import BIFReader

reader = BIFReader("asia.bif")
asia_model = reader.get_model()

asia_model.nodes()

asia_model.edges()

CPDs = asia_model.get_cpds()

# Doing exact inference using Variable Elimination
from pgmpy.inference import VariableElimination

asia_infer = VariableElimination(asia_model)

# Computing the probability of bronc given smoke.
q = asia_infer.query(variables=["bronc"], evidence={"smoke": 0}).values
print("p(bronchitis | smoke=0", q)

/usr/local/lib/python3.7/dist-packages/pgmpy/factors/discrete/DiscreteFactor.py:537: UserWarning: Found unknown state name. Trying to switch to using all state names as state numbers
  UserWarning,

0it [00:00, ?it/s]

0it [00:00, ?it/s]

p(bronchitis | smoke=0 [0.6 0.4]

"""
Sanity check.
 p(A=t|T=t) = p(A=t) p(T=t|A=t) / [
    p(A=t) p(T=t|A=t)  + p(A=f) p(T=t|A=f)]
= 0.01 * 0.05 / (0.01 * 0.05 + 0.99 * 0.01)
= 0.0481
"""
# 0 = True. 1 = False
q = asia_infer.query(variables=["asia"], evidence={"tub": 0}).values
print("p(asia | tb=1)", q)
assert np.allclose(q[0], 0.04, atol=1e-1)

/usr/local/lib/python3.7/dist-packages/pgmpy/factors/discrete/DiscreteFactor.py:537: UserWarning: Found unknown state name. Trying to switch to using all state names as state numbers
  UserWarning,

0it [00:00, ?it/s]

0it [00:00, ?it/s]

p(asia | tb=1) [0.04807692 0.95192308]