Basic Operations on Bayesian Networks

This notebook shows examples of some basic operations that can be performed on a Bayesian Network. We use the Protein Signalling network from the bnlearn repository as the example model: https://www.bnlearn.com/bnrepository/discrete-medium.html#sachs

The BayesianNetwork class in pgmpy inherits the networkx.DiGraph class, hence all the methods defined for networkx.DiGraph should also work for BayesianNetwork.

import pprint
from IPython.display import Image
import networkx as nx

# Load the sachs model.
# For other ways to define a model, please refer: https://pgmpy.org/examples/Creating%20a%20Discrete%20Bayesian%20Network.html
from pgmpy.utils import get_example_model
sachs_model = get_example_model('sachs')

# Visualize the model
viz = sachs_model.to_graphviz()
viz.draw('sachs.png', prog='dot')
Image('sachs.png')

Attributes of the Model Structure

# Get all the nodes/random variables in the model
all_nodes = sachs_model.nodes()
print(f"Nodes: {all_nodes} \n")

# Get all the edges in the model.
all_edges = sachs_model.edges()
print(f"Edges: {all_edges} \n")

# Get all the CPDs.
all_cpds = sachs_model.get_cpds()

# Get parents of a specific node
akt_parents = sachs_model.get_parents('Akt')
print(f"Parents of Akt: {akt_parents} \n")

# Get children of a specific node
pka_children = sachs_model.get_children('PKA')
print(f"Children of PKA: {pka_children} \n")

# Get all the leaf nodes of the model
leaves = sachs_model.get_leaves()
print(f"Leaf nodes in the model: {leaves} \n")

# Get the root nodes of the model
roots = sachs_model.get_roots()
print(f"Root nodes in the model: {roots} \n")

Nodes: ['Akt', 'Erk', 'Jnk', 'Mek', 'P38', 'PIP2', 'PIP3', 'PKA', 'PKC', 'Plcg', 'Raf']

Edges: [('Erk', 'Akt'), ('Mek', 'Erk'), ('PIP3', 'PIP2'), ('PKA', 'Akt'), ('PKA', 'Erk'), ('PKA', 'Jnk'), ('PKA', 'Mek'), ('PKA', 'P38'), ('PKA', 'Raf'), ('PKC', 'Jnk'), ('PKC', 'Mek'), ('PKC', 'P38'), ('PKC', 'PKA'), ('PKC', 'Raf'), ('Plcg', 'PIP2'), ('Plcg', 'PIP3'), ('Raf', 'Mek')]

Parents of Akt: ['Erk', 'PKA']

Children of PKA: ['Akt', 'Erk', 'Jnk', 'Mek', 'P38', 'Raf']

Leaf nodes in the model: ['Akt', 'Jnk', 'P38', 'PIP2']

Root nodes in the model: ['PKC', 'Plcg']

Modifying the Model Structure

# Adding nodes to the model.
sachs_model.add_node('new_node')
sachs_model.add_nodes_from(['new_node1', 'new_node2'])

# Adding edges to the model.
sachs_model.add_edge('Akt', 'new_node')
sachs_model.add_edges_from([('Akt', 'new_node1'), ('Akt', 'new_node2')])

# Removing edges from the model.
sachs_model.remove_edge('Akt', 'new_node')
sachs_model.remove_edges_from([('Akt', 'new_node1'), ('Akt', 'new_node2')])

# Removing nodes from the model
sachs_model.remove_node('new_node')
sachs_model.remove_nodes_from(['new_node1', 'new_node2'])

# At any point, check_model can be called to check if the specified model is correct.
sachs_model.check_model()

True

Modifying associated parameterization

# Getting an associated CPD
sachs_model.get_cpds('Akt')

# Adding new CPDs to the model
sachs_model.add_node('new_node')
new_cpd = TabularCPD('new_node', 2, [[0.2], [0.8]])
sachs_model.add_cpds(new_cpd)

# Removing the CPD and the node
sachs_model.remove_cpds('new_node')
sachs_model.remove_node('new_node')

sachs_model.check_model()

True

D-Separation

# Check if two variables in the network are conditionally / unconditionally d-connected.
print(sachs_model.is_dconnected('PKC', 'Akt'))
print(sachs_model.is_dconnected('PKC', 'Akt', observed=['Mek']))
print(sachs_model.is_dconnected('PKC', 'Akt', observed=['Mek', 'PKA']))

True
True
False

# List all the variables that are d-connected to a given variable.
print(sachs_model.active_trail_nodes('PKA'))
print(sachs_model.active_trail_nodes(['PKA', 'Raf']))

print()

# List all d-connected variables when conditioned on some other variables
print(sachs_model.active_trail_nodes('PKA', observed=['Mek', 'PKC']))
print(sachs_model.active_trail_nodes(['PKA', 'Raf'], observed=['Mek', 'PKC']))

{'PKA': {'Akt', 'Mek', 'PKC', 'Jnk', 'P38', 'Erk', 'PKA', 'Raf'}}
{'PKA': {'Akt', 'Mek', 'PKC', 'Jnk', 'P38', 'Erk', 'PKA', 'Raf'}, 'Raf': {'Akt', 'Mek', 'Jnk', 'P38', 'Erk', 'PKA', 'PKC', 'Raf'}}

{'PKA': {'Akt', 'Erk', 'Jnk', 'P38', 'Raf', 'PKA'}}
{'PKA': {'Akt', 'Erk', 'Jnk', 'P38', 'Raf', 'PKA'}, 'Raf': {'Akt', 'Erk', 'Jnk', 'P38', 'Raf', 'PKA'}}

# Find the minimal d-separator of any two variables
print(sachs_model.minimal_dseparator('PKC', 'Akt'))

{'Erk', 'PKA'}

Other Methods

# Get the Markov blanket of a variable
sachs_model.get_markov_blanket('Raf')

['PKA', 'Mek', 'PKC']

# List all local indpeendencies of a node
sachs_model.local_independencies('Raf')

(Raf ⟂ PIP3, Plcg, Jnk, P38, PIP2 | PKA, PKC)

# List all implied independencies in the network
sachs_model.get_independencies().independencies[:10]

[(Akt ⟂ PIP3, PIP2, Plcg),
 (Akt ⟂ PIP3, PIP2, Plcg | Mek),
 (Akt ⟂ PIP3, PIP2, Plcg | Jnk),
 (Akt ⟂ PIP3, PIP2, Plcg | P38),
 (Akt ⟂ PIP3, PIP2, Plcg | Erk),
 (Akt ⟂ Plcg, PIP3 | PIP2),
 (Akt ⟂ PIP3, PIP2, Plcg | PKA),
 (Akt ⟂ Plcg, PIP2 | PIP3),
 (Akt ⟂ PIP3, PIP2 | Plcg),
 (Akt ⟂ PIP3, PIP2, Plcg | PKC)]