To represent independencies, pgmpy has two classes, namely IndependenceAssertion and Independencies. The IndependenceAssertion class is used to represent individual assertions of the form of 
or 
. Let's see some code to represent assertions:
# Firstly we need to import IndependenceAssertion
In [1]: from pgmpy.independencies import IndependenceAssertion
# Each assertion is in the form of [X, Y, Z] meaning X is
# independent of Y given Z.
In [2]: assertion1 = IndependenceAssertion('X', 'Y')
In [3]: assertion1
Out[3]: (X _|_ Y)Here, assertion1 represents that the variable X is independent of the variable Y. To represent conditional assertions, we just need to add a third argument to IndependenceAssertion:
In [4]: assertion2 = IndependenceAssertion('X', 'Y', 'Z')
In [5]: assertion2
Out [5]: (X _|_ Y | Z)In the preceding example, assertion2 represents .
IndependenceAssertion also allows us to represent assertions in the form of 
. To do this, we just need to pass a list of random variables as arguments:
In [4]: assertion2 = IndependenceAssertion('X', 'Y', 'Z')
In [5]: assertion2
Out[5]: (X _|_ Y | Z)Moving on to the Independencies class, an Independencies object is used to represent a set of assertions. Often, in the case of Bayesian or Markov networks, we have more than one assertion corresponding to a given model, and to represent these independence assertions for the models, we generally use the Independencies object. Let's take a few examples:
In [8]: from pgmpy.independencies import Independencies # There are multiple ways to create an Independencies object, we # could either initialize an empty object or initialize with some # assertions. In [9]: independencies = Independencies() # Empty object In [10]: independencies.get_assertions() Out[10]: [] In [11]: independencies.add_assertions(assertion1, assertion2) In [12]: independencies.get_assertions() Out[12]: [(X _|_ Y), (X _|_ Y | Z)]
We can also directly initialize Independencies in these two ways:
In [13]: independencies = Independencies(assertion1, assertion2)
In [14]: independencies = Independencies(['X', 'Y'],
['A', 'B', 'C'])
In [15]: independencies.get_assertions()
Out[15]: [(X _|_ Y), (A _|_ B | C)]