JointProbabilityDistribution

class pgmpy.factors.discrete.JointProbabilityDistribution(variables, cardinality, values)

Bases: DiscreteFactor

Base class for Joint Probability Distribution

check_independence(event1, event2, event3=None, condition_random_variable=False)

Check if the Joint Probability Distribution satisfies the given independence condition.

Parameters:

event1: list

random variable whose independence is to be checked.

event2: list

random variable from which event1 is independent.

values: 2D array or list like or 1D array or list like

A 2D list of tuples of the form (variable_name, variable_state). A 1D list or array-like to condition over randome variables (condition_random_variable must be True) The values on which to condition the Joint Probability Distribution.

condition_random_variable: Boolean (Default false)

If true and event3 is not None than will check independence condition over random variable.

For random variables say X, Y, Z to check if X is independent of Y given Z.

event1 should be either X or Y.

event2 should be either Y or X.

event3 should Z.

Examples

>>> from pgmpy.factors.discrete import JointProbabilityDistribution as JPD
>>> prob = JPD(
...     variables=["I", "D", "G"],
...     cardinality=[2, 2, 3],
...     values=[
...         0.126,
...         0.168,
...         0.126,
...         0.009,
...         0.045,
...         0.126,
...         0.252,
...         0.0224,
...         0.0056,
...         0.06,
...         0.036,
...         0.024,
...     ],
... )
>>> prob.check_independence(event1=["I"], event2=["D"])
True
>>> prob.check_independence(["I"], ["D"], [("G", 1)])  # Conditioning over G_1
False
>>> # Conditioning over random variable G
>>> prob.check_independence(
...     ["I"], ["D"], ("G",), condition_random_variable=True
... )
False

conditional_distribution(values, inplace=True)

Returns Conditional Probability Distribution after setting values to 1.

Parameters:

values: list or array_like

A list of tuples of the form (variable_name, variable_state). The values on which to condition the Joint Probability Distribution.

inplace: Boolean (default True)

If False returns a new instance of JointProbabilityDistribution

Examples

>>> import numpy as np
>>> from pgmpy.factors.discrete import JointProbabilityDistribution
>>> prob = JointProbabilityDistribution(
...     variables=["x1", "x2", "x3"],
...     cardinality=[2, 2, 2],
...     values=np.ones(8) / 8,
... )
>>> prob.conditional_distribution(values=[("x1", 1)])
>>> print(prob)
+-------+-------+------------+
| x2    | x3    |   P(x2,x3) |
+=======+=======+============+
| x2(0) | x3(0) |     0.2500 |
+-------+-------+------------+
| x2(0) | x3(1) |     0.2500 |
+-------+-------+------------+
| x2(1) | x3(0) |     0.2500 |
+-------+-------+------------+
| x2(1) | x3(1) |     0.2500 |
+-------+-------+------------+

copy()

Returns A copy of JointProbabilityDistribution object

Examples

>>> import numpy as np
>>> from pgmpy.factors.discrete import JointProbabilityDistribution
>>> prob = JointProbabilityDistribution(
...     variables=["x1", "x2", "x3"],
...     cardinality=[2, 3, 2],
...     values=np.ones(12) / 12,
... )
>>> prob_copy = prob.copy()
>>> (prob_copy.values == prob.values).all()
np.True_
>>> prob_copy.variables == prob.variables
True
>>> prob_copy.variables[1] = "y"
>>> prob_copy.variables == prob.variables
False

get_independencies(condition=None)

Returns the independent variables in the joint probability distribution. Returns marginally independent variables if condition=None. Returns conditionally independent variables if condition!=None

Parameters:

condition: array_like

Random Variable on which to condition the Joint Probability Distribution.

Examples

>>> import numpy as np
>>> from pgmpy.factors.discrete import JointProbabilityDistribution
>>> prob = JointProbabilityDistribution(
...     variables=["x1", "x2", "x3"],
...     cardinality=[2, 3, 2],
...     values=np.ones(12) / 12,
... )
>>> prob.get_independencies()
(x1 ⟂ x2)
(x1 ⟂ x3)
(x2 ⟂ x3)

is_imap(model)

Checks whether the given DiscreteBayesianNetwork is Imap of JointProbabilityDistribution

Parameters:

modelAn instance of DiscreteBayesianNetwork Class, for which you want to

check the Imap

Returns:

Is IMAP: bool

True if given Bayesian Network is Imap for Joint Probability Distribution False otherwise

Examples

>>> from pgmpy.models import DiscreteBayesianNetwork
>>> from pgmpy.factors.discrete import TabularCPD
>>> from pgmpy.factors.discrete import JointProbabilityDistribution
>>> bm = DiscreteBayesianNetwork([("diff", "grade"), ("intel", "grade")])
>>> diff_cpd = TabularCPD("diff", 2, [[0.2], [0.8]])
>>> intel_cpd = TabularCPD("intel", 3, [[0.5], [0.3], [0.2]])
>>> grade_cpd = TabularCPD(
...     "grade",
...     3,
...     [
...         [0.1, 0.1, 0.1, 0.1, 0.1, 0.1],
...         [0.1, 0.1, 0.1, 0.1, 0.1, 0.1],
...         [0.8, 0.8, 0.8, 0.8, 0.8, 0.8],
...     ],
...     evidence=["diff", "intel"],
...     evidence_card=[2, 3],
... )
>>> bm.add_cpds(diff_cpd, intel_cpd, grade_cpd)
>>> val = [
...     0.01,
...     0.01,
...     0.08,
...     0.006,
...     0.006,
...     0.048,
...     0.004,
...     0.004,
...     0.032,
...     0.04,
...     0.04,
...     0.32,
...     0.024,
...     0.024,
...     0.192,
...     0.016,
...     0.016,
...     0.128,
... ]
>>> JPD = JointProbabilityDistribution(
...     ["diff", "intel", "grade"], [2, 3, 3], val
... )
>>> JPD.is_imap(bm)
True

marginal_distribution(variables, inplace=True)

Returns the marginal distribution over variables.

Parameters:

variables: string, list, tuple, set, dict

Variable or list of variables over which marginal distribution needs to be calculated

inplace: Boolean (default True)

If False return a new instance of JointProbabilityDistribution

Examples

>>> import numpy as np
>>> from pgmpy.factors.discrete import JointProbabilityDistribution
>>> values = np.random.rand(12)
>>> prob = JointProbabilityDistribution(
...     ["x1", "x2", "x3"], [2, 3, 2], values / np.sum(values)
... )
>>> prob.marginal_distribution(variables=["x1", "x2"])
>>> print(prob)
+-------+-------+------------+
| x1    | x2    |   P(x1,x2) |
+=======+=======+============+
| x1(0) | x2(0) |     0.1408 |
+-------+-------+------------+
| x1(0) | x2(1) |     0.3372 |
+-------+-------+------------+
| x1(0) | x2(2) |     0.1530 |
+-------+-------+------------+
| x1(1) | x2(0) |     0.2122 |
+-------+-------+------------+
| x1(1) | x2(1) |     0.0950 |
+-------+-------+------------+
| x1(1) | x2(2) |     0.0619 |
+-------+-------+------------+

minimal_imap(order)

Returns a Bayesian Model which is minimal IMap of the Joint Probability Distribution considering the order of the variables.

Parameters:

order: array-like

The order of the random variables.

Examples

>>> import numpy as np
>>> from pgmpy.factors.discrete import JointProbabilityDistribution
>>> prob = JointProbabilityDistribution(
...     variables=["x1", "x2", "x3"],
...     cardinality=[2, 3, 2],
...     values=np.ones(12) / 12,
... )
>>> bayesian_model = prob.minimal_imap(order=["x2", "x1", "x3"])
>>> bayesian_model
<pgmpy.models.DiscreteBayesianNetwork.DiscreteBayesianNetwork object at 0x...>
>>> bayesian_model.edges()
OutEdgeView([('x2', 'x3'), ('x1', 'x3')])

pmap()

to_factor()

Returns JointProbabilityDistribution as a DiscreteFactor object

Examples

>>> import numpy as np
>>> from pgmpy.factors.discrete import JointProbabilityDistribution
>>> prob = JointProbabilityDistribution(
...     ["x1", "x2", "x3"], [2, 3, 2], np.ones(12) / 12
... )
>>> phi = prob.to_factor()
>>> type(phi)
<class 'pgmpy.factors.discrete.DiscreteFactor.DiscreteFactor'>