import itertools
from operator import mul
from functools import reduce
import numpy as np
from pgmpy.factors.discrete import DiscreteFactor
from pgmpy.independencies import Independencies
[docs]class JointProbabilityDistribution(DiscreteFactor):
"""
Base class for Joint Probability Distribution
"""
def __init__(self, variables, cardinality, values):
"""
Initialize a Joint Probability Distribution class.
Defined above, we have the following mapping from variable
assignments to the index of the row vector in the value field:
+-----+-----+-----+-------------------------+
| x1 | x2 | x3 | P(x1, x2, x2) |
+-----+-----+-----+-------------------------+
| x1_0| x2_0| x3_0| P(x1_0, x2_0, x3_0) |
+-----+-----+-----+-------------------------+
| x1_1| x2_0| x3_0| P(x1_1, x2_0, x3_0) |
+-----+-----+-----+-------------------------+
| x1_0| x2_1| x3_0| P(x1_0, x2_1, x3_0) |
+-----+-----+-----+-------------------------+
| x1_1| x2_1| x3_0| P(x1_1, x2_1, x3_0) |
+-----+-----+-----+-------------------------+
| x1_0| x2_0| x3_1| P(x1_0, x2_0, x3_1) |
+-----+-----+-----+-------------------------+
| x1_1| x2_0| x3_1| P(x1_1, x2_0, x3_1) |
+-----+-----+-----+-------------------------+
| x1_0| x2_1| x3_1| P(x1_0, x2_1, x3_1) |
+-----+-----+-----+-------------------------+
| x1_1| x2_1| x3_1| P(x1_1, x2_1, x3_1) |
+-----+-----+-----+-------------------------+
Parameters
----------
variables: list
List of scope of Joint Probability Distribution.
cardinality: list, array_like
List of cardinality of each variable
value: list, array_like
List or array of values of factor.
A Joint Probability Distribution's values are stored in a row
vector in the value using an ordering such that the left-most
variables as defined in the variable field cycle through their
values the fastest.
Examples
--------
>>> import numpy as np
>>> from pgmpy.factors.discrete import JointProbabilityDistribution
>>> prob = JointProbabilityDistribution(['x1', 'x2', 'x3'], [2, 2, 2], np.ones(8)/8)
>>> print(prob)
x1 x2 x3 P(x1,x2,x3)
---- ---- ---- -------------
x1_0 x2_0 x3_0 0.1250
x1_0 x2_0 x3_1 0.1250
x1_0 x2_1 x3_0 0.1250
x1_0 x2_1 x3_1 0.1250
x1_1 x2_0 x3_0 0.1250
x1_1 x2_0 x3_1 0.1250
x1_1 x2_1 x3_0 0.1250
x1_1 x2_1 x3_1 0.1250
"""
if np.isclose(np.sum(values), 1):
super(JointProbabilityDistribution, self).__init__(
variables, cardinality, values
)
else:
raise ValueError("The probability values doesn't sum to 1.")
def __repr__(self):
var_card = ", ".join(
[f"{var}:{card}" for var, card in zip(self.variables, self.cardinality)]
)
return f"<Joint Distribution representing P({var_card}) at {hex(id(self))}>"
def __str__(self):
return self._str(phi_or_p="P")
[docs] def marginal_distribution(self, 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(['x1', 'x2'])
>>> print(prob)
x1 x2 P(x1,x2)
---- ---- ----------
x1_0 x2_0 0.1502
x1_0 x2_1 0.1626
x1_0 x2_2 0.1197
x1_1 x2_0 0.2339
x1_1 x2_1 0.1996
x1_1 x2_2 0.1340
"""
return self.marginalize(
list(
set(list(self.variables))
- set(
variables
if isinstance(variables, (list, set, dict, tuple))
else [variables]
)
),
inplace=inplace,
)
[docs] def check_independence(
self, 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(['I','D','G'],[2,2,3],
[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(['I'], ['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
"""
JPD = self.copy()
if isinstance(event1, str):
raise TypeError("Event 1 should be a list or array-like structure")
if isinstance(event2, str):
raise TypeError("Event 2 should be a list or array-like structure")
if event3:
if isinstance(event3, str):
raise TypeError("Event 3 cannot of type string")
elif condition_random_variable:
if not all(isinstance(var, str) for var in event3):
raise TypeError("Event3 should be a 1d list of strings")
event3 = list(event3)
# Using the definition of conditional independence
# If P(X,Y|Z) = P(X|Z)*P(Y|Z)
# This can be expanded to P(X,Y,Z)*P(Z) == P(X,Z)*P(Y,Z)
phi_z = JPD.marginal_distribution(event3, inplace=False).to_factor()
for variable_pair in itertools.product(event1, event2):
phi_xyz = JPD.marginal_distribution(
event3 + list(variable_pair), inplace=False
).to_factor()
phi_xz = JPD.marginal_distribution(
event3 + [variable_pair[0]], inplace=False
).to_factor()
phi_yz = JPD.marginal_distribution(
event3 + [variable_pair[1]], inplace=False
).to_factor()
if phi_xyz * phi_z != phi_xz * phi_yz:
return False
return True
else:
JPD.conditional_distribution(event3)
for variable_pair in itertools.product(event1, event2):
if JPD.marginal_distribution(
variable_pair, inplace=False
) != JPD.marginal_distribution(
variable_pair[0], inplace=False
) * JPD.marginal_distribution(
variable_pair[1], inplace=False
):
return False
return True
[docs] def get_independencies(self, 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(['x1', 'x2', 'x3'], [2, 3, 2], np.ones(12)/12)
>>> prob.get_independencies()
(x1 \u27C2 x2)
(x1 \u27C2 x3)
(x2 \u27C2 x3)
"""
JPD = self.copy()
if condition:
JPD.conditional_distribution(condition)
independencies = Independencies()
for variable_pair in itertools.combinations(list(JPD.variables), 2):
if JPD.marginal_distribution(
variable_pair, inplace=False
) == JPD.marginal_distribution(
variable_pair[0], inplace=False
) * JPD.marginal_distribution(
variable_pair[1], inplace=False
):
independencies.add_assertions(variable_pair)
return independencies
[docs] def conditional_distribution(self, 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(['x1', 'x2', 'x3'], [2, 2, 2], np.ones(8)/8)
>>> prob.conditional_distribution([('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
"""
JPD = self if inplace else self.copy()
JPD.reduce(values)
JPD.normalize()
if not inplace:
return JPD
[docs] def copy(self):
"""
Returns A copy of JointProbabilityDistribution object
Examples
---------
>>> import numpy as np
>>> from pgmpy.factors.discrete import JointProbabilityDistribution
>>> prob = JointProbabilityDistribution(['x1', 'x2', 'x3'], [2, 3, 2], np.ones(12)/12)
>>> prob_copy = prob.copy()
>>> prob_copy.values == prob.values
True
>>> prob_copy.variables == prob.variables
True
>>> prob_copy.variables[1] = 'y'
>>> prob_copy.variables == prob.variables
False
"""
return JointProbabilityDistribution(self.scope(), self.cardinality, self.values)
[docs] def minimal_imap(self, 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(['x1', 'x2', 'x3'], [2, 3, 2], np.ones(12)/12)
>>> bayesian_model = prob.minimal_imap(order=['x2', 'x1', 'x3'])
>>> bayesian_model
<pgmpy.models.models.models at 0x7fd7440a9320>
>>> bayesian_model.edges()
[('x1', 'x3'), ('x2', 'x3')]
"""
from pgmpy.models import BayesianNetwork
def get_subsets(u):
for r in range(len(u) + 1):
for i in itertools.combinations(u, r):
yield i
G = BayesianNetwork()
for variable_index in range(len(order)):
u = order[:variable_index]
for subset in get_subsets(u):
if len(subset) < len(u) and self.check_independence(
[order[variable_index]], set(u) - set(subset), subset, True
):
G.add_edges_from(
[(variable, order[variable_index]) for variable in subset]
)
return G
[docs] def is_imap(self, model):
"""
Checks whether the given BayesianNetwork is Imap of JointProbabilityDistribution
Parameters
----------
model : An instance of BayesianNetwork Class, for which you want to
check the Imap
Returns
-------
boolean : True if given bayesian model is Imap for Joint Probability Distribution
False otherwise
Examples
--------
>>> from pgmpy.models import BayesianNetwork
>>> from pgmpy.factors.discrete import TabularCPD
>>> from pgmpy.factors.discrete import JointProbabilityDistribution
>>> bm = BayesianNetwork([('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
"""
from pgmpy.models import BayesianNetwork
if not isinstance(model, BayesianNetwork):
raise TypeError("model must be an instance of BayesianNetwork")
factors = [cpd.to_factor() for cpd in model.get_cpds()]
factor_prod = reduce(mul, factors)
JPD_fact = DiscreteFactor(self.variables, self.cardinality, self.values)
if JPD_fact == factor_prod:
return True
else:
return False
[docs] def to_factor(self):
"""
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)
pgmpy.factors.DiscreteFactor.DiscreteFactor
"""
return DiscreteFactor(self.variables, self.cardinality, self.values)
def pmap(self):
pass