Belief Propagation

class pgmpy.inference.ExactInference.BeliefPropagation(model)

Class for performing inference using Belief Propagation method.

Creates a Junction Tree or Clique Tree (JunctionTree class) for the input probabilistic graphical model and performs calibration of the junction tree so formed using belief propagation.

Parameters:

model (DiscreteBayesianNetwork, DiscreteMarkovNetwork, FactorGraph, JunctionTree) – model for which inference is to performed

calibrate()

Calibration using belief propagation in junction tree or clique tree.

Examples

>>> from pgmpy.models import DiscreteBayesianNetwork
>>> from pgmpy.factors.discrete import TabularCPD
>>> from pgmpy.inference import BeliefPropagation
>>> G = DiscreteBayesianNetwork(
...     [
...         ("diff", "grade"),
...         ("intel", "grade"),
...         ("intel", "SAT"),
...         ("grade", "letter"),
...     ]
... )
>>> 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],
... )
>>> sat_cpd = TabularCPD(
...     "SAT",
...     2,
...     [[0.1, 0.2, 0.7], [0.9, 0.8, 0.3]],
...     evidence=["intel"],
...     evidence_card=[3],
... )
>>> letter_cpd = TabularCPD(
...     "letter",
...     2,
...     [[0.1, 0.4, 0.8], [0.9, 0.6, 0.2]],
...     evidence=["grade"],
...     evidence_card=[3],
... )
>>> G.add_cpds(diff_cpd, intel_cpd, grade_cpd, sat_cpd, letter_cpd)
>>> bp = BeliefPropagation(G)
>>> bp.calibrate()

get_clique_beliefs()

Returns clique beliefs. Should be called after the clique tree (or junction tree) is calibrated.

get_cliques()

Returns cliques used for belief propagation.

get_sepset_beliefs()

Returns sepset beliefs. Should be called after clique tree (or junction tree) is calibrated.

map_query(variables=None, evidence=None, virtual_evidence=None, show_progress=True)

MAP Query method using belief propagation. Returns the highest probable state in the joint distributon of variables.

Parameters:

• variables (list) – list of variables for which you want to compute the probability

• virtual_evidence (list (default:None)) – A list of pgmpy.factors.discrete.TabularCPD representing the virtual evidences.

• evidence (dict) – a dict key, value pair as {var: state_of_var_observed} None if no evidence

• show_progress (boolean) – If True, shows a progress bar.

Examples

>>> from pgmpy.factors.discrete import TabularCPD
>>> from pgmpy.models import DiscreteBayesianNetwork
>>> from pgmpy.inference import BeliefPropagation
>>> bayesian_model = DiscreteBayesianNetwork(
...     [("A", "J"), ("R", "J"), ("J", "Q"), ("J", "L"), ("G", "L")]
... )
>>> cpd_a = TabularCPD("A", 2, [[0.2], [0.8]])
>>> cpd_r = TabularCPD("R", 2, [[0.4], [0.6]])
>>> cpd_j = TabularCPD(
...     "J", 2, [[0.9, 0.6, 0.7, 0.1], [0.1, 0.4, 0.3, 0.9]], ["R", "A"], [2, 2]
... )
>>> cpd_q = TabularCPD("Q", 2, [[0.9, 0.2], [0.1, 0.8]], ["J"], [2])
>>> cpd_l = TabularCPD(
...     "L",
...     2,
...     [[0.9, 0.45, 0.8, 0.1], [0.1, 0.55, 0.2, 0.9]],
...     ["G", "J"],
...     [2, 2],
... )
>>> cpd_g = TabularCPD("G", 2, [[0.6], [0.4]])
>>> bayesian_model.add_cpds(cpd_a, cpd_r, cpd_j, cpd_q, cpd_l, cpd_g)
>>> belief_propagation = BeliefPropagation(bayesian_model)
>>> belief_propagation.map_query(
...     variables=["J", "Q"], evidence={"A": 0, "R": 0, "G": 0, "L": 1}
... )

max_calibrate()

Max-calibration of the junction tree using belief propagation.

Examples

>>> from pgmpy.models import DiscreteBayesianNetwork
>>> from pgmpy.factors.discrete import TabularCPD
>>> from pgmpy.inference import BeliefPropagation
>>> G = DiscreteBayesianNetwork(
...     [
...         ("diff", "grade"),
...         ("intel", "grade"),
...         ("intel", "SAT"),
...         ("grade", "letter"),
...     ]
... )
>>> 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],
... )
>>> sat_cpd = TabularCPD(
...     "SAT",
...     2,
...     [[0.1, 0.2, 0.7], [0.9, 0.8, 0.3]],
...     evidence=["intel"],
...     evidence_card=[3],
... )
>>> letter_cpd = TabularCPD(
...     "letter",
...     2,
...     [[0.1, 0.4, 0.8], [0.9, 0.6, 0.2]],
...     evidence=["grade"],
...     evidence_card=[3],
... )
>>> G.add_cpds(diff_cpd, intel_cpd, grade_cpd, sat_cpd, letter_cpd)
>>> bp = BeliefPropagation(G)
>>> bp.max_calibrate()

query(variables, evidence=None, virtual_evidence=None, joint=True, show_progress=True)

Query method using belief propagation.

Parameters:

• variables (list) – list of variables for which you want to compute the probability

• evidence (dict) – a dict key, value pair as {var: state_of_var_observed} None if no evidence

• virtual_evidence (list (default:None)) – A list of pgmpy.factors.discrete.TabularCPD representing the virtual evidences.

• joint (boolean) – If True, returns a Joint Distribution over variables. If False, returns a dict of distributions over each of the variables.

• show_progress (boolean) – If True shows a progress bar.

Examples

>>> from pgmpy.factors.discrete import TabularCPD
>>> from pgmpy.models import DiscreteBayesianNetwork
>>> from pgmpy.inference import BeliefPropagation
>>> bayesian_model = DiscreteBayesianNetwork(
...     [("A", "J"), ("R", "J"), ("J", "Q"), ("J", "L"), ("G", "L")]
... )
>>> cpd_a = TabularCPD("A", 2, [[0.2], [0.8]])
>>> cpd_r = TabularCPD("R", 2, [[0.4], [0.6]])
>>> cpd_j = TabularCPD(
...     "J", 2, [[0.9, 0.6, 0.7, 0.1], [0.1, 0.4, 0.3, 0.9]], ["R", "A"], [2, 2]
... )
>>> cpd_q = TabularCPD("Q", 2, [[0.9, 0.2], [0.1, 0.8]], ["J"], [2])
>>> cpd_l = TabularCPD(
...     "L",
...     2,
...     [[0.9, 0.45, 0.8, 0.1], [0.1, 0.55, 0.2, 0.9]],
...     ["G", "J"],
...     [2, 2],
... )
>>> cpd_g = TabularCPD("G", 2, [[0.6], [0.4]])
>>> bayesian_model.add_cpds(cpd_a, cpd_r, cpd_j, cpd_q, cpd_l, cpd_g)
>>> belief_propagation = BeliefPropagation(bayesian_model)
>>> belief_propagation.query(
...     variables=["J", "Q"], evidence={"A": 0, "R": 0, "G": 0, "L": 1}
... )