Dynamic Bayesian Network Inference

class pgmpy.inference.dbn_inference.DBNInference(model)

Class for performing inference using Belief Propagation method for the input Dynamic Bayesian Network.

For the exact inference implementation, the interface algorithm is used which is adapted from [1].

Parameters:

model (Dynamic Bayesian Network) – Model for which inference is to performed

Examples

>>> from pgmpy.factors.discrete import TabularCPD
>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> from pgmpy.inference import DBNInference
>>> dbnet = DBN()
>>> dbnet.add_edges_from([(('Z', 0), ('X', 0)), (('X', 0), ('Y', 0)),
...                       (('Z', 0), ('Z', 1))])
>>> z_start_cpd = TabularCPD(('Z', 0), 2, [[0.5], [0.5]])
>>> x_i_cpd = TabularCPD(('X', 0), 2, [[0.6, 0.9],
...                                    [0.4, 0.1]],
...                      evidence=[('Z', 0)],
...                      evidence_card=[2])
>>> y_i_cpd = TabularCPD(('Y', 0), 2, [[0.2, 0.3],
...                                    [0.8, 0.7]],
...                      evidence=[('X', 0)],
...                      evidence_card=[2])
>>> z_trans_cpd = TabularCPD(('Z', 1), 2, [[0.4, 0.7],
...                                        [0.6, 0.3]],
...                      evidence=[('Z', 0)],
...                      evidence_card=[2])
>>> dbnet.add_cpds(z_start_cpd, z_trans_cpd, x_i_cpd, y_i_cpd)
>>> dbnet.initialize_initial_state()
>>> dbn_inf = DBNInference(dbnet)
>>> dbn_inf.start_junction_tree.nodes()
NodeView(((('X', 0), ('Y', 0)), (('X', 0), ('Z', 0))))
>>> dbn_inf.one_and_half_junction_tree.nodes()
NodeView(((('Z', 1), ('Z', 0)), (('Y', 1), ('X', 1)), (('Z', 1), ('X', 1))))

References

[1] Dynamic Bayesian Networks: Representation, Inference and Learning

by Kevin Patrick Murphy http://www.cs.ubc.ca/~murphyk/Thesis/thesis.pdf

backward_inference(variables, evidence=None)

Backward inference 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

Examples

>>> from pgmpy.factors.discrete import TabularCPD
>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> from pgmpy.inference import DBNInference
>>> dbnet = DBN()
>>> dbnet.add_edges_from([(('Z', 0), ('X', 0)), (('X', 0), ('Y', 0)),
...                       (('Z', 0), ('Z', 1))])
>>> z_start_cpd = TabularCPD(('Z', 0), 2, [[0.5], [0.5]])
>>> x_i_cpd = TabularCPD(('X', 0), 2, [[0.6, 0.9],
...                                    [0.4, 0.1]],
...                      evidence=[('Z', 0)],
...                      evidence_card=[2])
>>> y_i_cpd = TabularCPD(('Y', 0), 2, [[0.2, 0.3],
...                                    [0.8, 0.7]],
...                      evidence=[('X', 0)],
...                      evidence_card=[2])
>>> z_trans_cpd = TabularCPD(('Z', 1), 2, [[0.4, 0.7],
...                                        [0.6, 0.3]],
...                      evidence=[('Z', 0)],
...                      evidence_card=[2])
>>> dbnet.add_cpds(z_start_cpd, z_trans_cpd, x_i_cpd, y_i_cpd)
>>> dbnet.initialize_initial_state()
>>> dbn_inf = DBNInference(dbnet)
>>> dbn_inf.backward_inference([('X', 0)], {('Y', 0):0, ('Y', 1):1, ('Y', 2):1})[('X', 0)].values
array([0.66594382, 0.33405618])

forward_inference(variables, evidence=None, args=None)

Forward inference 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

Examples

>>> from pgmpy.factors.discrete import TabularCPD
>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> from pgmpy.inference import DBNInference
>>> dbnet = DBN()
>>> dbnet.add_edges_from([(('Z', 0), ('X', 0)), (('X', 0), ('Y', 0)),
...                       (('Z', 0), ('Z', 1))])
>>> z_start_cpd = TabularCPD(('Z', 0), 2, [[0.5], [0.5]])
>>> x_i_cpd = TabularCPD(('X', 0), 2, [[0.6, 0.9],
...                                    [0.4, 0.1]],
...                      evidence=[('Z', 0)],
...                      evidence_card=[2])
>>> y_i_cpd = TabularCPD(('Y', 0), 2, [[0.2, 0.3],
...                                    [0.8, 0.7]],
...                      evidence=[('X', 0)],
...                      evidence_card=[2])
>>> z_trans_cpd = TabularCPD(('Z', 1), 2, [[0.4, 0.7],
...                                        [0.6, 0.3]],
...                      evidence=[('Z', 0)],
...                      evidence_card=[2])
>>> dbnet.add_cpds(z_start_cpd, z_trans_cpd, x_i_cpd, y_i_cpd)
>>> dbnet.initialize_initial_state()
>>> dbn_inf = DBNInference(dbnet)
>>> dbn_inf.forward_inference([('X', 2)], {('Y', 0):1, ('Y', 1):0, ('Y', 2):1})[('X', 2)].values
array([0.76738736, 0.23261264])

query(variables, evidence=None, args='exact')

Query method for Dynamic Bayesian Network using Interface Algorithm.

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

Examples

>>> from pgmpy.factors.discrete import TabularCPD
>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> from pgmpy.inference import DBNInference
>>> dbnet = DBN()
>>> dbnet.add_edges_from([(('Z', 0), ('X', 0)), (('X', 0), ('Y', 0)),
...                       (('Z', 0), ('Z', 1))])
>>> z_start_cpd = TabularCPD(('Z', 0), 2, [[0.5], [0.5]])
>>> x_i_cpd = TabularCPD(('X', 0), 2, [[0.6, 0.9],
...                                    [0.4, 0.1]],
...                      evidence=[('Z', 0)],
...                      evidence_card=[2])
>>> y_i_cpd = TabularCPD(('Y', 0), 2, [[0.2, 0.3],
...                                    [0.8, 0.7]],
...                      evidence=[('X', 0)],
...                      evidence_card=[2])
>>> z_trans_cpd = TabularCPD(('Z', 1), 2, [[0.4, 0.7],
...                                        [0.6, 0.3]],
...                      evidence=[('Z', 0)],
...                      evidence_card=[2])
>>> dbnet.add_cpds(z_start_cpd, z_trans_cpd, x_i_cpd, y_i_cpd)
>>> dbnet.initialize_initial_state()
>>> dbn_inf = DBNInference(dbnet)
>>> dbn_inf.query([('X', 0)], {('Y', 0):0, ('Y', 1):1, ('Y', 2):1})[('X', 0)].values
array([0.66594382, 0.33405618])