MPLP

class pgmpy.inference.mplp.Mplp(model)

Class for performing approximate inference using Max-Product Linear Programming method.

We derive message passing updates that result in monotone decrease of the dual of the MAP LP Relaxation.

Parameters:

model (MarkovNetwork for which inference is to be performed.)

Examples

>>> import numpy as np
>>> from pgmpy.models import MarkovNetwork
>>> from pgmpy.inference import Mplp
>>> from pgmpy.factors.discrete import DiscreteFactor
>>> student = MarkovNetwork()
>>> student.add_edges_from([('A', 'B'), ('B', 'C'), ('C', 'D'), ('E', 'F')])
>>> factor_a = DiscreteFactor(['A'], cardinality=[2], values=np.array([0.54577, 1.8323]))
>>> factor_b = DiscreteFactor(['B'], cardinality=[2], values=np.array([0.93894, 1.065]))
>>> factor_c = DiscreteFactor(['C'], cardinality=[2], values=np.array([0.89205, 1.121]))
>>> factor_d = DiscreteFactor(['D'], cardinality=[2], values=np.array([0.56292, 1.7765]))
>>> factor_e = DiscreteFactor(['E'], cardinality=[2], values=np.array([0.47117, 2.1224]))
>>> factor_f = DiscreteFactor(['F'], cardinality=[2], values=np.array([1.5093, 0.66257]))
>>> factor_a_b = DiscreteFactor(['A', 'B'], cardinality=[2, 2],
...                             values=np.array([1.3207, 0.75717, 0.75717, 1.3207]))
>>> factor_b_c = DiscreteFactor(['B', 'C'], cardinality=[2, 2],
...                             values=np.array([0.00024189, 4134.2, 4134.2, 0.00024189]))
>>> factor_c_d = DiscreteFactor(['C', 'D'], cardinality=[2, 2],
...                             values=np.array([0.0043227, 231.34, 231.34, 0.0043227]))
>>> factor_d_e = DiscreteFactor(['E', 'F'], cardinality=[2, 2],
...                             values=np.array([31.228, 0.032023, 0.032023, 31.228]))
>>> student.add_factors(factor_a, factor_b, factor_c, factor_d, factor_e, factor_f, factor_a_b,
...                     factor_b_c, factor_c_d, factor_d_e)
>>> mplp = Mplp(student)

class Cluster(intersection_set_variables, cluster_potential)

Inner class for representing a cluster. A cluster is a subset of variables.

Parameters:

• set_of_variables (tuple) – This is the set of variables that form the cluster.

• intersection_set_variables (set containing frozensets.) – collection of intersection of all pairs of cluster variables. For eg: {{C_1 cap C_2}, {C_2 cap C_3}, {C_3 cap C_1} } for clusters C_1, C_2 & C_3.

• cluster_potential (DiscreteFactor) – Each cluster has an initial probability distribution provided beforehand.

find_triangles()

Finds all the triangles present in the given model

Examples

>>> from pgmpy.models import MarkovNetwork
>>> from pgmpy.factors.discrete import DiscreteFactor
>>> from pgmpy.inference import Mplp
>>> mm = MarkovNetwork()
>>> mm.add_nodes_from(['x1', 'x2', 'x3', 'x4', 'x5', 'x6', 'x7'])
>>> mm.add_edges_from([('x1', 'x3'), ('x1', 'x4'), ('x2', 'x4'),
...                    ('x2', 'x5'), ('x3', 'x6'), ('x4', 'x6'),
...                    ('x4', 'x7'), ('x5', 'x7')])
>>> phi = [DiscreteFactor(edge, [2, 2], np.random.rand(4)) for edge in mm.edges()]
>>> mm.add_factors(*phi)
>>> mplp = Mplp(mm)
>>> mplp.find_triangles()

get_integrality_gap()

Returns the integrality gap of the current state of the Mplp algorithm. The lesser it is, the closer we are

towards the exact solution.

Examples

>>> from pgmpy.models import MarkovNetwork
>>> from pgmpy.factors.discrete import DiscreteFactor
>>> from pgmpy.inference import Mplp
>>> mm = MarkovNetwork()
>>> mm.add_nodes_from(['x1', 'x2', 'x3', 'x4', 'x5', 'x6', 'x7'])
>>> mm.add_edges_from([('x1', 'x3'), ('x1', 'x4'), ('x2', 'x4'),
...                    ('x2', 'x5'), ('x3', 'x6'), ('x4', 'x6'),
...                    ('x4', 'x7'), ('x5', 'x7')])
>>> phi = [DiscreteFactor(edge, [2, 2], np.random.rand(4)) for edge in mm.edges()]
>>> mm.add_factors(*phi)
>>> mplp = Mplp(mm)
>>> mplp.map_query()
>>> int_gap = mplp.get_integrality_gap()

map_query(init_iter=1000, later_iter=20, dual_threshold=0.0002, integrality_gap_threshold=0.0002, tighten_triplet=True, max_triplets=5, max_iterations=100, prolong=False)

MAP query method using Max Product LP method. This returns the best assignment of the nodes in the form of a dictionary.

Parameters:

• init_iter (integer) – Number of maximum iterations that we want MPLP to run for the first time.

• later_iter (integer) – Number of maximum iterations that we want MPLP to run for later iterations

• dual_threshold (double) – This sets the minimum width between the dual objective decrements. If the decrement is lesser than the threshold, then that means we have stuck on a local minima.

• integrality_gap_threshold (double) – This sets the threshold for the integrality gap below which we say that the solution is satisfactory.

• tighten_triplet (bool) – set whether to use triplets as clusters or not.

• max_triplets (integer) – Set the maximum number of triplets that can be added at once.

• max_iterations (integer) – Maximum number of times we tighten the relaxation. Used only when tighten_triplet is set True.

• prolong (bool) – If set False: The moment we exhaust of all the triplets the tightening stops. If set True: The tightening will be performed max_iterations number of times irrespective of the triplets.

References

Section 3.3: The Dual Algorithm; Tightening LP Relaxation for MAP using Message Passing (2008) By Sontag Et al.

Examples

>>> from pgmpy.models import MarkovNetwork
>>> from pgmpy.factors.discrete import DiscreteFactor
>>> from pgmpy.inference import Mplp
>>> import numpy as np
>>> student = MarkovNetwork()
>>> student.add_edges_from([('A', 'B'), ('B', 'C'), ('C', 'D'), ('E', 'F')])
>>> factor_a = DiscreteFactor(['A'], cardinality=[2], values=np.array([0.54577, 1.8323]))
>>> factor_b = DiscreteFactor(['B'], cardinality=[2], values=np.array([0.93894, 1.065]))
>>> factor_c = DiscreteFactor(['C'], cardinality=[2], values=np.array([0.89205, 1.121]))
>>> factor_d = DiscreteFactor(['D'], cardinality=[2], values=np.array([0.56292, 1.7765]))
>>> factor_e = DiscreteFactor(['E'], cardinality=[2], values=np.array([0.47117, 2.1224]))
>>> factor_f = DiscreteFactor(['F'], cardinality=[2], values=np.array([1.5093, 0.66257]))
>>> factor_a_b = DiscreteFactor(['A', 'B'], cardinality=[2, 2],
...                             values=np.array([1.3207, 0.75717, 0.75717, 1.3207]))
>>> factor_b_c = DiscreteFactor(['B', 'C'], cardinality=[2, 2],
...                             values=np.array([0.00024189, 4134.2, 4134.2, 0.0002418]))
>>> factor_c_d = DiscreteFactor(['C', 'D'], cardinality=[2, 2],
...                             values=np.array([0.0043227, 231.34, 231.34, 0.0043227]))
>>> factor_d_e = DiscreteFactor(['E', 'F'], cardinality=[2, 2],
...                             values=np.array([31.228, 0.032023, 0.032023, 31.228]))
>>> student.add_factors(factor_a, factor_b, factor_c, factor_d, factor_e, factor_f,
...                     factor_a_b, factor_b_c, factor_c_d, factor_d_e)
>>> mplp = Mplp(student)
>>> result = mplp.map_query()
>>> result
{'B': 0.93894, 'C': 1.121, 'A': 1.8323, 'F': 1.5093, 'D': 1.7765, 'E': 2.12239}