Source code for pgmpy.factors.discrete.JointProbabilityDistribution

import itertools
from operator import mul

import numpy as np

from pgmpy.factors.discrete import DiscreteFactor
from pgmpy.independencies import Independencies
from pgmpy.extern.six.moves import range, zip
from pgmpy.extern import six


[docs]class JointProbabilityDistribution(DiscreteFactor): """ Base class for Joint Probability Distribution Public Methods -------------- conditional_distribution(values) create_bayesian_model() get_independencies() pmap() marginal_distribution(variables) minimal_imap() is_imap(model) """ 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(['{var}:{card}'.format(var=var, card=card) for var, card in zip(self.variables, self.cardinality)]) return "<Joint Distribution representing P({var_card}) at {address}>".format(address=hex(id(self)), var_card=var_card) def __str__(self): if six.PY2: return self._str(phi_or_p='P', tablefmt='pqsl') else: 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, six.string_types): raise TypeError('Event 1 should be a list or array-like structure') if isinstance(event2, six.string_types): raise TypeError('Event 2 should be a list or array-like structure') if event3: if isinstance(event3, six.string_types): raise TypeError('Event 3 cannot of type string') elif condition_random_variable: if not all(isinstance(var, six.string_types) 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 Parameter --------- 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 _|_ x2) (x1 _|_ x3) (x2 _|_ 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 BayesianModel def get_subsets(u): for r in range(len(u) + 1): for i in itertools.combinations(u, r): yield i G = BayesianModel() 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 BayesianModel is Imap of JointProbabilityDistribution Parameters ----------- model : An instance of BayesianModel 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 BayesianModel >>> from pgmpy.factors.discrete import TabularCPD >>> from pgmpy.factors.discrete import JointProbabilityDistribution >>> bm = BayesianModel([('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 BayesianModel if not isinstance(model, BayesianModel): raise TypeError("model must be an instance of BayesianModel") factors = [cpd.to_factor() for cpd in model.get_cpds()] factor_prod = six.moves.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