def local_independencies(self, variables): """ Returns an instance of Independencies containing the local independencies of each of the variables. Parameters ---------- variables: str or array like variables whose local independencies are to found. Examples -------- >>> from pgmpy.models import NaiveBayes >>> model = NaiveBayes() >>> model.add_edges_from([('a', 'b'), ('a', 'c'), ('a', 'd')]) >>> ind = model.local_independencies('b') >>> ind (b _|_ d, c | a) """ independencies = Independencies() for variable in [variables] if isinstance(variables, str) else variables: if variable != self.parent_node: independencies.add_assertions([ variable, list(set(self.children_nodes) - set(variable)), self.parent_node ]) return independencies
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 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
def local_independencies(self, variables): """ Returns an instance of Independencies containing the local independencies of each of the variables. Parameters ---------- variables: str or array like variables whose local independencies are to found. Examples -------- >>> from pgmpy.models import NaiveBayes >>> model = NaiveBayes() >>> model.add_edges_from([('a', 'b'), ('a', 'c'), ('a', 'd')]) >>> ind = model.local_independencies('b') >>> ind (b _|_ d, c | a) """ independencies = Independencies() for variable in [variables] if isinstance(variables, str) else variables: if variable != self.parent_node: independencies.add_assertions([variable, list(set(self.children_nodes) - set(variable)), self.parent_node]) return independencies
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 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
def get_independencies(self, latex=False): """ Computes independencies in the Bayesian Network, by checking d-seperation. Parameters ---------- latex: boolean If latex=True then latex string of the independence assertion would be created. Examples -------- >>> from pgmpy.models import BayesianModel >>> chain = BayesianModel([('X', 'Y'), ('Y', 'Z')]) >>> chain.get_independencies() (X _|_ Z | Y) (Z _|_ X | Y) """ independencies = Independencies() for start in (self.nodes()): rest = set(self.nodes()) - {start} for r in range(len(rest)): for observed in itertools.combinations(rest, r): d_seperated_variables = rest - set(observed) - set( self.active_trail_nodes(start, observed=observed)[start]) if d_seperated_variables: independencies.add_assertions([start, d_seperated_variables, observed]) independencies.reduce() if not latex: return independencies else: return independencies.latex_string()
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 -------- >>> from pgmpy.factors import JointProbabilityDistribution >>> prob = JointProbabilityDistribution(['x1', 'x2', 'x3'], [2, 3, 2], np.ones(8)/8) >>> prob.get_independencies() """ if condition: self.conditional_distribution(condition) independencies = Independencies() from itertools import combinations for variable_pair in combinations(list(self.variables), 2): from copy import deepcopy if JointProbabilityDistribution.marginal_distribution(deepcopy(self), variable_pair) == \ JointProbabilityDistribution.marginal_distribution(deepcopy(self), variable_pair[0]) * \ JointProbabilityDistribution.marginal_distribution(deepcopy(self), variable_pair[1]): independencies.add_assertions(variable_pair) return independencies
def get_independencies(self, latex=False): """ Compute independencies in Bayesian Network. Parameters ---------- latex: boolean If latex=True then latex string of the independence assertion would be created. Examples -------- >>> from pgmpy.models import BayesianModel >>> student = BayesianModel() >>> student.add_nodes_from(['diff', 'intel', 'grades', 'letter', 'sat']) >>> student.add_edges_from([('diff', 'grades'), ('intel', 'grades'), ('grade', 'letter'), ... ('intel', 'sat')]) >>> student.get_independencies() """ independencies = Independencies() for start in (self.nodes()): for r in (1, len(self.nodes())): for observed in itertools.combinations(self.nodes(), r): independent_variables = self.active_trail_nodes(start, observed=observed) independent_variables = set(independent_variables) - {start} if independent_variables: independencies.add_assertions([start, independent_variables, observed]) independencies.reduce() if not latex: return independencies else: return independencies.latex_string()
def get_independencies(self, latex=False): """ Computes independencies in the Bayesian Network, by checking d-seperation. Parameters ---------- latex: boolean If latex=True then latex string of the independence assertion would be created. Examples -------- >>> from pgmpy.models import BayesianModel >>> chain = BayesianModel([('X', 'Y'), ('Y', 'Z')]) >>> chain.get_independencies() (X _|_ Z | Y) (Z _|_ X | Y) """ independencies = Independencies() for start in (self.nodes()): rest = set(self.nodes()) - {start} for r in range(len(rest)): for observed in itertools.combinations(rest, r): d_seperated_variables = rest - set(observed) - set( self.active_trail_nodes(start, observed=observed)) if d_seperated_variables: independencies.add_assertions( [start, d_seperated_variables, observed]) independencies.reduce() if not latex: return independencies else: return independencies.latex_string()
def local_independencies(self, variables): """ Returns a independencies object containing the local independencies of each of the variables. Parameters ---------- variables: str or array like variables whose local independencies are to found. Examples -------- >>> from pgmpy.models import BayesianModel >>> student = BayesianModel() >>> student.add_edges_from([('diff', 'grade'), ('intel', 'grade'), >>> ('grade', 'letter'), ('intel', 'SAT')]) >>> ind = student.local_independencies('grade') >>> ind.event1 {'grade'} >>> ind.event2 {'SAT'} >>> ind.event3 {'diff', 'intel'} """ def dfs(node): """ Returns the descendents of node. Since there can't be any cycles in the Bayesian Network. This is a very simple dfs which doen't remember which nodes it has visited. """ descendents = [] visit = [node] while visit: n = visit.pop() neighbors = self.neighbors(n) visit.extend(neighbors) descendents.extend(neighbors) return descendents from pgmpy.independencies import Independencies independencies = Independencies() for variable in [variables] if isinstance(variables, str) else variables: independencies.add_assertions([ variable, set(self.nodes()) - set(dfs(variable)) - set(self.get_parents(variable)) - {variable}, set(self.get_parents(variable)) ]) return independencies
def local_independencies(self, variables): """ Returns a independencies object containing the local independencies of each of the variables. Parameters ---------- variables: str or array like variables whose local independencies are to found. Examples -------- >>> from pgmpy.models import BayesianModel >>> student = BayesianModel() >>> student.add_edges_from([('diff', 'grade'), ('intel', 'grade'), >>> ('grade', 'letter'), ('intel', 'SAT')]) >>> ind = student.local_independencies('grade') >>> ind.event1 {'grade'} >>> ind.event2 {'SAT'} >>> ind.event3 {'diff', 'intel'} """ def dfs(node): """ Returns the descendents of node. Since there can't be any cycles in the Bayesian Network. This is a very simple dfs which doen't remember which nodes it has visited. """ descendents = [] visit = [node] while visit: n = visit.pop() neighbors = self.neighbors(n) visit.extend(neighbors) descendents.extend(neighbors) return descendents from pgmpy.independencies import Independencies independencies = Independencies() for variable in [variables] if isinstance(variables, str) else variables: independencies.add_assertions([variable, set(self.nodes()) - set(dfs(variable)) - set(self.get_parents(variable)) - {variable}, set(self.get_parents(variable))]) return independencies
def local_independencies(self, variables): """ Returns an instance of Independencies containing the local independencies of each of the variables. Parameters ---------- variables: str or array like variables whose local independencies are to be found. Examples -------- >>> from pgmpy.models import BayesianModel >>> student = BayesianModel() >>> student.add_edges_from([('diff', 'grade'), ('intel', 'grade'), >>> ('grade', 'letter'), ('intel', 'SAT')]) >>> ind = student.local_independencies('grade') >>> ind (grade _|_ SAT | diff, intel) """ def dfs(node): """ Returns the descendents of node. Since Bayesian Networks are acyclic, this is a very simple dfs which does not remember which nodes it has visited. """ descendents = [] visit = [node] while visit: n = visit.pop() neighbors = self.neighbors(n) visit.extend(neighbors) descendents.extend(neighbors) return descendents independencies = Independencies() for variable in variables if isinstance(variables, (list, tuple)) else [variables]: non_descendents = set(self.nodes()) - {variable} - set( dfs(variable)) parents = set(self.get_parents(variable)) if non_descendents - parents: independencies.add_assertions( [variable, non_descendents - parents, parents]) return independencies
def get_local_independencies(self, latex=False): """ Returns all the local independencies present in the markov model. Local independencies are the independence assertion in the form of .. math:: {X \perp W - {X} - MB(X) | MB(X)} where MB is the markov blanket of all the random variables in X Parameters ---------- latex: boolean If latex=True then latex string of the indepedence assertion would be created Examples -------- >>> from pgmpy.models import MarkovModel >>> mm = MarkovModel() >>> 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')]) >>> mm.get_local_independecies() """ from pgmpy.exceptions import RequiredError local_independencies = Independencies() all_vars = set(self.nodes()) for node in self.nodes(): markov_blanket = set(self.markov_blanket(node)) rest = all_vars - set([node]) - markov_blanket try: local_independencies.add_assertions( [node, list(rest), list(markov_blanket)]) except RequiredError: pass local_independencies.reduce() if latex: return local_independencies.latex_string() else: return local_independencies
def local_independencies(self, variables): """ Returns an instance of Independencies containing the local independencies of each of the variables. Parameters ---------- variables: str or array like variables whose local independencies are to be found. Examples -------- >>> from pgmpy.models import BayesianModel >>> student = BayesianModel() >>> student.add_edges_from([('diff', 'grade'), ('intel', 'grade'), >>> ('grade', 'letter'), ('intel', 'SAT')]) >>> ind = student.local_independencies('grade') >>> ind (grade _|_ SAT | diff, intel) """ def dfs(node): """ Returns the descendents of node. Since Bayesian Networks are acyclic, this is a very simple dfs which does not remember which nodes it has visited. """ descendents = [] visit = [node] while visit: n = visit.pop() neighbors = self.neighbors(n) visit.extend(neighbors) descendents.extend(neighbors) return descendents independencies = Independencies() for variable in variables if isinstance(variables, (list, tuple)) else [variables]: non_descendents = set(self.nodes()) - {variable} - set(dfs(variable)) parents = set(self.get_parents(variable)) if non_descendents - parents: independencies.add_assertions([variable, non_descendents - parents, parents]) return independencies
def get_local_independencies(self, latex=False): """ Returns all the local independencies present in the markov model. Local independencies are the independence assertion in the form of .. math:: {X \perp W - {X} - MB(X) | MB(X)} where MB is the markov blanket of all the random variables in X Parameters ---------- latex: boolean If latex=True then latex string of the indepedence assertion would be created Examples -------- >>> from pgmpy.models import MarkovModel >>> mm = MarkovModel() >>> 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')]) >>> mm.get_local_independecies() """ from pgmpy.exceptions import RequiredError local_independencies = Independencies() all_vars = set(self.nodes()) for node in self.nodes(): markov_blanket = set(self.markov_blanket(node)) rest = all_vars - set([node]) - markov_blanket try: local_independencies.add_assertions([node, list(rest), list(markov_blanket)]) except RequiredError: pass local_independencies.reduce() if latex: return local_independencies.latex_string() else: return local_independencies
def get_independencies(self, latex=False): """ Compute independencies in Bayesian Network. Parameters ---------- latex: boolean If latex=True then latex string of the independence assertion would be created. Examples -------- >>> from pgmpy.models import BayesianModel >>> student = BayesianModel() >>> student.add_nodes_from(['diff', 'intel', 'grades', 'letter', 'sat']) >>> student.add_edges_from([('diff', 'grades'), ('intel', 'grades'), ('grade', 'letter'), ... ('intel', 'sat')]) >>> student.get_independencies() """ independencies = Independencies() for start in (self.nodes()): for r in (1, len(self.nodes())): for observed in itertools.combinations(self.nodes(), r): independent_variables = self.active_trail_nodes( start, observed=observed) independent_variables = set(independent_variables) - { start } if independent_variables: independencies.add_assertions( [start, independent_variables, observed]) independencies.reduce() if not latex: return independencies else: return independencies.latex_string()
def local_independencies(self, variables): """ Returns an instance of Independencies containing the local independencies of each of the variables. Parameters ---------- variables: str or array like variables whose local independencies are to be found. Examples -------- >>> from pgmpy.models import DAG >>> student = DAG() >>> student.add_edges_from([('diff', 'grade'), ('intel', 'grade'), >>> ('grade', 'letter'), ('intel', 'SAT')]) >>> ind = student.local_independencies('grade') >>> ind (grade _|_ SAT | diff, intel) """ independencies = Independencies() for variable in ( variables if isinstance(variables, (list, tuple)) else [variables] ): non_descendents = ( set(self.nodes()) - {variable} - set(nx.dfs_preorder_nodes(self, variable)) ) parents = set(self.get_parents(variable)) if non_descendents - parents: independencies.add_assertions( [variable, non_descendents - parents, parents] ) return independencies
from pgmpy.independencies import Independencies # There are multiple ways to create an Independencies object, we # could either initialize an empty object or initialize with some # assertions. independencies = Independencies() # Empty object independencies.get_assertions() independencies.add_assertions(assertion1, assertion2) independencies.get_assertions()