import copy from enum import Enum import numpy as np import itertools from functools import reduce import networkx as nx from beliefs.models.base_models import BayesianModel from beliefs.factors.bernoulli_or_cpd import BernoulliOrCPD class InvalidLambdaMsgToParent(Exception): """Computed invalid lambda msg to send to parent.""" pass class MessageType(Enum): LAMBDA = 'lambda' PI = 'pi' class BeliefUpdateNodeModel(BayesianModel): """ A Bayesian model storing nodes (e.g. Node or BernoulliOrNode) implementing properties and methods for Pearl's belief update algorithm. ref: "Fusion, Propagation, and Structuring in Belief Networks" Artificial Intelligence 29 (1986) 241-288 """ def __init__(self, nodes_dict): """ Input: nodes_dict: dict a dict key, value pair as {label_id: instance_of_node_class_or_subclass} """ super().__init__(edges=self._get_edges_from_nodes(nodes_dict.values()), variables=list(nodes_dict.keys()), cpds=[node.cpd for node in nodes_dict.values()]) self.nodes_dict = nodes_dict @classmethod def init_from_edges(cls, edges, node_class): """Create nodes from the same node class. Input: edges: list of edge tuples of form ('parent', 'child') node_class: the Node class or subclass from which to create all the nodes from edges. """ nodes = set() g = nx.DiGraph(edges) for label in set(itertools.chain(*edges)): node = node_class(label_id=label, children=list(g.successors(label)), parents=list(g.predecessors(label))) nodes.add(node) nodes_dict = {node.label_id: node for node in nodes} return cls(nodes_dict) @staticmethod def _get_edges_from_nodes(nodes): """ Return list of all directed edges in nodes. Args: nodes: an iterable of objects of the Node class or subclass Returns: edges: list of edge tuples """ edges = set() for node in nodes: if node.parents: edge_tuples = zip(node.parents, [node.label_id]*len(node.parents)) edges.update(edge_tuples) return list(edges) def set_boundary_conditions(self): """ 1. Root nodes: if x is a node with no parents, set Pi(x) = prior probability of x. 2. Leaf nodes: if x is a node with no children, set Lambda(x) to an (unnormalized) unit vector, of length the cardinality of x. """ for root in self.get_roots(): self.nodes_dict[root].pi_agg = self.nodes_dict[root].cpd.values for leaf in self.get_leaves(): self.nodes_dict[leaf].lambda_agg = np.ones([self.nodes_dict[leaf].cardinality]) @property def all_nodes_are_fully_initialized(self): """ Returns True if, for all nodes in the model, all lambda and pi messages and lambda_agg and pi_agg are not None, else False. """ for node in self.nodes_dict.values(): if not node.is_fully_initialized: return False return True def copy(self): """ Returns a copy of the model. """ copy_nodes = copy.deepcopy(self.nodes_dict) copy_model = self.__class__(nodes_dict=copy_nodes) return copy_model class Node: """A node in a DAG with methods to compute the belief (marginal probability of the node given evidence) and compute pi/lambda messages to/from its neighbors to update its belief. Implemented from Pearl's belief propagation algorithm. """ def __init__(self, label_id, children, parents, cardinality, cpd): """ Args label_id: str children: set of strings parents: set of strings cardinality: int, cardinality of the random variable the node represents cpd: an instance of a conditional probability distribution, e.g. BernoulliOrCPD or TabularCPD """ self.label_id = label_id self.children = children self.parents = parents self.cardinality = cardinality self.cpd = cpd self.pi_agg = None # np.array dimensions [1, cardinality] self.lambda_agg = None # np.array dimensions [1, cardinality] self.pi_received_msgs = self._init_received_msgs(parents) self.lambda_received_msgs = self._init_received_msgs(children) @classmethod def from_cpd_class(cls, label_id, children, parents, cardinality, cpd_class): cpd = cpd_class(label_id, parents) return cls(label_id, children, parents, cardinality, cpd) @property def belief(self): if self.pi_agg.any() and self.lambda_agg.any(): belief = np.multiply(self.pi_agg, self.lambda_agg) return self._normalize(belief) else: return None def _normalize(self, value): return value/value.sum() @staticmethod def _init_received_msgs(keys): return {k: None for k in keys} def _return_msgs_received_for_msg_type(self, message_type): """ Input: message_type: MessageType enum Returns: msg_values: list of message values (each an np.array) """ if message_type == MessageType.LAMBDA: msg_values = [msg for msg in self.lambda_received_msgs.values()] elif message_type == MessageType.PI: msg_values = [msg for msg in self.pi_received_msgs.values()] return msg_values def validate_and_return_msgs_received_for_msg_type(self, message_type): """ Check that all messages have been received from children (parents). Raise error if all messages have not been received. Called before calculating lambda_agg (pi_agg). Input: message_type: MessageType enum Returns: msg_values: list of message values (each an np.array) """ msg_values = self._return_msgs_received_for_msg_type(message_type) if any(msg is None for msg in msg_values): raise ValueError( "Missing value for {msg_type} msg from child: can't compute {msg_type}_agg." .format(msg_type=message_type.value) ) else: return msg_values def compute_pi_agg(self): # TODO: implement explict factor product operation raise NotImplementedError def compute_lambda_agg(self): if not self.children: return self.lambda_agg else: lambda_msg_values = self.validate_and_return_msgs_received_for_msg_type(MessageType.LAMBDA) self.lambda_agg = reduce(np.multiply, lambda_msg_values) return self.lambda_agg def _update_received_msg_by_key(self, received_msg_dict, key, new_value): if key not in received_msg_dict.keys(): raise ValueError("Label id '{}' to update message isn't in allowed set of keys: {}" .format(key, received_msg_dict.keys())) if not isinstance(new_value, np.ndarray): raise TypeError("Expected a new value of type numpy.ndarray, but got type {}" .format(type(new_value))) if new_value.shape != (self.cardinality,): raise ValueError("Expected new value to be of dimensions ({},) but got {} instead" .format(self.cardinality, new_value.shape)) received_msg_dict[key] = new_value def update_pi_msg_from_parent(self, parent, new_value): self._update_received_msg_by_key(received_msg_dict=self.pi_received_msgs, key=parent, new_value=new_value) def update_lambda_msg_from_child(self, child, new_value): self._update_received_msg_by_key(received_msg_dict=self.lambda_received_msgs, key=child, new_value=new_value) def compute_pi_msg_to_child(self, child_k): lambda_msg_from_child = self.lambda_received_msgs[child_k] if lambda_msg_from_child is not None: with np.errstate(divide='ignore', invalid='ignore'): # 0/0 := 0 return self._normalize( np.nan_to_num(np.divide(self.belief, lambda_msg_from_child))) else: raise ValueError("Can't compute pi message to child_{} without having received a lambda message from that child.") def compute_lambda_msg_to_parent(self, parent_k): # TODO: implement explict factor product operation raise NotImplementedError @property def is_fully_initialized(self): """ Returns True if all lambda and pi messages and lambda_agg and pi_agg are not None, else False. """ lambda_msgs = self._return_msgs_received_for_msg_type(MessageType.LAMBDA) if any(msg is None for msg in lambda_msgs): return False pi_msgs = self._return_msgs_received_for_msg_type(MessageType.PI) if any(msg is None for msg in pi_msgs): return False if (self.pi_agg is None) or (self.lambda_agg is None): return False return True class BernoulliOrNode(Node): def __init__(self, label_id, children, parents): super().__init__(label_id=label_id, children=children, parents=parents, cardinality=2, cpd=BernoulliOrCPD(label_id, parents)) def compute_pi_agg(self): if not self.parents: self.pi_agg = self.cpd.values else: pi_msg_values = self.validate_and_return_msgs_received_for_msg_type(MessageType.PI) parents_p0 = [p[0] for p in pi_msg_values] p_0 = reduce(lambda x, y: x*y, parents_p0) p_1 = 1 - p_0 self.pi_agg = np.array([p_0, p_1]) return self.pi_agg def compute_lambda_msg_to_parent(self, parent_k): if np.array_equal(self.lambda_agg, np.ones([self.cardinality])): return np.ones([self.cardinality]) else: # TODO: cleanup this validation _ = self.validate_and_return_msgs_received_for_msg_type(MessageType.PI) p0_excluding_k = [msg[0] for par_id, msg in self.pi_received_msgs.items() if par_id != parent_k] p0_product = reduce(lambda x, y: x*y, p0_excluding_k, 1) lambda_0 = self.lambda_agg[1] + (self.lambda_agg[0] - self.lambda_agg[1])*p0_product lambda_1 = self.lambda_agg[1] lambda_msg = np.array([lambda_0, lambda_1]) if not any(lambda_msg): raise InvalidLambdaMsgToParent return self._normalize(lambda_msg)