Source code for pgmpy.inference.CausalInference

import numpy as np
import networkx as nx

from pgmpy.models.BayesianModel import BayesianModel
from pgmpy.estimators.LinearModel import LinearEstimator
from pgmpy.utils.sets import _powerset, _variable_or_iterable_to_set


[docs]class CausalInference(object): """ This is an inference class for performing Causal Inference over Bayesian Networks or Strucural Equation Models. This class will accept queries of the form: P(Y | do(X)) and utilize it's methods to provide an estimand which: * Identifies adjustment variables * Backdoor Adjustment * Front Door Adjustment * Instrumental Variable Adjustment Parameters ---------- model: CausalGraph The model that we'll perform inference over. set_nodes: list[node:str] or None A list (or set/tuple) of nodes in the Bayesian Network which have been set to a specific value per the do-operator. Examples -------- Create a small Bayesian Network. >>> from pgmpy.models.BayesianModel import BayesianModel >>> game = CausalGraph([('X', 'A'), ('A', 'Y'), ('A', 'B')]) Load the graph into the CausalInference object to make causal queries. >>> from pgmpy.inference.causal_inferece import CausalInference >>> inference = CausalInference(game) >>> inference.get_all_backdoor_adjustment_sets(X="X", Y="Y") >>> inference.get_all_frontdoor_adjustment_sets(X="X", Y="Y") References ---------- 'Causality: Models, Reasoning, and Inference' - Judea Pearl (2000) Many thanks to @ijmbarr for their implementation of Causal Graphical models available. It served as an invaluable reference. Available on GitHub: https://github.com/ijmbarr/causalgraphicalmodels """ def __init__(self, model, latent_vars=None, set_nodes=None): if not isinstance(model, BayesianModel): raise NotImplementedError( "Causal Inference is only implemented for BayesianModels at this time." ) self.dag = model self.graph = self.dag.to_undirected() self.latent_variables = _variable_or_iterable_to_set(latent_vars) self.set_nodes = _variable_or_iterable_to_set(set_nodes) self.observed_variables = frozenset(self.dag.nodes()).difference( self.latent_variables ) def __repr__(self): variables = ", ".join(map(str, sorted(self.observed_variables))) return "{classname}({vars})".format(self.__class__.__name__, variables) def _is_d_separated(self, X, Y, Z=None): return not self.dag.is_active_trail(X, Y, observed=Z)
[docs] def is_valid_backdoor_adjustment_set(self, X, Y, Z=[]): """ Test whether Z is a valid backdoor adjustment set for estimating the causal impact of X on Y. Parameters ---------- X: str Intervention Variable Y: str Target Variable Z: str or set[str] Adjustment variables Returns ------- boolean: True if Z is a valid backdoor adjustment set. Examples -------- >>> game1 = BayesianModel([('X', 'A'), ('A', 'Y'), ('A', 'B')]) >>> inference = CausalInference(game1) >>> inference.is_valid_backdoor_adjustment_set("X", "Y") True """ Z_ = list(Z) observed = [X] + Z_ parents_d_sep = [] for p in self.dag.predecessors(X): parents_d_sep.append(self._is_d_separated(p, Y, Z=observed)) return all(parents_d_sep)
[docs] def get_all_backdoor_adjustment_sets(self, X, Y): """ Returns a list of all adjustment sets per the back-door criterion. A set of variables Z satisfies the back-door criterion relative to an ordered pair ofvariabies (Xi, Xj) in a DAG G if: (i) no node in Z is a descendant of Xi; and (ii) Z blocks every path between Xi and Xj that contains an arrow into Xi. TODO: * Backdoors are great, but the most general things we could implement would be Ilya Shpitser's ID and IDC algorithms. See [his Ph.D. thesis for a full explanation] (https://ftp.cs.ucla.edu/pub/stat_ser/shpitser-thesis.pdf). After doing a little reading it is clear that we do not need to immediatly implement this. However, in order for us to truly account for unobserved variables, we will need not only these algorithms, but a more general implementation of a DAG. Most DAGs do not allow for bidirected edges, but it is an important piece of notation which Pearl and Shpitser use to denote graphs with latent variables. Parameters ---------- X: str Intervention Variable Returns ------- frozenset: A frozenset of frozensets Y: str Target Variable Examples -------- >>> game1 = BayesianModel([('X', 'A'), ('A', 'Y'), ('A', 'B')]) >>> inference = CausalInference(game1) >>> inference.get_all_backdoor_adjustment_sets("X", "Y") frozenset([]) References ---------- "Causality: Models, Reasoning, and Inference", Judea Pearl (2000). p.79. """ try: assert X in self.observed_variables assert Y in self.observed_variables except AssertionError: raise AssertionError("Make sure both X and Y are observed.") if self.is_valid_backdoor_adjustment_set(X, Y, Z=frozenset()): return frozenset() possible_adjustment_variables = ( set(self.observed_variables) - {X} - {Y} - set(nx.descendants(self.dag, X)) ) valid_adjustment_sets = [] for s in _powerset(possible_adjustment_variables): super_of_complete = [] for vs in valid_adjustment_sets: super_of_complete.append(vs.intersection(set(s)) == vs) if any(super_of_complete): continue if self.is_valid_backdoor_adjustment_set(X, Y, s): valid_adjustment_sets.append(frozenset(s)) return frozenset(valid_adjustment_sets)
[docs] def is_valid_frontdoor_adjustment_set(self, X, Y, Z=None): """ Test whether Z is a valid frontdoor adjustment set for estimating the causal impact of X on Y via the frontdoor adjustment formula. Parameters ---------- X: str Intervention Variable Y: str Target Variable Z: set Adjustment variables Returns ------- boolean: True if Z is a valid frontdoor adjustment set. """ Z = _variable_or_iterable_to_set(Z) # 0. Get all directed paths from X to Y. Don't check further if there aren't any. directed_paths = list(nx.all_simple_paths(self.dag, X, Y)) if directed_paths == []: return False # 1. Z intercepts all directed paths from X to Y unblocked_directed_paths = [ path for path in directed_paths if not any(zz in path for zz in Z) ] if unblocked_directed_paths: return False # 2. there is no backdoor path from X to Z unblocked_backdoor_paths_X_Z = [ zz for zz in Z if not self.is_valid_backdoor_adjustment_set(X, zz) ] if unblocked_backdoor_paths_X_Z: return False # 3. All back-door paths from Z to Y are blocked by X valid_backdoor_sets = [] for zz in Z: valid_backdoor_sets.append(self.is_valid_backdoor_adjustment_set(zz, Y, X)) if not all(valid_backdoor_sets): return False return True
[docs] def get_all_frontdoor_adjustment_sets(self, X, Y): """ Identify possible sets of variables, Z, which satisify the front-door criterion relative to given X and Y. Z satisifies the front-door critierion if: (i) Z intercepts all directed paths from X to Y (ii) there is no backdoor path from X to Z (iii) all back-door paths from Z to Y are blocked by X Returns ------- frozenset: a frozenset of frozensets References ---------- Causality: Models, Reasoning, and Inference, Judea Pearl (2000). p.82. """ assert X in self.observed_variables assert Y in self.observed_variables possible_adjustment_variables = set(self.observed_variables) - {X} - {Y} valid_adjustment_sets = frozenset( [ frozenset(s) for s in _powerset(possible_adjustment_variables) if self.is_valid_frontdoor_adjustment_set(X, Y, s) ] ) return valid_adjustment_sets
[docs] def get_distribution(self): """ Returns a string representing the factorized distribution implied by the CGM. """ products = [] for node in nx.topological_sort(self.dag): if node in self.set_nodes: continue parents = list(self.dag.predecessors(node)) if not parents: p = "P({})".format(node) else: parents = [ "do({})".format(n) if n in self.set_nodes else str(n) for n in parents ] p = "P({}|{})".format(node, ",".join(parents)) products.append(p) return "".join(products)
[docs] def simple_decision(self, adjustment_sets=[]): """ Selects the smallest set from provided adjustment sets. Parameters ---------- adjustment_sets: iterable A frozenset or list of valid adjustment sets Returns ------- frozenset """ adjustment_list = list(adjustment_sets) if adjustment_list == []: return frozenset([]) return adjustment_list[np.argmin(adjustment_list)]
[docs] def estimate_ate( self, X, Y, data, estimand_strategy="smallest", estimator_type="linear", **kwargs ): """ Estimate the average treatment effect (ATE) of X on Y. Parameters ---------- X: str Intervention Variable Y: str Target Variable data: pandas DataFrame All observed data for this Bayesian Network. estimand_strategy: str or frozenset Either specify a specific backdoor adjustment set or a strategy. The available options are: smallest: Use the smallest estimand of observed variables all: Estimate the ATE from each identified estimand estimator_type: str The type of model to be used to estimate the ATE. All of the linear regression classes in statsmodels are available including: * GLS: generalized least squares for arbitrary covariance * OLS: ordinary least square of i.i.d. errors * WLS: weighted least squares for heteroskedastic error Specify them with their acronym (e.g. "OLS") or simple "linear" as an alias for OLS. **kwargs: dict Keyward arguments specific to the selected estimator. linear: missing: str Available options are "none", "drop", or "raise" Returns ------- float: The average treatment effect Examples -------- >>> game1 = BayesianModel([('X', 'A'), ('A', 'Y'), ('A', 'B')]) >>> data = pd.DataFrame(np.random.randint(2, size=(1000, 4)), columns=['X', 'A', 'B', 'Y']) >>> inference = CausalInference(model=game1) >>> inference.estimate_ate("X", "Y", data=data, estimator_type="linear") """ valid_estimators = ["linear"] try: assert estimator_type in valid_estimators except AssertionError: print( "{} if not a valid estimator_type. Please select from {}".format( estimator_type, valid_estimators ) ) if isinstance(estimand_strategy, frozenset): adjustment_set = frozenset({estimand_strategy}) assert self.is_valid_backdoor_adjustment_set(X, Y, Z=adjustment_set) elif estimand_strategy in ["smallest", "all"]: adjustment_sets = self.get_all_backdoor_adjustment_sets(X, Y) if estimand_strategy == "smallest": adjustment_sets = frozenset({self.simple_decision(adjustment_sets)}) if estimator_type == "linear": self.estimator = LinearEstimator(self.dag) ate = [ self.estimator.fit(X=X, Y=Y, Z=s, data=data, **kwargs)._get_ate() for s in adjustment_sets ] return np.mean(ate)