Causal Inference¶
- class pgmpy.inference.CausalInference.CausalInference(model, set_nodes=None)[source]¶
This is an inference class for performing Causal Inference over Bayesian Networks or Structural Equation Models.
- This class will accept queries of the form: P(Y | do(X)) and utilize its methods to provide an estimand which:
Identifies adjustment variables
Backdoor Adjustment
Front Door Adjustment
Instrumental Variable Adjustment
- Parameters
Examples
Create a small Bayesian Network. >>> from pgmpy.models import BayesianNetwork >>> game = BayesianNetwork([(‘X’, ‘A’), … (‘A’, ‘Y’), … (‘A’, ‘B’)])
Load the graph into the CausalInference object to make causal queries. >>> from pgmpy.inference.CausalInference 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
- estimate_ate(X, Y, data, estimand_strategy='smallest', estimator_type='linear', **kwargs)[source]¶
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
- Return type
The average treatment effect
Examples
>>> import pandas as pd >>> game1 = BayesianNetwork([('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")
- get_all_backdoor_adjustment_sets(X, Y)[source]¶
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 of variabies (Xi, Xj) in a DAG G if:
no node in Z is a descendant of Xi; and
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 = BayesianNetwork([('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.
- get_all_frontdoor_adjustment_sets(X, Y)[source]¶
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:
Z intercepts all directed paths from X to Y
there is no backdoor path from X to Z
all back-door paths from Z to Y are blocked by X
- Returns
frozenset
- Return type
a frozenset of frozensets
References
Causality: Models, Reasoning, and Inference, Judea Pearl (2000). p.82.
- get_distribution()[source]¶
Returns a string representing the factorized distribution implied by the CGM.
- get_minimal_adjustment_set(X, Y)[source]¶
Method to test whether adjustment_set is a valid adjustment set for identifying the causal effect of X on Y.
- Parameters
- Returns
set or None – If None, no adjutment set is possible.
- Return type
A set of variables which are the minimal possible adjustment set.
Examples
References
[1] Perkovic, Emilija, et al. “Complete graphical characterization and construction of adjustment sets in Markov equivalence classes of ancestral graphs.” The Journal of Machine Learning Research 18.1 (2017): 8132-8193.
- get_proper_backdoor_graph(X, Y, inplace=False)[source]¶
Returns a proper backdoor graph for the exposure X and outcome Y. A proper backdoor graph is a graph which remove the first edge of every proper causal path from X to Y.
- Parameters
Examples
>>> from pgmpy.models import BayesianNetwork >>> from pgmpy.inference import CausalInference >>> model = BayesianNetwork([("x1", "y1"), ("x1", "z1"), ("z1", "z2"), ... ("z2", "x2"), ("y2", "z2")]) >>> c_infer = CausalInference(model) >>> c_infer.get_proper_backdoor_graph(X=["x1", "x2"], Y=["y1", "y2"]) <pgmpy.models.BayesianNetwork.BayesianNetwork at 0x7fba501ad940>
References
[1] Perkovic, Emilija, et al. “Complete graphical characterization and construction of adjustment sets in Markov equivalence classes of ancestral graphs.” The Journal of Machine Learning Research 18.1 (2017): 8132-8193.
- is_valid_adjustment_set(X, Y, adjustment_set)[source]¶
Method to test whether adjustment_set is a valid adjustment set for identifying the causal effect of X on Y.
- Parameters
- Returns
boolean – identifying the effect of X on Y. Else returns False.
- Return type
Returns True if adjustment_set is a valid adjustment set for
Examples
>>> from pgmpy.models import BayesianNetwork >>> from pgmpy.inference import CausalInference >>> model = BayesianNetwork([("x1", "y1"), ("x1", "z1"), ("z1", "z2"), ... ("z2", "x2"), ("y2", "z2")]) >>> c_infer = CausalInference(model) >>> c_infer.is_valid_adjustment_set(X=['x1', 'x2'], Y=['y1', 'y2'], adjustment_set=['z1', 'z2']) True
References
[1] Perkovic, Emilija, et al. “Complete graphical characterization and construction of adjustment sets in Markov equivalence classes of ancestral graphs.” The Journal of Machine Learning Research 18.1 (2017): 8132-8193.
- is_valid_backdoor_adjustment_set(X, Y, Z=[])[source]¶
Test whether Z is a valid backdoor adjustment set for estimating the causal impact of X on Y.
- Parameters
- Returns
boolean
- Return type
True if Z is a valid backdoor adjustment set.
Examples
>>> game1 = BayesianNetwork([('X', 'A'), ... ('A', 'Y'), ... ('A', 'B')]) >>> inference = CausalInference(game1) >>> inference.is_valid_backdoor_adjustment_set("X", "Y") True
- is_valid_frontdoor_adjustment_set(X, Y, Z=None)[source]¶
Test whether Z is a valid frontdoor adjustment set for estimating the causal impact of X on Y via the frontdoor adjustment formula.
- query(variables, do=None, evidence=None, adjustment_set=None, inference_algo='ve', show_progress=True, **kwargs)[source]¶
Performs a query on the model of the form where is variables, is do and Z is the evidence.
- Parameters
variables (list) – list of variables in the query i.e. X in .
do (dict (default: None)) – Dictionary of the form {variable_name: variable_state} representing the variables on which to apply the do operation i.e. Y in .
evidence (dict (default: None)) – Dictionary of the form {variable_name: variable_state} repesenting the conditional variables in the query i.e. Z in .
adjustment_set (str or list (default=None)) – Specifies the adjustment set to use. If None, uses the parents of the do variables as the adjustment set.
inference_algo (str or pgmpy.inference.Inference instance) – The inference algorithm to use to compute the probability values. String options are: 1) ve: Variable Elimination 2) bp: Belief Propagation.
kwargs (Any) – Additional paramters which needs to be passed to inference algorithms. Please refer to the pgmpy.inference.Inference for details.
- Returns
pgmpy.factor.DiscreteFactor – over the variables in variables.
- Return type
A factor object representing the joint distribution
Examples
>>> from pgmpy.utils import get_example_model >>> model = get_example_model('alarm') >>> infer = CausalInference(model) >>> infer.query(['HISTORY'], do={'CVP': 'LOW'}, evidence={'HR': 'LOW'}) <DiscreteFactor representing phi(HISTORY:2) at 0x7f4e0874c2e0>