Causal Inference (a.k.a. do-calculus)

Obtaining and evaluating a CausalFormula is done using one these functions :

pyagrum.causal.causalImpact(cm, on, doing, knowing=None, values=None)

Determines the causal impact of interventions.

Determines the causal impact of the interventions specified in doing on the single or list of variables on knowing the states of the variables in knowing (optional). These last parameters is dictionary <variable name>:<value>. The causal impact is determined in the causal DAG cm. This function returns a triplet with a latex format formula used to compute the causal impact, a tensor representing the probability distribution of on given the interventions and observations as parameters, and an explanation of the method allowing the identification. If there is no impact, the joint probability of on is simply returned. If the impact is not identifiable the formula and the adjustment will be None but an explanation is still given.

Parameters:

  • cm (CausalModel) – the causal model

  • on (str|NameSet) – variable name or variable names set of interest

  • doing (str|NameSet) – the interventions

  • knowing (str|NameSet) – the observations

  • values (Dict[str,int] default=None) – the values of interventions and observations

Returns:

the CausalFormula, the computation, the explanation

Return type:

Tuple[CausalFormula,pyagrum.Tensor,str]

pyagrum.causal.doCalculusWithObservation(cm, on, doing, knowing=None)

Compute the CausalFormula for an impact analysis given the causal model, the observed variables and the variable on which there will be intervention.

Parameters:

  • cm (CausalModel) – the causal model

  • on (Set[str]) – the variables of interest

  • doing (Set[str]) – the interventions

  • knowing (Set[str] default=None) – the observations

Returns:

if possible, returns the formula to compute this intervention

Return type:

CausalFormula

Raises:

HedgeException, UnidentifiableException – if this calculous is not possible

pyagrum.causal.identifyingIntervention(cm, Y, X, P=None)

Following Shpitser, Ilya and Judea Pearl. ‘Identification of Conditional Interventional Distributions.’ UAI2006 and ‘Complete Identification Methods for the Causal Hierarchy’ JMLR 2008

Parameters:

  • cm (CausalModel) – the causal model

  • Y (Set[str]) – The variables of interest (named following the paper)

  • X (Set[str]) – The variable of intervention (named following the paper)

  • P (ASTtree) – The ASTtree representing the calculus in construction

Return type:

ASTtree

Returns:

the ASTtree representing the calculus

Other functions for causal inference

CausalFormula is the class that represents a causal query within a causal model. It mainly consists of:

  • a reference to the associated pyagrum.CausalModel,

  • three sets of variable names representing the groups in the query $P(set1 | do(set2), know(set3))$,

  • and an abstract syntax tree (AST) used to compute or display the query.

class pyagrum.causal.CausalFormula(cm, root, on, doing, knowing=None)

Represents a causal query in a causal model. The query is encoded as an CausalFormula that can be evaluated in the causal model : $P(on|knowing, overhook (doing))$

Parameters:

  • cm (CausalModel) – the causal model

  • root (ASTtree) – the syntax tree

  • on (str|Set[str]) – the variable or the set of variables of interest

  • doing (str|Set[str]) – the intervention variable(s)

  • knowing (None|str|Set[str]) – the observation variable(s)

property cm: CausalModel
Returns:

the causal model

Return type:

CausalModel

copy()

Copy theAST. Note that the causal model is just referenced. The tree is copied.

Returns:

the copu

Return type:

CausalFormula

eval()

Compute the Tensor from the CausalFormula over vars using cond as value for others variables

Returns:

The resulting distribution

Return type:

pyagrum.Tensor

latexQuery(values=None)

Returns a string representing the query compiled by this Formula. If values, the query is annotated with the values in the dictionary.

Parameters:

values (None|Dict[str,str]) – the values to add in the query representation

Returns:

the LaTeX representation of the causal query for this CausalFormula

Return type:

str

property root: ASTtree
Returns:

the causalFormula as an ASTtree

Return type:

ASTtree

toLatex()
Returns:

a LaTeX representation of the CausalFormula

Return type:

str

pyagrum.causal.backdoor_generator(bn, cause, effect, not_bd=None)

Generates backdoor sets for the pair of nodes (cause, effect) in the graph bn excluding the nodes in the set not_bd (optional)

Parameters:
Yields:

List[int] – the different backdoors

pyagrum.causal.frontdoor_generator(bn, x, y, not_fd=None)

Generates frontdoor sets for the pair of nodes (x, y) in the graph bn excluding the nodes in the set not_fd (optional)

Parameters:
Yields:

List[int] – the different frontdoors