Identification

Identification algorithms.

Identification

Algorithm	Implementation
ID [shpitser2006]	y0.algorithm.identifiy.id_std
IDC [shpitser2008]	y0.algorithm.identifiy.idc
ID* [shpitser2012]	y0.algorithm.identifiy.id_star
IDC* [shpitser2012]	y0.algorithm.identifiy.idc_star
Cyclic ID [forre2019]	Issue #71
gID [correa2019]	Issue #72
gID* [correa2021]	Issue #121
Data ID [nabi2020]	Issue #73

This table partially draws from [tikka2021], which made a nice review of non-counterfactual identification methods.

Transport

Algorithm	Implementation
Surrogate Outcomes [tikka2018]	y0.algorithm.transport
Transportability [correa2020]	y0.algorithm.transport
Counterfactual Transportability [correa2022]	PR #197

[shpitser2006] (1,2)

Identification of joint interventional distributions in recursive semi-Markovian causal models

[shpitser2008] (1,2)

Complete Identification Methods for the Causal Hierarchy

[shpitser2012] (1,2,3,4)

https://dl.acm.org/doi/10.5555/1597348.1597382

[tikka2018]

https://arxiv.org/abs/1806.07172

[correa2020]

General Transportability: Synthesis of Experiments from Heterogeneous Domains

[correa2022]

Counterfactual Transportability: A Formal Approach

[forre2019]

Causal Calculus in the Presence of Cycles, Latent Confounders and Selection Bias

[nabi2020]

Full Law Identification In Graphical Models Of Missing Data: Completeness Results

[correa2019]

General Identifiability with Arbitrary Surrogate Experiments

[correa2021]

Nested Counterfactual Identification from Arbitrary Surrogate Experiments

[tikka2021]

Causal Effect Identification from Multiple Incomplete Data Sources: A General Search-based Approach

identify_outcomes(graph: NxMixedGraph, treatments: Variable | set[Variable], outcomes: Variable | set[Variable], conditions: None | Variable | set[Variable] = None) → Expression | None

Calculate the estimand for the treatment(s)m outcome(s), and optional condition(s).

Parameters:

• graph – An acyclic directed mixed graph

• treatments – The node or nodes that are treated

• outcomes – The node or nodes that are outcomes

• conditions – Optional condition or condition nodes. If given, uses the IDC algorithm via y0.algorithm.identify.idc(). Otherwise, uses the ID algorithm via y0.algorithm.identify.identify().

Returns:

An expression representing the estimand if the query is identifiable. If the query is not identifiable, returns none.

identify(identification: Identification) → Expression

Run the ID algorithm from [shpitser2006].

Parameters:

identification – The identification tuple

Returns:

the expression corresponding to the identification

Raises:

Unidentifiable – If no appropriate identification can be found

See also identify_outcomes() for a more idiomatic way of running the ID algorithm given a graph, treatments, and outcomes.

id_star(graph: NxMixedGraph, event: Dict[Variable, Intervention], *, _number_recursions: int = 0) → Expression

Apply the ID* algorithm to the graph from [shpitser2012].

idc(identification: Identification) → Expression

Run the IDC algorithm from [shpitser2008].

Parameters:

identification – The identification tuple

Returns:

An expression created by the identify() algorithm after simplifying the original query

Raises “Unidentifiable” if no appropriate identification can be found.

idc_star(graph: NxMixedGraph, outcomes: Dict[Variable, Intervention], conditions: Dict[Variable, Intervention], *, _number_recursions: int = 0) → Expression

Run the IDC* algorithm from [shpitser2012].

Parameters:

• graph – The causal graph

• outcomes – The outcome events corresponds to \(\gamma\)

• conditions – The condition events corresponds to \(\delta\)

• _number_recursions – The number of times the algorithm has recurred

Returns:

An expression created by the idc_star() algorithm after simplifying the original query

Raises:

ValueError – If ID* returns zero

class Query(outcomes: Variable | set[Variable], treatments: Variable | set[Variable], conditions: None | Variable | set[Variable] = None)

An identification query.

Instantiate an identification.

Parameters:

• outcomes – The outcomes in the query

• treatments – The treatments in the query (e.g., counterfactual variables)

• conditions – The conditions in the query (e.g., coming after the bar)

classmethod from_str(outcomes: str | Iterable[str], treatments: str | Iterable[str], conditions: Iterable[str] | None = None) → Query

Construct a query from text variable names.

classmethod from_expression(query: Probability | Distribution) → Query

Instantiate an identification.

Parameters:

query – The query probability expression

Returns:

An identification tuple

Raises:

ValueError – If there are ragged counterfactual variables in the query

exchange_observation_with_action(variables: Variable | Iterable[Variable]) → Query

Move the condition variable(s) to the treatments.

exchange_action_with_observation(variables: Variable | Iterable[Variable]) → Query

Move the treatment variable(s) to the conditions.

with_treatments(extra_treatments: Iterable[Variable]) → Query

Create a new identification with additional treatments.

uncondition() → Query

Move the conditions to outcomes.

property expression: Expression

Return the query as a Probabilistic expression.

exception Unidentifiable

Raised on failure of the identification algorithm.

class Identification(query: Query, graph: NxMixedGraph, estimand: Expression | None = None)

A package of a query and resulting estimand from identification on a graph.

Instantiate an identification.

Parameters:

• query – The generalized identification query (outcomes/treatments/conditions)

• graph – The graph

• estimand – If none is given, will use the joint distribution over all variables in the graph.

classmethod from_parts(outcomes: set[Variable], treatments: set[Variable], graph: NxMixedGraph, estimand: Expression | None = None, conditions: set[Variable] | None = None) → Identification

Instantiate an identification.

Parameters:

• outcomes – The outcomes in the query

• treatments – The treatments in the query (e.g., counterfactual variables)

• conditions – The conditions in the query (e.g., coming after the bar)

• graph – The graph

• estimand – If none is given, will use the joint distribution over all variables in the graph.

Returns:

An identification object

classmethod from_expression(*, query: Probability | Distribution, graph: NxMixedGraph, estimand: Expression | None = None) → Identification

Instantiate an identification.

Parameters:

• query – The query probability expression

• graph – The graph

• estimand – If none is given, will use the joint distribution over all variables in the graph.

Returns:

An identification object

property outcomes: set[Variable]

Return this identification object’s query’s outcomes.

property treatments: set[Variable]

Return this identification object’s query’s treatments.

property conditions: set[Variable]

Return this identification object’s query’s conditions.

exchange_observation_with_action(variables: Variable | Iterable[Variable]) → Identification

Move the condition variable(s) to the treatments.

exchange_action_with_observation(variables: Variable | Iterable[Variable]) → Identification

Move the treatment variable(s) to the conditions.

with_treatments(extra_treatments: Iterable[Variable]) → Identification

Create a new identification with additional treatments.

uncondition() → Identification

Move the conditions to outcomes.