Latent Variable DAGs
Implement Robin Evans’ simplification algorithms from [evans2012] and [evans2016].
- evans_simplify(graph: NxMixedGraph, *, latents: None | Variable | Iterable[Variable] = None, tag: str | None = None) NxMixedGraph[source]
Reduce the ADMG based on Evans’ simplification rules in [evans2012] and [evans2016].
- Parameters:
graph – an NxMixedGraph
latents – Additional variables to mark as latent, in addition to the ones created by undirected edges
tag – The tag for which variables are latent
- Returns:
the new graph after simplification
- simplify_latent_dag(graph: DiGraph, *, tag: str | None = None) SimplifyResults[source]
Apply Robin Evans’ four rules in succession, in place from [evans2012] and [evans2016].
- class SimplifyResults(graph: DiGraph, widows: Set[Variable], redundant: Set[Variable], unidirectional_latents: Set[Variable])[source]
Results from the simplification of a LV-DAG.
Create new instance of SimplifyResults(graph, widows, redundant, unidirectional_latents)
- remove_widow_latents(graph: DiGraph, tag: str | None = None) Tuple[DiGraph, Set[Variable]][source]
Remove latents with no children (in-place).
- Parameters:
graph – A latent variable DAG
tag – The tag for which variables are latent
- Returns:
The graph, modified in place
- transform_latents_with_parents(graph: DiGraph, tag: str | None = None, suffix: str | None = None) DiGraph[source]
Transform latent variables with parents into exogenous latent variables.
An exogenous latent variable is a node with no parents.
- Parameters:
graph – A latent variable DAG
tag – The tag for which variables are latent
suffix – The suffix to postpend to transformed latent variables.
- Returns:
The graph, modified in place
- remove_redundant_latents(graph: DiGraph, tag: str | None = None) Tuple[DiGraph, Set[Variable]][source]
Remove redundant latent variables.
W is a redundant latent variable if children of W are a subset of another latent variable.
- Parameters:
graph – A latent variable DAG
tag – The tag for which variables are latent
- Returns:
The graph, modified in place
- remove_unidirectional_latents(graph: DiGraph, tag: str | None = None) Tuple[DiGraph, Set[Variable]][source]
Remove latents with one child (in-place).
- Parameters:
graph – A latent variable DAG
tag – The tag for which variables are latent
- Returns:
The graph, modified in place
An implementation of Sara Taheri’s algorithm for using causal queries for experimental design.
See also
https://docs.google.com/presentation/d/1klBOjGtRkXOMSDgOCLChBTBJZ0dFxJPn9IPRLAlv_N8/edit?usp=sharing
- taheri_design_admg(graph: NxMixedGraph, cause: str | Variable, effect: str | Variable, *, tag: str | None = None, stop: int | None = None) List[Result][source]
Run the brute force implementation of the Taheri Design algorithm on an ADMG.
- Parameters:
graph – An ADMG
cause – The node that gets perturbed.
effect – The node that we’re interested in.
tag – The key for node data describing whether it is latent. If None, defaults to
y0.graph.DEFAULT_TAG.stop – Largest combination to get (None means length of the list and is the default)
- Returns:
A list of LV-DAG identifiability results. Will be length \(2^{(\|V\| - 2 - # bidirected edges)}\)
- taheri_design_dag(graph: DiGraph, cause: str | Variable, effect: str | Variable, *, tag: str | None = None, stop: int | None = None) List[Result][source]
Run the brute force implementation of the Taheri Design algorithm on a DAG.
Identify all latent variable configurations inducible over the given DAG that result in an identifiable ADMG under the causal query corresponding to the given cause/effect.
- Parameters:
graph – A regular DAG
cause – The node that gets perturbed.
effect – The node that we’re interested in.
tag – The key for node data describing whether it is latent. If None, defaults to
y0.graph.DEFAULT_TAG.stop – Largest combination to get (None means length of the list and is the default)
- Returns:
A list of LV-DAG identifiability results. Will be length \(2^(|V| - 2)\)
- class Result(identifiable: bool, estimand: Expression | None, pre_nodes: int, pre_edges: int, post_nodes: int, post_edges: int, latents: List[Variable], observed: List[Variable], lvdag: DiGraph, admg: NxMixedGraph)[source]
Results from the LV-DAG check.
Create new instance of Result(identifiable, estimand, pre_nodes, pre_edges, post_nodes, post_edges, latents, observed, lvdag, admg)
- estimand: Expression | None
The estimand returned from the related identification algorithm. Is none if not identifiable.
- admg: NxMixedGraph
Alias for field number 9