Identifying Causal Effects Under Functional Dependencies.

Area of Science:

• Causal inference
• Graphical models
• Statistical learning

Background:

• Causal effect identifiability is crucial for observational studies.
• Functional variables in causal graphs can impact identifiability.
• Positivity assumptions are common but interact with functional dependencies.

Purpose of the Study:

• To investigate how functional variables improve causal effect identifiability.
• To develop methods for simplifying causal graphs by removing functional variables.
• To provide a formal treatment of positivity assumptions in the presence of functional dependencies.

Main Methods:

• An elimination procedure to remove functional variables from causal graphs.
• Analysis of how functional dependencies affect identifiability conditions.
• Systematic treatment of positivity assumptions in conjunction with functional dependencies.

Main Results:

• Functional variables can render previously unidentifiable causal effects identifiable.
• Certain functional variables can be removed without compromising identifiability, reducing data requirements.
• The proposed elimination procedure preserves key causal graph properties, including identifiability.

Conclusions:

• Leveraging functional variable information enhances causal effect identification.
• The developed methods offer practical benefits by reducing the need for extensive observational data.
• This work provides a unified framework for handling functional dependencies and positivity assumptions in causal inference.