Compositional Causal Identification from Imperfect or Disturbing Observations

Area of Science:

• Causal inference
• Graphical causal models
• Process theories

Background:

• Traditional causal identification relies on observational data or controlled experiments.
• Generic data collection schemes, including noisy or coarse-grained observations, are increasingly relevant.
• Existing methods may not fully leverage information from these diverse data sources.

Purpose of the Study:

• To investigate causal identification using probabilities from generic data collection instruments.
• To extend causal inference frameworks to accommodate non-standard observation schemes.
• To establish conditions under which such data suffice for identifying causal quantities.

Main Methods:

• Utilizing process theories (symmetric monoidal categories) to model graphical causal models.
• Formulating causal identification problems with arbitrary sets of data collection instruments.
• Introducing and analyzing the property of 'marginal informational completeness' for instruments.

Main Results:

• Generic instruments satisfying 'marginal informational completeness' can be used for causal identification.
• For Markovian models, these instruments suffice for identifying interventional quantities.
• This extends the applicability of causal inference beyond perfect passive observations.

Conclusions:

• The study demonstrates the sufficiency of 'marginally informationally complete' instruments for causal identification in Markovian models.
• It highlights a distinction between the Markovianity of causal models and probability distributions.
• Suggests a broader scope for causal inference within a process-theoretic framework.