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Often in data science, we have partial knowledge of the causal DAG structure. Regarding some of the possible edges in the DAG, we are in doubt.

Are there any resources to tackle this setting? The resources might belong to the following classes -

  1. Learning materials - Materials that shed light on causal discovery in the face of partially available DAG structure.
    Currently, I am thinking of using the rules of PC algorithm based on immoralities (mentioned in Daphne Koller's book, page 89). Anything beyond this I should know about?
  2. Benchmarking efforts - Any proposed solution approach needs to be tested in a realistic setting. I have found papers related to benchmarking causal effect estimators. But not causal discovery in the face of partial knowledge availability. Hence any testing ground for this.
  3. Earlier work - Finally, references to earlier work that has been done on this front. This helps understand the roadblocks that might lie ahead.

Note: I have read that causal discovery from scratch is not yet a solved domain. Theoretically too, we cannot go beyond Markov equivalent structures. However, with availability of confident knowledge for majority of the edges, it might not be a dead end. Hence this query.

Anirban Chakraborty
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    It is possible to go beyond the Markov equivalence classes and discover the underlying DAG when we are willing to make additional assumptions (which, admittedly, are often not very realistic). A popular example is the LiNGAM method, and there are many other ones. – Scriddie Sep 11 '23 at 11:52
  • @Scriddie could you please refer to a possible assumption, as example, to clarify what you mean when you refer to - "willing to make additional assumptions (which, admittedly, are often not very realistic)"? This is to ensure we understand the same thing when we say "partially known causal DAG". – Anirban Chakraborty Sep 12 '23 at 11:12
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    Probably the most common assumption is that of linear functions and additive noise (LiNGAM additionally requires the noise to be non-Gaussian). More generally speaking, these are assumptions about the functional form of the structural equations. – Scriddie Sep 12 '23 at 11:47

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