Question regarding testing for conditional independence

[adam2392]

Hi Professor Mooij,

I really enjoyed reading your paper here: https://arxiv.org/abs/1807.03024. I saw that the implementation relies on the ASP formulation of conditional independences. I wanted to ask if this was mainly because it is easier to formulate the additional constraints that the structure learning algorithm for sigma-connection-graphs needs (e.g. compared to say FCI). Is there any technical limitation that I might have missed that would prevent a practitioner from using this algorithm, but implementing it with traditional CI hypothesis testing?

Should this in principle be able to be formulated under traditional constraint-based with conditional-independence testing algorithms (e.g. like the PC, or FCI algorithm)?

Thanks!

[jorismooij]

Dear Adam,

The only reason we built on an existing ASP formulation is that this was straightforward.

Meanwhile we also provided other implementations, for example, based on FCI (see e.g. "Constraint-Based Causal Discovery with Partial Ancestral Graphs in the presence of Cycles" Joris M. Mooij, Tom Claassen Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI-20) also available on my homepage)

Best wishes, Joris

On Mon, Aug 01, 2022 at 12:01:55PM -0700, Adam Li wrote:

Hi Professor Mooij,

I really enjoyed reading your paper here: https://arxiv.org/abs/1807.03024. I saw that the implementation relies on the ASP formulation of conditional independences. I wanted to ask if this was mainly because it is easier to formulate the additional constraints that the structure learning algorithm for sigma-connection-graphs needs (e.g. compared to say FCI). Is there any technical limitation that I might have missed that would prevent a practitioner from using this algorithm, but implementing it with traditional CI hypothesis testing?

Should this in principle be able to be formulated under traditional constraint-based with conditional-independence testing algorithms (e.g. like the PC, or FCI algorithm)?

Thanks!

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[adam2392]

Really liked that paper btw! It is a very elegant approach to making FCI/PC work w/ cyclicity.

The idea of sigma-separation seems relatively "new", so I'm wondering if there is any "efficient" algorithm for determining if $X \perp_{\sigma} Y | Z$?

I guess converting a cyclic graph into its acyclicified graph and then running d-separation could be a naive approach to solving that, with pretty decent average O performance.