[ENH] Add the ability to check the validity of a PAG

[aryan26roy]

Fixes #67

Changes proposed in this pull request:

• Add a function that takes in a PAG and checks if it is valid or not.

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[aryan26roy]

Just to list the procedure out:

• Convert the PAG to MAG
• Check if the MAG is valid or not
• Convert the MAG back to PAG
• Check if the converted and original PAGs are equivalent or not

@adam2392 is this the right pseudo-algorithm?

[adam2392]

Just to list the procedure out:

• Convert the PAG to MAG
• Check if the MAG is valid or not
• Convert the MAG back to PAG
• Check if the converted and original PAGs are equivalent or not

@adam2392 is this the right pseudo-algorithm?

Yes with the added check at the very beginning that the graph is a valid PAG.

[aryan26roy]

Yes with the added check at the very beginning that the graph is a valid PAG.

For this, is it enough to check if the graph has any circle edges or not?

[adam2392]

Same skeleton as MAG so checking acyclicity, ancestral, and maximalist of the non-circle edge subgraph.

A PAG could be fully oriented which results in no circle edges.

[aryan26roy]

• Check if the converted and original PAGs are equivalent or not

For this, I think I have to determine that the two PAGs have the same set of conditional independence relations since they might be structurally different yet markov equivalent?

[adam2392]

• Check if the converted and original PAGs are equivalent or not

For this, I think I have to determine that the two PAGs have the same set of diff conditional independence relations since they might be structurally different yet markov equivalent?

No that is only the case for MAGs.

The two PAGs should be exactly the same, otherwise they encode some set of conditional independences. This assumes that all of the FCI orientation rules no longer can be applied to the PAG (i.e. it is as oriented as possible).

[aryan26roy]

Ah so simply checking that all of the edges are the same in both the PAGs should suffice.

[aryan26roy]

Same skeleton as MAG so checking acyclicity, ancestral, and maximalist of the non-circle edge subgraph.

Hey @adam2392 I am done with the applications, so back to work! One question though, when checking acyclicity in the non-circle edge subgraph, do I only look for directed cycles? Or is the cycle supposed to be direction agnostic?

[adam2392]

Nice! Congrats.

Can you remind me what part requires the acyclicity check?

[aryan26roy]

Yes with the added check at the very beginning that the graph is a valid PAG.

Before actually checking for the validity, you asked me to check if it was valid-valid.

[aryan26roy]

Maybe there is a better term for it somewhere.

[adam2392]

Ah I see. Yeah it's just the same check as a MAG

That's cuz we can't have cycles in the directed edges or almost directed cycles.

You would only do this for the non circle edges tho. So any edge with a circle endpoint is dropped.

A fully oriented PAG is just a MAG

[aryan26roy]

Ah I see. Yeah it's just the same check as a MAG

That's cuz we can't have cycles in the directed edges or almost directed cycles.

You would only do this for the non circle edges tho. So any edge with a circle endpoint is dropped.

A fully oriented PAG is just a MAG

Got it!

[aryan26roy]

@adam2392 right now I am checking for cycles, almost directed cycles and for inducing paths between any two non-adjacent nodes. Is that enough?

[adam2392]

Yep!

[aryan26roy]

@adam2392 How do I add dodiscover to the list of dependencies?

[adam2392]

For now, just run locally and check it.

Dodiscover isn't on pypi yet but planning on making a release.

[aryan26roy]

@adam2392 can you describe how to convert a mag back to pag? Is it simply running the FCI algorithm using dodiscover?

[adam2392]

@adam2392 can you describe how to convert a mag back to pag? Is it simply running the FCI algorithm using dodiscover?

Yes

[adam2392]

Left some comments on the example.

[aryan26roy]

@adam2392 Now the example is complete (along with some review suggestions being incorporated).
I also changed the function call in intro_causal_graphs.py from "is_d_separator" -> "d_separated" since it was failing for me.

[adam2392]

Looking good! I think last round of comments. Please read the example over and see if it makes sense.

Thanks for the efforts @aryan26roy!

[adam2392]

LGTM once CI passes

[aryan26roy]

This was a big one!

[adam2392]

Thanks for the PR @aryan26roy!