CPT from causalImpact not adding up to 1

[kenneth-lee-ch]

How should I interpret this CPT when the entries do not add up to 1? I was running a randomBN with 32 nodes and arc_ratio =3. then I manually added 8 latent variables with at least 1 being connected to the variable X30. Is there a way to avoid this?

[phwuil]

Hi, Kenneth, I think we need a bit more information to answer that. Can you provide a minimal example ?

[kenneth-lee-ch]

@phwuil It is pretty hard to generate the exact same bn by using fastBN since I generated the bn by using randomBN() with n=32 and ratio_arc = 3. I saved it to a BIF file. I cannot upload it here due to BIF format, but I can attach a link and you can download it here:
https://drive.google.com/file/d/16IVhqGFEsjY4kyJZxYRjlXAXEQwJsGnZ/view?usp=sharing

bn_no_latent =gum.loadBN("bnfile.bif")
bn_latent_spec = [('U0', ('X3', 'X24')), ('U1', ('X29', 'X30')), ('U2', ('X1', 'X22')), ('U3', ('X18', 'X23')), ('U4', ('X22', 'X30')), ('U5', ('X5', 'X26')), ('U6', ('X0', 'X20')), ('U7', ('X13', 'X29'))]
cm2 = csl.CausalModel(bn_no_latent, bn_latent_spec,  keepArcs= True)
_, prob, _ = csl.causalImpact(cm2, on = set(['X30', 'X1', 'X22', 'X29']), doing= set(['X3', 'X20', 'X18', 'X4', 'X21', 'X23', 'X28', 'X24', 'X17', 'X11', 'X12']))
prob

This is what I see after running the above code:

[phwuil]

Hello @kenneth-lee-ch , the result is correct : your on = set(['X30', 'X1', 'X22', 'X29']) expresses that you want to compute the joint distribution over X30, X1, X22, X29 , conditioned by interventions on 'X3', 'X20', 'X18', 'X4', 'X21', 'X23', 'X28', 'X24', 'X17', 'X11', 'X12'.

So it does sum to 1 but over all variables of set(['X30', 'X1', 'X22', 'X29']).

[kenneth-lee-ch]

@phwuil Then, I am a bit confused. Shouldn't the table of
P(X30| do(X3, X20, X18, X4, X21, X23, X28, X24, X17, X11, X12), X1, X22, X29) be the same as that of
P(X30, X1, X22, X29| do(X3, X20, X18, X4, X21, X23, X28, X24, X17, X11, X12)) according to Theorem 20 from llya's paper: (https://www.jmlr.org/papers/volume9/shpitser08a/shpitser08a.pdf)?

There are backdoor paths from each of X1, X22, X29 to X30 according to the graph I exported from the causal model (attached here).

I also tried out the exact same bn with the query P(X30| do(X3, X20, X18, X4, X21, X23, X28, X24, X17, X11, X12), X1, X22, X29)

_, prob, _ = csl.causalImpact(cm2, on = set(['X30']), doing= set(['X3', 'X20', 'X18', 'X4', 'X21', 'X23', 'X28', 'X24', 'X17', 'X11', 'X12']), knowing= set(['X1', 'X22', 'X29']))
prob

It produces the following table and clearly, it is different than P(X30, X1, X22, X29| do(X3, X20, X18, X4, X21, X23, X28, X24, X17, X11, X12))

[phwuil]

Theorem 20 shows a way to swap between intervention do(z) and observation (given z) in certain cases.

But note that it is always P...(y|....) : y does not change. In your formula, P(X30|...) becomes P(X30, X1, X22, X29|...). So you change the Y of the theorem 20. It is not the theorem 20.

If you sum out X1, X22, X29 in the first code, I guess you will find the result of your second code.

[kenneth-lee-ch]

Oh, I see. I overlooked it. Thanks!