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QUESTION-346: On confounded causal systems larger than toy models, with a known causal partition, does gradient search for the causal information bottleneck through an adjustment set find the partition by p(y | do(x)) reliably, and how often does it fail?

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Properties4
StatusOpen
Tagscausality, information-theory
Lineformal-apparatus
Cited as “bears on” byTHEORY-1146 — Under confounding the partition of a variable X by what it predicts about a target Y can differ from its partition by what setting it does to Y, so the information bottleneck at full sufficiency can learn distinctions no intervention could use and miss ones only intervention reveals, as it did in two confounded toy models, while the causal information bottleneck, computed from observational data through a backdoor set, recovered the causal partition in all three toy models, projected gradient search finding it in 95 to 100 percent of runs

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Why it is a question

Simoes, Dastani and van Ommen (2025), LIT-1802, show that at full causal control the causal information bottleneck is optimised by the partition of X by p(y | do(x)) (THEORY-1125), and that projected gradient search found it in 95 to 100 percent of runs on three toy models whose X has at most 16 values (THEORY-1146). The search needed ensembles of 4 to 12 optimisers and a penalty against unused values of T, and the authors expect local minima to need “modifications” at scale. They do not claim that it scales.

What would answer it

Results on causal systems larger than toy SCMs, with confounding and a known causal partition, in which the information bottleneck at full sufficiency recovers the observational partition by p(y | x) and the causal bottleneck, computed through an adjustment set, recovers the partition by p(y | do(x)), reliably and with the optimiser’s failure rate reported; or a case where the observational and causal partitions differ and the causal bottleneck does not find the latter.

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