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THEORY-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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Properties5
StatusActive
Version2
Tagscausality, information-theory
SourceLIT-1802 — The Causal Information Bottleneck and Optimal Causal Variable Abstractions
Bears onQUESTION-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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Source

Simoes, Dastani and van Ommen (2025), LIT-1802, §8 (pp. 5–7) and Appendices E–F (pp. 16–20) of arXiv 2410.00535v5; read in NOTE-1347.

What was actually shown

Three SCMs (Figs. 2 and 4). Odd and Even: X uniform on {0, …, 6}, Y its parity with noise, no confounding. Confounded Addition: Y depends on X₁ + X₂, and W confounds X₁ and Y. Genetic Mutations: Y = S + X₁ + X₂ + (2 − X₃)X₁X₂ + noise, with the strain S driving X₃ and X₄. Only the joint distribution and a backdoor set are given to the method (p. 6).

The CIB. At γ = 1 the causal ground truth (parity, X₁ + X₂, and the four-valued θ(X)) was found in 100%, 98% and 95% of runs (pp. 6–7), with ensembles of 4, 6 and 12 optimisers. At γ = 0 the abstractions carry no information about X, and causal information gain does not decrease with γ, in all three and for other noise settings (Figs. 1, 5).

The IB. Run on the same data, the ordinary bottleneck at γ = 1 finds the ground truth only in the unconfounded Odd and Even case (Appendix F.2, p. 18). On Confounded Addition it gives (X₁, X₂) = (0, 1) and (1, 0) different values, though they have the same effect on Y (Table 1, p. 19). On Genetic Mutations it does not separate X₃’s protective effect and is not invariant in X₄, which has no effect on Y (Table 2, p. 20).

My check. On the Genetic Mutations SCM the observational partition has ten classes and the causal one four (NOTE-1347).

What could have failed. The local search could have stuck in poor optima, as the authors report it did before they added a penalty against encoders that leave values of T unused (p. 17).

What this does not say

  • That the method scales. The largest X has 16 values; the authors expect local minima to need “modifications” at scale (p. 8).
  • That the IB’s failure is a finding about the IB. It follows from the definitions: the IB targets p(y | x). The experiment shows the difference matters in these cases.
  • That intermediate γ is meaningful. Only monotonicity is checked there.
  • That the causal knowledge is free. The backdoor set is an input; without one the causal partition is not identifiable this way.
  • That the abstractions reveal causal structure better than direct inspection. The paper argues it (p. 7) and compares with nothing.

Note of 2026-10-30: narrowed and promoted

The title said the partitions differ under confounding and that the bottleneck learns and misses distinctions, as if always; it now says what confounding makes possible and what the toy models showed. Whether the search scales is QUESTION-346.

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