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LIT-1802: The Causal Information Bottleneck and Optimal Causal Variable Abstractions

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Properties5
StatusActive — read in full 2026-10-29 (NOTE-1347) from arXiv v5; worth reading as an exact, small-scale statement of the difference between compressing for prediction and compressing for control: at full control the optimum is the partition of X by p(y | do(x)), which the ordinary bottleneck misses under confounding. Toy problems only.
Version3
Tagscausality, information-theory
Cited as “paper” byNOTE-1347 — Simoes, Dastani and van Ommen — Causal information bottleneck
Cited as “source” byTHEORY-1125 — For discrete X and Y, with an intervention on a variable abstraction T of X defined as the mixture of interventions on X weighted by Bayes inversion of the encoder under a protocol prior, no abstraction gains causal information about Y over X itself, and at full weight on causal control the causal information bottleneck is optimised by the partition of X by p(y | do(x)), mapped one class to one value of T, uniquely up to relabelling when T has exactly as many values as there are classes; these are Chalupka et al.'s causal macrovariables, 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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Simoes, F. N. F. Q., Dastani, M., & van Ommen, T. (2025). The causal information bottleneck and optimal causal variable abstractions. UAI 2025, PMLR 286, 3878–3897.

Why this is here

A7 joined three of the record’s ideas through it: task-relative fidelity (CLAIM-259), legibility for a bounded receiver (CLAIM-455), and the difference between supporting prediction and supporting control. A rendering may keep what a task’s control needs while losing most of the source. CLAIM-348’s caution stands: optimizing for one task does not make it the task that matters.

The reading (NOTE-1347) bears this out, with one addition: control here is relative to a chosen intervention protocol as well as to the target, and the intervention on T is a stipulation, not a mechanism.

Note of 2026-10-29: whose causal macrovariables, and why not extends

The summary identifies the full-control optimum with “Chalupka et al.’s causal macrovariables”. Two of the Chalupka papers are now registered and read: the multi-level cause–effect paper, LIT-1833 (NOTE-1420), and the overview, LIT-1834 (NOTE-1415). Checked against arXiv 2410.00535v5 on 2026-10-29: this paper takes its Definition 19, of causal classes, partitions and macrovariables, from Chalupka et al. 2016a, “Unsupervised discovery of El Nino using causal feature learning on microlevel climate data” (arXiv:1605.09370), which is not registered. The multi-level paper is its 2016b and the overview its 2017, and Appendix B.3 shows the coincidence with “the causal macrovariables from Chalupka et al. [2016a, 2017]”. Its related work presents them as “one other line of work investigating a problem related to our search”, with a definition “distinct from our definition”, and says “Our method subsumes theirs”. So the paper recovers Chalupka et al.’s partition as a special case; it does not build on LIT-1833, and no extends is added. The same partition, from the cause side under a protocol, is THEORY-1125’s; THEORY-1169 finds it, with effects as well, where EI under one common distribution loses nothing.

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