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LIT-1833: Multi-Level Cause-Effect Systems

1 min read

Properties8
StatusActive — read 2026-10-29 (NOTE-1420) in full, from arXiv 1512.07942v1 with its supplementary material; worth reading as the source of the two-sided form of causal feature learning that the overview (LIT-1834) restates: the fundamental cause and effect are the partitions of micro causes by P(J | man(i)) and of micro effects by P(j | man(·)), learned jointly; the fundamental causal coarsening theorem says both generically coarsen the observational partitions; and the authors decline, "following Pearl", to put any distribution on the interventions. Read it knowing that its one demonstration is a simulated neural population, built with the macro structure it recovers; that its claim that the effect partition is the minimal sufficient partition is wrong where two effect states have proportional but unequal columns (NOTE-1420); and that it compares itself with Hoel et al. 2013 in one sentence and computes nothing on their systems.
Version2
Tagscausality, complex-systems, probabilistic-modeling, anthology-candidate
RivalsLIT-1038 — Quantifying causal emergence shows that macro can beat micro
Cited as “extends” byLIT-1834 — Causal feature learning: an overview
Cited as “grounds” byARG-041 — From the effective-information bound and its ties to proportionality: a gain that depends on the intervention distribution is not a property of the system, the coarse-grainings that lose nothing are, and the coarsest of them is where the causes are, CLAIM-497 — A system's causes are found at the coarsest description whose interventions are unambiguous: a macro description is causally proportionate where it merges only micro states that intervention cannot tell apart, and no coarse-graining carries more causal information than the micro description it supervenes on
Cited as “paper” byNOTE-1420 — Chalupka, Perona and Eberhardt — Multi-level cause-effect systems
Cited as “source” byTHEORY-1169 — For a discrete mechanism scored with one full-support intervention distribution over micro causes at both levels, a coarse-graining of cause and effect keeps all of the micro effective information if and only if it merges only causes with identical rows P(Y | do(x)) and only effects with proportional columns, whatever the distribution; so the coarsest coarse-graining that ties the micro is the causal partition of causal feature learning, with effects grouped by normalized likelihood, and any merge of causes with different effects loses information under every such distribution

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Chalupka, K., Perona, P. & Eberhardt, F. (2016). Multi-level cause-effect systems. In Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (AISTATS 2016), PMLR 51, 361–369. arXiv:1512.07942

Read in full on 2026-10-29 (NOTE-1420). One account was drawn from it and from NOTE-1415: THEORY-1169.

Why this is here

Eberhardt and Lee (LIT-1839, NOTE-1413) recommend causal feature learning as the alternative to effective information. QUESTION-204’s second half asks whether a coarse-graining chosen by a causal criterion agrees with an independent interventionist test of which level the effects track. This is the paper that defines the test for cause and effect together, which is the form Hoel’s coarse-grainings of a transition matrix need, and that says it assumes no intervention distribution. Its partition of causes by P(y | do(x)) is the optimum of the causal information bottleneck (LIT-1802, THEORY-1125).

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