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arxiv: 1906.11583 · v2 · pith:NHSWR6WSnew · submitted 2019-06-27 · 💻 cs.AI

Approximate Causal Abstraction

Sander Beckers , Frederick Eberhardt , Joseph Y. Halpern This is my paper

Pith reviewed 2026-05-25 14:43 UTC · model grok-4.3

classification 💻 cs.AI
keywords causal abstractionapproximate causal modelsinterventionsexplanationsprobabilistic causal modelsmodel discrepancy
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The pith

Causal models can approximate the true system while still supporting interventions and explanations at different levels of detail.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends an existing exact theory of abstraction between causal models to the realistic case of approximate abstractions. It shows how this handles cases where a high-level causal description disagrees with the low-level description of the same system. A sympathetic reader would care because scientific models are almost always approximations yet still need to license interventions and explanations. The work also supplies a standalone account of what it means for one causal model to approximate another and extends the framework to probabilistic models.

Core claim

We extend the exact account of causal abstraction to approximate abstractions between causal models. This extension handles the discrepancies that arise between low- and high-level models of the same system, supplies a general account of how one causal model approximates another, and indicates how uncertainty enters when the framework is applied to probabilistic causal models.

What carries the argument

The definition of an approximate abstraction relation between causal models that preserves intervention and explanation properties to a useful degree.

If this is right

  • Discrepancies between levels of description become quantifiable rather than fatal.
  • Interventions licensed by an approximate high-level model remain approximately valid.
  • Explanations can still be given at a coarser granularity even when exact abstraction fails.
  • Uncertainty in probabilistic models can be localized to the approximation step.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The framework could be used to decide when a simplified model is good enough for a given decision task.
  • It offers a way to compare competing models at different scales without requiring one to be a strict abstraction of the other.

Load-bearing premise

A useful notion of approximation between causal models can be defined so that it still supports interventions and explanations.

What would settle it

An example pair of causal models where the proposed approximate-abstraction relation holds but an intervention at the abstract level produces an outcome that diverges from the outcome produced by the corresponding intervention at the concrete level.

Figures

Figures reproduced from arXiv: 1906.11583 by Frederick Eberhardt, Joseph Y. Halpern, Sander Beckers.

Figure 1
Figure 1. Figure 1: Climate example adapted from Chalupka et [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The climate model exemplifies constructive ab [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Approximate abstraction in the climate exam [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Probabilistic approximate abstraction for the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
read the original abstract

Scientific models describe natural phenomena at different levels of abstraction. Abstract descriptions can provide the basis for interventions on the system and explanation of observed phenomena at a level of granularity that is coarser than the most fundamental account of the system. Beckers and Halpern (2019), building on work of Rubenstein et al. (2017), developed an account of abstraction for causal models that is exact. Here we extend this account to the more realistic case where an abstract causal model offers only an approximation of the underlying system. We show how the resulting account handles the discrepancy that can arise between low- and high-level causal models of the same system, and in the process provide an account of how one causal model approximates another, a topic of independent interest. Finally, we extend the account of approximate abstractions to probabilistic causal models, indicating how and where uncertainty can enter into an approximate abstraction.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. The manuscript extends the exact causal abstraction framework of Beckers and Halpern (2019), which itself builds on Rubenstein et al. (2017), to the approximate setting. It introduces definitions for when an abstract causal model approximates an underlying system, shows how the framework handles discrepancies between low- and high-level models of the same system, provides a general account of approximation between causal models, and generalizes the approach to probabilistic causal models while indicating where uncertainty enters.

Significance. If the definitions are internally consistent and preserve the intervention and explanation properties from the exact case, the work supplies a needed formal treatment of approximate abstractions, which is more realistic for applications. The independent account of how one causal model approximates another is a useful contribution to the literature on causal modeling.

minor comments (1)
  1. Ensure that the introduction explicitly contrasts the new approximate definitions with the exact ones in Beckers and Halpern (2019) to highlight the technical differences.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript, their positive summary of our contributions, and their recommendation to accept. No major comments were raised in the report.

Circularity Check

0 steps flagged

Minor self-citation to prior exact abstraction; new definitions are independent and non-reductive

full rationale

The paper extends the exact causal abstraction framework from the authors' prior work (Beckers & Halpern 2019, building on Rubenstein et al. 2017) by introducing new definitions for approximate abstractions that handle model discrepancies while preserving intervention and explanation properties. This is a definitional contribution rather than any derivation, prediction, or first-principles result that reduces to fitted inputs or self-referential constructions. The self-citation supports the exact baseline case but is not load-bearing for the novel approximate account or its probabilistic extension. No steps match the enumerated circularity patterns; the work is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Relies on the exact abstraction framework from cited prior work as the base; no new free parameters, invented entities, or ad-hoc axioms visible in the abstract.

axioms (1)
  • domain assumption Exact causal abstraction is well-defined as in Beckers and Halpern (2019) and Rubenstein et al. (2017)
    The paper states it builds directly on this prior exact account.

pith-pipeline@v0.9.0 · 5670 in / 948 out tokens · 31742 ms · 2026-05-25T14:43:01.675154+00:00 · methodology

discussion (0)

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Reference graph

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9 extracted references · 9 canonical work pages · 1 internal anchor

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