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arxiv: 2605.31254 · v1 · pith:QYR6AD5Unew · submitted 2026-05-29 · 💻 cs.AI

Formalizing and falsifying causal pathways of rare events

Anahita Haghighat , Dominik Janzing This is my paper

Pith reviewed 2026-06-28 22:30 UTC · model grok-4.3

classification 💻 cs.AI
keywords causal pathwaysrare eventsstructural equation modelscausal abstractionroot cause analysisoutliersfalsificationtestable implications
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The pith

A formal definition of causal pathways for rare events lets their testable implications depend only on an abstraction rather than the full causal graph.

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

The paper proposes a formal definition of a causal pathway in structural equation models and derives its testable implications. It identifies conditions under which those implications are fully determined by a causal abstraction consisting of the pathway of rare events, without needing the rest of the graph. This creates a bridge between simple verbal causal stories about outliers and complete structural models, making pathways falsifiable from limited information. A sympathetic reader would care because it offers a way to evaluate causal claims about rare events without reconstructing every variable and edge.

Core claim

Building on recent formalizations of root cause analysis for rare events in structural equation models, we propose a formal definition of a causal pathway and discuss its testable implications. We identify conditions under which these implications depend only on a causal abstraction defined by the pathway of rare events, rather than on the full causal graph of the underlying system. Accordingly, we introduce an abstraction of causal structure to pathways of rare events that bridges simple verbal causal explanations and detailed causal modeling.

What carries the argument

The abstraction of causal structure to pathways of rare events, which carries the argument by making the testable implications of a pathway depend only on the rare-events component rather than the entire structural equation model.

If this is right

  • Testable implications of a causal pathway can be checked using only the abstraction defined by the rare events pathway.
  • Causal pathways for outliers become falsifiable without reconstructing the complete causal graph.
  • The abstraction bridges verbal causal explanations and full structural equation models.
  • Conditions exist under which implications of the pathway are independent of the remaining graph structure.

Where Pith is reading between the lines

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

  • The abstraction could simplify causal analysis in domains where only rare-event sequences are observable, such as certain failure logs or extreme weather records.
  • If the conditions hold, the method might be applied to evaluate competing verbal explanations of the same rare event without committing to one full graph.
  • A direct test would compare predictions derived from the abstraction against those from the full model on held-out data involving the rare events.

Load-bearing premise

Structural equation models supply an appropriate framework in which the formal definition of a causal pathway and the identified abstraction conditions can be stated and tested without additional unstated assumptions on the data-generating process.

What would settle it

A dataset or simulation in which the observable implications of a proposed causal pathway for rare events differ when computed from the full graph versus from the rare-events abstraction alone.

Figures

Figures reproduced from arXiv: 2605.31254 by Anahita Haghighat, Dominik Janzing.

Figure 1
Figure 1. Figure 1: Example showing that whether a node should be con￾sidered a root cause does not depend on its position in the DAG: to show this, the text describes parameters for which B1 and B3 should be considered root causes, while B4 is only a root cause if we target a higher pathway explanation score. It is important to note that BS need not necessarily be medi￾ators that propagate the information from BR to Bt. We w… view at source ↗
Figure 2
Figure 2. Figure 2: (Pathway) explanation scores E1→2 = E {1,2} 1→2 for the binary cause effect pair obtained from thresholding a linear causal relation of Gaussians. For y ≈ ρx (points near the red line) the explanation score reaches 80% whenever x is an outlier of strength 3 or more. X Y Z B1 B2 B3 B1 B2 B3 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Left: DAG with three real-valued variables, where we perturb Y . Middle: the same DAG with binary variables B1, B2, B3. To explain the impact of the intervention do(B2 = 1) (root cause node shown in gray) on the target B3, we need a pathway P that also contains the confounder B1 as context (right). In Example 4.8 where B1, B2, B3 are binarizations of X, Y, Z they stand for the events |X| ≤ |x|, Y ≥ y, Z ≥ … view at source ↗
Figure 4
Figure 4. Figure 4: Explanation scores and abstraction accuracies for Example 4.8, comparing the bivariate abstraction B2 → B3 with the trivariate abstraction B1 → B3 ← B2. In all figures x = 1, and parameters are α = −0.9, β = 0.9, and γ = 0.9. The trivariate abstraction achieves higher explanation scores and accuracies in the region y ≥ 2, z ≥ 2 because B1 captures contextual information that is lost in the bivariate abstra… view at source ↗
Figure 5
Figure 5. Figure 5: (a) Causal DAG with binary variables X, Y , and Z, where X influences the target Z directly and indirectly via the mediator Y . (b): Pathway abstraction with accuracy 1, which is always possible because the indirect and direct links can always be merged into one direct link. (c): Pathway abstraction whose accuracy r depends on the relevance of the direct link X → Y for the outlier event at Z (d): Pathway a… view at source ↗
read the original abstract

Building on recent formalizations of root cause analysis for rare events (``outliers'') in structural equation models, we propose a formal definition of a causal pathway and discuss its testable implications. We identify conditions under which these implications depend only on a causal abstraction defined by the pathway of rare events, rather than on the full causal graph of the underlying system. Accordingly, we introduce an abstraction of causal structure to pathways of rare events that bridges simple verbal causal explanations and detailed causal modeling.

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 / 0 minor

Summary. The manuscript builds on recent formalizations of root cause analysis for rare events (outliers) in structural equation models. It proposes a formal definition of a causal pathway, discusses its testable implications, and identifies conditions under which these implications depend only on a causal abstraction defined by the pathway of rare events rather than the full causal graph of the underlying system. It introduces an abstraction of causal structure to pathways of rare events that bridges simple verbal causal explanations and detailed causal modeling.

Significance. If the formal definition and the identified conditions for abstraction can be rigorously established with clear testable implications, the work could provide a useful bridge between high-level verbal causal claims and full structural equation models for analyzing rare events. No machine-checked proofs, reproducible code, or parameter-free derivations are described in the available material.

Simulated Author's Rebuttal

0 responses · 1 unresolved

We thank the referee for their review and for recognizing the potential of the work to bridge verbal causal claims and full structural equation models. The major comments section of the report contains no specific items, so we have no point-by-point responses to provide. We acknowledge the observation in the significance assessment regarding the absence of machine-checked proofs and code.

standing simulated objections not resolved
  • The manuscript does not include machine-checked proofs, reproducible code, or parameter-free derivations.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained proposal of definition

full rationale

The paper proposes a new formal definition of causal pathway for rare events in SEMs and identifies conditions for abstraction depending only on the pathway rather than the full graph. No equations, fitted parameters, or derivation steps are provided that reduce by construction to inputs. The abstract references building on recent formalizations but presents the definition and testable implications as the contribution itself. No self-citation is shown to be load-bearing for the central claim, and no renaming of known results or ansatz smuggling is evident. This matches the common case of an honest non-finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the assumption that structural equation models are suitable for rare events and that abstraction conditions exist; no free parameters, invented entities, or explicit axioms are stated.

axioms (1)
  • domain assumption Structural equation models are an appropriate framework for formalizing causal pathways of rare events.
    The abstract builds on formalizations within this framework without stating alternatives.

pith-pipeline@v0.9.1-grok · 5594 in / 1114 out tokens · 21914 ms · 2026-06-28T22:30:26.086798+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

11 extracted references · 3 canonical work pages

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    Beckers, S

    URL https://www.sciencedirect.com/ science/article/pii/S0304414911000238. Beckers, S. Causal sufficiency and actual causation.Journal of Philosophical Logic, 50(6):1341–1374, 2021. Beckers, S. Causal explanations and xai. InConference on causal learning and reasoning, pp. 90–109. PMLR, 2022. Beckers, S. and Halpern, J. Y . Abstracting causal mod- els. InP...

    work page arXiv 2021

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    doi: https://doi.org/ 10.1016/B978-0-12-407795-9.00001-3

    ISBN 978-0-12-407795-9. doi: https://doi.org/ 10.1016/B978-0-12-407795-9.00001-3. URL https: //www.sciencedirect.com/science/ article/pii/B9780124077959000013. 10 Formalizing and Falsifying Causal Pathways of Rare Events Ikram, A., Lee, K., Agarwal, S., Saini, S. K., Bagchi, S., and Kocaoglu, M. Root cause analysis of failures from partial causal structur...

    work page doi:10.1016/b978-0-12-407795-9.00001-3 2025

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    Pearl, J.Causality

    URL https://openreview.net/forum? id=7Nxq4RQApu. Pearl, J.Causality. Cambridge University Press, 2000. Pearl, J. Direct and indirect effects. InProceedings of the Seventh Conference on Uncertainty in Artificial In- telligence (UAI), pp. 411–420, San Francisco, CA, 2001. Morgan Kaufmann. Pearl, J. and Mackenzie, J.The book of why. Basic Books, USA, 2018. P...

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    Sch¨olkopf, B., Locatello, F., Bauer, S., Ke, N

    URL https://openreview.net/forum? id=VElPLJUr2G. Sch¨olkopf, B., Locatello, F., Bauer, S., Ke, N. R., Kalch- brenner, N., Goyal, A., and Bengio, Y . Towards causal representation learning.Proceedings of the IEEE, 109(5): 1–23, 2021. Shapley, L. S. A value for n-person games. In Kuhn, H. W. and Tucker, A. W. (eds.),Contributions to the Theory of Games II, ...

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    doi: 10.1086/425058. Tian, J. and Pearl, J. Probabilities of causation: Bounds and identification.Annals of Mathematics and Artificial Intelligence, 28(1):287–313, 2000. Wang, J., Wiens, J., and Lundberg, S. Shapley flow: A graph-based approach to interpreting model predictions. In Banerjee, A. and Fukumizu, K. (eds.),The 24th Inter- national Conference o...

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    12 Formalizing and Falsifying Causal Pathways of Rare Events A

    URL https://proceedings.mlr.press/ v236/zhu24a.html. 12 Formalizing and Falsifying Causal Pathways of Rare Events A. More Details on Explanation Scores A.1. Cluster Explanation Score and Distribution Change Lemma A.1(distribution change attribution).Let δ1 denote the point mass on the event B=1 . Then, for any i∈K , the cluster explanation scoreE i→k can ...

    2021

  7. [7]

    Y= 1 would not have occurred if X had been set to 0 (for that particular statistical unit)

    =q 2. Assume q1 ≪q 2 = q3 ≪1 . Then B1 = 1 explains B2 = 1 with explanation score close to 1 because logq 2/(logq 1 + logq 2)≈0 . Further, B2 = 1 explains B3 = 1 with explanation score 1. Hence, both non-root cause nodes B2 and B3 have explanation score close to1, but the pathway explanation score of the root causeB 1 = 1for the targetB 3 = 1reads E K 1→3...

    2000

  8. [8]

    Baseline context: Someone who has gone 8 months without income and lost housing is likely experiencing severe crisis - possibly involving mental health issues, substance abuse, or other destabilizing factors

  9. [9]

    Psychotic episodes can involve behavior that severely damages relationships (paranoid accusations, erratic actions, inability to recognize loved ones’ intentions)

    The psychotic episode element: This is specific - it implies a serious mental health condition. Psychotic episodes can involve behavior that severely damages relationships (paranoid accusations, erratic actions, inability to recognize loved ones’ intentions)

  10. [10]

    Conditional factors: • The housing loss suggests someone who didn’t have family support to fall back on - this may indicate pre-existing strain • 8 months without income suggests possible disability, mental health crisis, or other severe impairment • Sibling relationships severed “during” a psychotic episode suggests the break happens in crisis, not gradually

  11. [11]

    This is a specific tragic pathway

    However: Most people who lose housing don’t have psychotic episodes, and most psychotic episodes don’t permanently sever all family ties. This is a specific tragic pathway. Estimation: • The scenario C already selects for vulnerable individuals • But complete family estrangement with this specific pattern remains relatively uncommon • Partial estrangement...