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arxiv: 2605.16620 · v1 · pith:EBI7PWWQnew · submitted 2026-05-15 · 💻 cs.LG

SCOUT: Cyclic Causal Discovery Under Soft Interventions with Unknown Targets

Alpar Turkoglu , Muralikrishnna G. Sethuraman , Faramarz Fekri This is my paper

Pith reviewed 2026-05-20 19:50 UTC · model grok-4.3

classification 💻 cs.LG
keywords causal discoverycyclic causal graphssoft interventionsunknown intervention targetsnormalizing flowsnonlinear modelsgraph recovery
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The pith

SCOUT recovers nonlinear cyclic causal graphs and unknown intervention targets from soft interventional data using normalizing flows.

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

The paper introduces SCOUT to learn nonlinear cyclic causal relationships from soft interventional data where intervention targets are unknown. Most prior methods assume acyclic structures, Gaussian noise, or known targets, limiting their applicability to real systems. SCOUT maximizes the data log-likelihood with contractive residual flows and neural spline flows to recover both the graph and the targets. This matters because it enables causal discovery in more realistic settings that violate standard assumptions.

Core claim

SCOUT recovers the cyclic causal graph structure and the unknown targets of soft interventions by maximizing the log-likelihood of the observed data using two normalizing flow architectures: contractive residual flows and neural spline flows.

What carries the argument

Contractive residual flows combined with neural spline flows for modeling the likelihood under cyclic nonlinear causal models with unknown soft intervention targets.

If this is right

  • SCOUT identifies causal graphs containing cycles from interventional data.
  • It recovers the specific targets of interventions without them being provided.
  • It applies to nonlinear relationships without requiring Gaussian noise assumptions.
  • Outperforms existing methods in recovering both graphs and targets across different settings.

Where Pith is reading between the lines

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

  • SCOUT could be applied to real-world problems like gene regulatory networks that exhibit cyclic behavior.
  • Improving the flow models might allow handling of higher-dimensional data.
  • Similar likelihood maximization techniques could be explored for other causal discovery challenges with unknown interventions.

Load-bearing premise

The data-generating process can be accurately captured by maximizing likelihood under the chosen contractive residual flow and neural spline flow architectures.

What would settle it

Running SCOUT on a synthetic dataset with a known cyclic nonlinear structure and soft interventions on unknown targets, and finding that the recovered graph or targets do not match the ground truth.

Figures

Figures reproduced from arXiv: 2605.16620 by Alpar Turkoglu, Faramarz Fekri, Muralikrishnna G. Sethuraman.

Figure 2
Figure 2. Figure 2: Graph recovery performance comparison between SCOUT and baselines under non-linear SEM and shift interven￾tions. The number of nodes is varied from d = 10 to 70 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: Graph recovery performance comparison between SCOUT and baselines under non-linear SEM and various interven￾tional and exogenous noise settings, evaluated using AUPRC (the higher the better). The box plots show the median and interquartile ranges across ten independent trials. In all cases, the number of nodes is fixed at d = 10. 3, SCOUT’s structure recovery performance remains rela￾tively high, whereas o… view at source ↗
Figure 3
Figure 3. Figure 3: Graph recovery performance comparison between SCOUT and baselines under non-linear SEM and scale interven￾tions. The number of nodes is varied from d = 10 to 70 While SCOUT-noNSF retains the ability to model soft in￾terventions and includes an interventional target matrix for handling unknown targets, it lacks the flexibility to trans￾form non-Gaussian noise distributions. In contrast, SCOUT incorporates t… view at source ↗
Figure 5
Figure 5. Figure 5: Graph recovery performance comparison between SCOUT, SCOUT-noNSF, and NODAGS for known intervention targets under nonlinear SEM and various interventional and ex￾ogenous noise settings, evaluated using AUPRC. In all cases, the number of nodes is fixed at d = 10. contains gene expressions taken from 218,331 melanoma cells split over three different cell conditions: (i) control, (ii) co-culture, and (iii) IF… view at source ↗
Figure 4
Figure 4. Figure 4: Graph recovery performance comparison between SCOUT, SCOUT-noNSF, and NODAGS under nonlinear SEM and various interventional and exogenous noise settings, evaluated using AUPRC. In all cases, the number of nodes is fixed at d = 10. Additional experiments, including performance evaluations on non-contractive SEMs (DAGs) in Appendix C.1, linear SEMs in Appendix C.2, hard interventions in Appendix C.4, and kno… view at source ↗
Figure 6
Figure 6. Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Illustration of the augmented graph G I corresponding to the set of interventional targets I = {∅, {X3}, {X4}}. To integrate multiple interventional settings in a single causal graph, we adopt the idea of joint causal model proposed by (Mooij et al., 2016) by introducing a new set of context variables CI = (C1, . . . , CK) each representing another interventional setting. (The scenario where Ck = ∅ for all… view at source ↗
Figure 9
Figure 9. Figure 9: Graph recovery performance comparison between SCOUT and baselines under non-contractive DAG’s and various interventional and exogenous noise settings, evaluated using AUPRC. In all cases, the number of nodes is fixed at d = 10. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Graph recovery performance comparison between SCOUT and baselines under linear SEM and various interventional and exogenous noise settings, evaluated using AUPRC. In all cases, the number of nodes is fixed at d = 10. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Graph recovery performance comparison between SCOUT and baselines for known intervention targets under nonlinear SEM and various interventional and exogenous noise settings, evaluated using AUPRC. In all cases, the number of nodes is fixed at d = 10. C.4. Experiments for Hard (Perfect) Interventions We run experiments on SCOUT and the baselines to evaluate their structures and target recovery performance … view at source ↗
Figure 12
Figure 12. Figure 12: Graph recovery performance comparison between SCOUT and baselines under nonlinear SEM and hard interventions with various exogenous noise settings, evaluated using AUPRC. In all cases, the number of nodes is fixed at d = 10. C.5. Ablation Studies C.5.1. IMPACT OF NUMBER OF MAXIMUM INTERVENTIONAL TARGETS In this section, we evaluated SCOUT’s performance alongside baselines while varying the maximum number … view at source ↗
Figure 13
Figure 13. Figure 13: Graph recovery performance comparison between SCOUT and baselines under non-linear SEM and shift interventions. The number of maximum intervention targets per experiment is varied from 1 to 5. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Graph recovery performance comparison between SCOUT and baselines under non-linear SEM and shift interventions. The number of samples per experiment is varied from 250 to 1500 [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Graph recovery performance comparison between SCOUT and baselines under non-linear SEM and shift interventions. The number of expected outgoing edge density is varied from 1 to 4 [PITH_FULL_IMAGE:figures/full_fig_p025_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Graph recovery performance comparison between SCOUT and baselines under non-linear SEM and shift interventions. The shift parameter is varied from 0 (observational case) to 2. C.5.5. IMPACT OF SCALE PARAMETER In this section, we vary the scale parameter to see its effect on the performance of SCOUT and baselines. We change it from 0.25 to 2 (0.5 is the observational case). The results are given in [PITH_… view at source ↗
Figure 17
Figure 17. Figure 17: Graph recovery performance comparison between SCOUT and baselines under non-linear SEM and shift interventions. The scale parameter is varied from 0.25 to 2. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Graph recovery performance comparison between SCOUT and baselines under non-linear SEM and shift interventions. The number of cycles are varied from 0 to 8 [PITH_FULL_IMAGE:figures/full_fig_p027_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: KL-divergence comparison between noisy function, shift, and scale interventions under all the single node interventions for a graph with d = 10 nodes. C.7. Additional Experiments on Perturb-CITE-seq Dataset We test how well SCOUT performs compared to other baselines when the intervention targets are known on the Perturb￾CITE-seq dataset (Frangieh et al., 2021). Additionally, we compared the baselines’ per… view at source ↗
Figure 20
Figure 20. Figure 20 [PITH_FULL_IMAGE:figures/full_fig_p029_20.png] view at source ↗
Figure 21
Figure 21. Figure 21 [PITH_FULL_IMAGE:figures/full_fig_p029_21.png] view at source ↗
Figure 22
Figure 22. Figure 22 [PITH_FULL_IMAGE:figures/full_fig_p029_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: The adjacency matrix learnt by SCOUT for co-culture cell condition of Perturb-CITE-seq dataset (Frangieh et al., 2021). |α| ≤ 1. Then, the combined interventional causal mechanism f (Ik) ≜ (Ukf + (1d − Uk)f˜) remains contractive. Proof. We should show that f (Ik) ≜ (Ukf + (1d − Uk)f˜) will still be contractive if f is contractive and f˜= αf where |α| ≤ 1. f (Ik) (x) = Uk + α(I − Uk)  f(x) = A f(x), where… view at source ↗
Figure 24
Figure 24. Figure 24: reports the training times of SCOUT and the baseline methods. In contrast to the gradient-based approaches, LLC and BACKSHIFT require no stochastic optimization; as a result, they are substantially faster. NODAGS-Flow has lower runtime than SCOUT, but its formulation does not support unknown-target estimation or neural spline flows for exogenous noise transformation. All runtimes are measured on graphs wi… view at source ↗
read the original abstract

Learning causal relationships between variables from data is a fundamental research area with many applications across disciplines. Most existing causal discovery algorithms rely on the assumptions that (i) the underlying system is acyclic, (ii) the exogenous noise variables are Gaussian, and (iii) the intervention targets for the data-generating experiments are known. While these assumptions simplify the analysis, they are violated in real-life systems. Most existing methods that address these issues either assume the underlying model is linear or are constrained to operate in limited interventional settings. To that end, we propose SCOUT, a novel causal discovery framework for learning nonlinear cyclic causal relationships from soft interventional data with unknown targets. Our approach maximizes the data log-likelihood to recover the graph structure, using two normalizing-flow architectures: contractive residual flows and neural spline flows. Through experiments on synthetic and real-world data, we show that SCOUT outperforms state-of-the-art methods in both causal graph recovery and unknown target recovery across various interventional and noise settings.

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

2 major / 2 minor

Summary. The manuscript proposes SCOUT, a causal discovery framework for recovering nonlinear cyclic causal graphs from soft interventional data when intervention targets are unknown. The method maximizes the data log-likelihood using two normalizing-flow architectures (contractive residual flows and neural spline flows) to jointly infer the graph structure and the unknown targets, and reports outperformance relative to existing methods on both synthetic and real-world datasets across multiple interventional and noise regimes.

Significance. If the empirical and algorithmic claims hold, the work would constitute a meaningful advance by relaxing the standard assumptions of acyclicity, Gaussian noise, and known targets that constrain most prior causal discovery algorithms. The use of expressive flow models to perform likelihood-based structure recovery in cyclic nonlinear settings is a technically interesting direction, though its reliability rests on whether the fitted flows can distinguish the true structure from observationally equivalent alternatives.

major comments (2)
  1. [Abstract] Abstract: the claim that SCOUT 'outperforms state-of-the-art methods in both causal graph recovery and unknown target recovery' is presented without any description of experimental design, choice of baselines, number of runs, error bars, or data-exclusion criteria. This absence makes it impossible to evaluate whether the reported gains are robust or sensitive to post-hoc decisions.
  2. [Method] The central recovery procedure (likelihood maximization under the contractive residual flow and neural spline flow models) assumes that the maximum-likelihood parameters correspond to the ground-truth cyclic graph and target assignment. In nonlinear cyclic models with soft interventions, multiple distinct graphs can induce the same joint distribution once the flows are sufficiently expressive; the manuscript provides neither an identifiability theorem nor explicit diagnostics (e.g., multiple random initializations or likelihood comparisons across candidate graphs) to rule out observationally equivalent solutions. This assumption is load-bearing for the claim that the recovered graph and targets are causally meaningful.
minor comments (2)
  1. The precise parameterization of the contractive residual flows (e.g., contraction constant, residual block architecture) and the neural spline flows (e.g., number of bins, tail bound) should be stated explicitly, together with any regularization used to enforce contractivity.
  2. Notation for the soft intervention parameters and the mapping from flow parameters to graph edges should be introduced once and used consistently; currently the transition from flow outputs to adjacency matrix is described only at a high level.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment point by point below, outlining specific revisions where appropriate. Our goal is to improve the clarity of the experimental claims and to strengthen the discussion around the recovery procedure.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that SCOUT 'outperforms state-of-the-art methods in both causal graph recovery and unknown target recovery' is presented without any description of experimental design, choice of baselines, number of runs, error bars, or data-exclusion criteria. This absence makes it impossible to evaluate whether the reported gains are robust or sensitive to post-hoc decisions.

    Authors: We agree that the abstract would benefit from additional context to allow readers to assess the reported results. In the revised manuscript we will expand the final sentence of the abstract to briefly describe the experimental protocol: synthetic data generated under multiple noise regimes and intervention densities, real-world datasets, comparison against representative baselines from the cyclic and interventional causal discovery literature, and aggregation over multiple independent runs with standard errors. These additions will be kept concise while providing the necessary information on design and variability. revision: yes

  2. Referee: [Method] The central recovery procedure (likelihood maximization under the contractive residual flow and neural spline flow models) assumes that the maximum-likelihood parameters correspond to the ground-truth cyclic graph and target assignment. In nonlinear cyclic models with soft interventions, multiple distinct graphs can induce the same joint distribution once the flows are sufficiently expressive; the manuscript provides neither an identifiability theorem nor explicit diagnostics (e.g., multiple random initializations or likelihood comparisons across candidate graphs) to rule out observationally equivalent solutions. This assumption is load-bearing for the claim that the recovered graph and targets are causally meaningful.

    Authors: We acknowledge the theoretical subtlety raised. The manuscript currently relies on empirical recovery performance rather than a formal identifiability result. In revision we will add a dedicated paragraph in the method section that (i) explains how the contractive residual flow architecture restricts the function class in a manner that reduces the set of observationally equivalent graphs, (ii) reports results from multiple random initializations showing convergence to the same recovered graph and target set, and (iii) includes likelihood comparisons between the recovered structure and a small set of plausible alternatives. We will also explicitly note that the current claims rest on these empirical diagnostics and that a complete identifiability theorem remains an open question for future work. These changes address the concern without overstating theoretical guarantees. revision: partial

Circularity Check

0 steps flagged

No significant circularity; likelihood maximization recovers structure from external data without definitional reduction.

full rationale

The paper proposes SCOUT as a method that maximizes data log-likelihood under contractive residual flows and neural spline flows to jointly recover cyclic graph structure and unknown soft intervention targets. This is an empirical fitting procedure applied to synthetic and real-world datasets, with performance measured by comparison to ground-truth structures and baselines. No step in the provided abstract or description reduces a claimed prediction or recovery result to a quantity defined by the fitted parameters themselves, nor does it rely on load-bearing self-citations or imported uniqueness theorems that would make the output equivalent to the input by construction. The approach is self-contained against external benchmarks and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; the approach rests on standard causal discovery modeling assumptions plus the representational capacity of the two flow families.

axioms (1)
  • domain assumption The observed data is generated by a structural causal model that may contain cycles and is compatible with soft interventions whose targets are unobserved.
    Invoked in the problem setup to justify the likelihood-based recovery procedure.

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