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arxiv: 2605.22335 · v1 · pith:ZRNTM3DMnew · submitted 2026-05-21 · 💻 cs.LG

Learning Causal Orderings for In-Context Tabular Prediction

Sascha Xu , Sarah Mameche , Jilles Vreeken This is my paper

Pith reviewed 2026-05-22 07:19 UTC · model grok-4.3

classification 💻 cs.LG
keywords causal orderingtabular predictionin-context learningattention constraintunsupervised structure learningimputationdistribution shiftbiological data
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The pith

A tabular model learns an unsupervised causal ordering of variables and restricts predictions to use only earlier features in that order.

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

The paper develops a method to discover and then enforce a causal ordering among variables inside an in-context predictor for tabular data. Instead of letting every feature influence every prediction through standard attention, the model only attends to variables that precede the target in the learned order. This ordering is found without any labels by maximizing a likelihood objective that the authors justify for common functional models such as additive noise. The approach remains useful even when some observations are missing, a frequent issue in real tables. A reader would care because ordinary correlation-driven predictors degrade under distribution shift or intervention, while an enforced causal order supplies a structural guardrail that can survive such changes.

Core claim

TabOrder learns a topological ordering of variables in an unsupervised fashion through a likelihood-based objective and then performs prediction and imputation by constraining attention so that each target only receives information from features that precede it in the ordering; the authors show that this recovers accurate orderings, supports both prediction and imputation, and yields interpretable insights on biological data collected under interventions.

What carries the argument

Causal order-constrained attention that bases each prediction solely on variables earlier in a learned topological ordering of the features.

If this is right

  • Accurate variable orderings can be recovered even when tabular samples contain missing entries.
  • The same learned ordering supports both prediction and imputation tasks without separate training.
  • The approach supplies causal insight on real biological data recorded after interventions.
  • The likelihood objective for ordering learning is justified under common functional model classes such as additive noise.

Where Pith is reading between the lines

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

  • The same constrained-attention idea could be tested on time-series or graph-structured data where a natural ordering exists.
  • Combining the ordering learner with existing causal-discovery algorithms might reduce the need for purely unsupervised likelihood training.
  • If the ordering remains stable across multiple interventions, the method could serve as a lightweight way to detect which variables are causes versus effects in new domains.

Load-bearing premise

An optimal causal ordering of the variables exists and can be recovered from unlabeled data by maximizing likelihood under standard functional assumptions, and enforcing that ordering will still help prediction when some samples contain missing values.

What would settle it

On a dataset with known ground-truth causal directions and an intervened test distribution, the learned ordering either fails to match the true directions or produces no improvement in prediction accuracy over an unconstrained baseline.

Figures

Figures reproduced from arXiv: 2605.22335 by Jilles Vreeken, Sarah Mameche, Sascha Xu.

Figure 1
Figure 1. Figure 1: Prediction under Intervention with and without Order Constrained Attention. For prediction of a mediator Y in a chain X → Y → Z, we measure test error without resp. with intervention on Y → Z. The generating mechanism f(X) is shown in black. TABPFN (a) accurately models X → Y when no intervention is present (green), but fails under intervention (orange). TABORDER (b) remains accurate in both settings by le… view at source ↗
Figure 2
Figure 2. Figure 2: Overview over TABORDER. For a dataset D we map each column i to an order score si . From these scores, we construct a hard/soft attention mask to constrain attention according to the learned order (left). To predict missing entries in D, we alternate row-wise attention (unrestricted) and column-wise causal attention (order-constrained). From the resulting cell embeddings, we decode the conditional mean and… view at source ↗
Figure 3
Figure 3. Figure 3: Effect of Missingness. In an addi￾tive noise model, X3 = X1 + (X2) 2 + N where N, X1, X2 ∼ N (0, 1), when either parent of X3 is missing, the model increments the variance σˆ 2 (Eq. (7)) by a learned amount (blue for X1, green for X2) that reflects the effect of missingness of causal parents. Prediction under Partial Observation. Since the model predicts potentially multiple missing entries per row, missin… view at source ↗
Figure 4
Figure 4. Figure 4: Causal Order Inference. Shown is the topological divergence (dTOP, lower is better) of estimated causal orders on synthetic datasets generated from nonlinear Gaussian process ANMs (a) and on the real-world causal discovery benchmark by Sachs et al. [2005] (b). 5 Experiments We evaluate whether TABORDER achieves a favorable trade-off between I. causal order learning and II. tabular prediction and imputation… view at source ↗
Figure 5
Figure 5. Figure 5: Order Impact. Shown is the effect of replacing learned orders at test time. Incorrect orders degrade prediction (NLL) as the considered order diverges from the true causal order (dTOP). Order Impact. Next we assess predictive performance in relation to the quality of the learned causal order. We impose different orders when evaluating TABORDER, includ￾ing a correct causal order, the learned order, and mult… view at source ↗
Figure 6
Figure 6. Figure 6: Predictive Performance (Trade Off II). Shown is the average rank of imputation (a, c) and downstream prediction (b, d) performance on the CTR23 (left) and CC18 (right) datasets. TABORDER is the most accurate imputation method for ≥ 40% missingness. a given causal DAG reflects causal cell signaling pathways among 11 variables. The main results ( [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Intervention-Robust Prediction. Shown is the MSE for predicting Y in the three￾variable chain on an i.i.d. and an intervened sample Y → Z (mechanism shift). TABOR￾DER remains accurate under the intervention via the learned causal order, while TABPFN and XGBOOST degrade in performance [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Changes in Inferred Orders under Intervention. In the Sachs et al. [2005] data, we compare two interventional conditions (a, b) to the reference condition, and count flips in node positions in the order by TABORDER (darker for more flips). An upstream intervention (a) leads to global changes in the order; a downstream one (b) to a local change of one target. Unknown Biological Interventions. Last, to study… view at source ↗
Figure 9
Figure 9. Figure 9: Consensus Causal Structure for the Data by Sachs et al. [2005]. We show the causal DAG that we consider in the evaluations (a), as well as the effects of perturbations applied in each experimental condition (b). Dashed colored nodes correspond to activators (green) and inhibitors (blue), cf [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Causal Order Inference (extends Fig. 4a). Shown is the average topological divergence (dTOP, lower is better) between ground truth and estimated causal orders on synthetic datasets, generated from a nonlinear additive noise model with functions drawn from a Gaussian process, with both a variant where functional mechanisms are additive (left), respectively non-additive (right), in the causal parents. D.2 C… view at source ↗
Figure 11
Figure 11. Figure 11: Causal Order Inference in Real-World Data (extends Fig. 4b). Shown is the average topological divergence (dTOP, lower is better) between ground truth and estimated causal orders on the real-world causal discovery benchmark by Sachs et al. [2005]. For each available dataset c (vertical) corresponding to one experimental condition, we show each method (horizontal) and how the causal order πˆc it discovers i… view at source ↗
Figure 12
Figure 12. Figure 12: Predictive Performance (extends [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Intervention-Robust Prediction (extends Fig.7). Test MSE for predicting Y in the three-variable chain, split by mechanism family (GP vs. spline) and intervention type. does not perform competitively, indicating that fine-tuning or alternatively training on different synthetic data is necessary to achieve strong imputation performance. D.4 Intervention-Robust Prediction ( [PITH_FULL_IMAGE:figures/full_fig… view at source ↗
Figure 14
Figure 14. Figure 14: Scalability (extends Fig. 4a). Shown are scalability comparisons for TABORDER and baselines on causal order discovery. This experiment uses the same data generation and evaluation as in [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Changes in Inferred Orders under Intervention. The heatmaps compare the topological orders inferred by TABORDER across all Sachs experimental conditions relative to the reference condition cd3cd28. Top: node-wise rank shifts, where positive (negative) values indicate downstream (upstream) movement in the inferred order compared to the baseline condition. Bottom: fraction of pairwise order flips involving … view at source ↗
Figure 16
Figure 16. Figure 16: Changes in Inferred Orders under Intervention (extends [PITH_FULL_IMAGE:figures/full_fig_p025_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Example Changes in Inferred Orders. Each panel compares the baseline order inferred by TABORDER on cd3cd28 to the order inferred under the intervention. Nodes in the baseline order are shown in light blue; nodes in the interventional condition are colored in dark blue depending on their pairwise flip fraction relative to the baseline. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_17.png] view at source ↗
read the original abstract

In-context learning for tabular data sets strong predictive standards in observational settings; it however primarily relies on correlational structure, which becomes unreliable under distribution shift or intervention. While established methods to discover causal structure exist, they are often focused on structure identifiability and decoupled from the predictive architectures that could benefit from them. To bridge these perspectives, we study how to simultaneously infer and enforce causal structure in the form of topological variable orderings into tabular prediction. Unlike standard architectures, our model TabOrder uses causal order-constrained attention, basing predictions only on features that precede a target under a learned causal order. Similar to causal discovery methods, TabOrder learns the optimal variable ordering in an unsupervised manner through a likelihood-based objective. We justify this choice under standard functional model classes and also study how sample missingness, a common challenge in tabular data, interacts with causal direction identification. Empirically, we confirm that TabOrder recovers accurate variable orderings while addressing prediction and imputation tasks, as well as gives insight into real-world biological data under intervention.

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

3 major / 2 minor

Summary. The paper proposes TabOrder, a tabular in-context learning model that learns a topological variable ordering in an unsupervised manner via a likelihood objective (justified under standard functional model classes such as additive noise), then enforces this ordering via a causal order-constrained attention mask so that predictions for a target use only preceding features. The work also examines interactions with sample missingness and reports empirical results on recovering accurate orderings, prediction/imputation performance, and insights from real-world biological data under intervention.

Significance. If the central claims hold, the work would usefully integrate causal ordering discovery directly into predictive architectures for tabular data, potentially yielding better robustness to interventions and distribution shift than purely correlational in-context methods. The unsupervised likelihood framing and missingness study address practical tabular challenges, and any reproducible code or falsifiable predictions on biological interventions would strengthen the contribution.

major comments (3)
  1. [Abstract, §3] Abstract and §3 (method): the justification that the unsupervised likelihood objective recovers causal (rather than merely statistical) orderings under standard functional model classes is stated but not derived or proven; without an explicit identifiability argument or counter-example analysis, it is unclear whether the ordering remains meaningful when the data-generating process deviates modestly from the assumed class, which is load-bearing for the robustness claims.
  2. [Empirical evaluation] Empirical section (presumably §5 or §6): the abstract asserts that TabOrder 'recovers accurate variable orderings' and addresses prediction/imputation, yet the provided text contains no quantitative metrics, error bars, ablation studies on ordering accuracy versus baselines, or controls for functional-class violations; this absence makes the central empirical claim difficult to evaluate.
  3. [Missingness study] Missingness interaction study: while the abstract notes examination of how sample missingness interacts with causal direction identification, no specific experimental design, results, or analysis of identifiability failure modes under missingness is visible, which is relevant to the practical tabular setting.
minor comments (2)
  1. [§3] Notation for the order-constrained attention mask should be introduced with an explicit equation or diagram early in the method section to improve readability.
  2. [Method] Clarify whether the likelihood objective is computed jointly with the predictive loss or in a separate unsupervised phase, as the current description leaves the training procedure ambiguous.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We will revise the manuscript to include an explicit identifiability argument, expand quantitative empirical details with metrics and ablations, and elaborate on the missingness experiments and their design. Point-by-point responses follow.

read point-by-point responses

  1. Referee: [Abstract, §3] Abstract and §3 (method): the justification that the unsupervised likelihood objective recovers causal (rather than merely statistical) orderings under standard functional model classes is stated but not derived or proven; without an explicit identifiability argument or counter-example analysis, it is unclear whether the ordering remains meaningful when the data-generating process deviates modestly from the assumed class, which is load-bearing for the robustness claims.

    Authors: We agree an explicit derivation strengthens the work. The current text justifies the likelihood objective under standard classes such as additive noise models, but the revision will add a theorem and proof sketch in §3 establishing identifiability of the topological ordering. We will also include a short counter-example analysis for modest deviations (e.g., non-additive interactions) to clarify robustness limits. revision: yes

  2. Referee: [Empirical evaluation] Empirical section (presumably §5 or §6): the abstract asserts that TabOrder 'recovers accurate variable orderings' and addresses prediction/imputation, yet the provided text contains no quantitative metrics, error bars, ablation studies on ordering accuracy versus baselines, or controls for functional-class violations; this absence makes the central empirical claim difficult to evaluate.

    Authors: Section 5 reports quantitative ordering recovery via Kendall tau distance to ground-truth orderings on synthetic data from known DAGs, with means and standard deviations over repeated runs, plus comparisons to random and correlation baselines and tests under mild functional-class violations. To improve visibility we will add error bars to figures, include a dedicated ablation table, and move key metrics into the abstract. revision: partial

  3. Referee: [Missingness study] Missingness interaction study: while the abstract notes examination of how sample missingness interacts with causal direction identification, no specific experimental design, results, or analysis of identifiability failure modes under missingness is visible, which is relevant to the practical tabular setting.

    Authors: The experiments section describes simulating random and structured missingness, then measuring effects on ordering recovery and imputation. The revision will expand this with a clearer experimental design subsection, quantitative results on specific failure modes (e.g., when missingness correlates with variables), and discussion of identifiability limits under missing data. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained under stated assumptions

full rationale

The paper derives the variable ordering from an unsupervised likelihood objective justified under standard functional model classes (additive noise etc.), then enforces the resulting order inside the attention mask for downstream prediction and imputation. This chain does not reduce to self-definition or fitted-input-as-prediction because the ordering is obtained from the data-generating likelihood independently of the final predictive loss; the two tasks share the same model but the ordering step is not tautological with the prediction step. No load-bearing self-citations, uniqueness theorems imported from the authors' prior work, or ansatz smuggling are present in the provided text. The approach is therefore self-contained against external benchmarks once the functional-class assumption is granted.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence of standard functional model classes that justify the likelihood objective for ordering recovery, plus an implicit assumption that missingness does not destroy identifiability of causal directions.

axioms (2)
  • domain assumption Standard functional model classes allow the likelihood-based objective to recover the correct causal ordering.
    Explicitly invoked in the abstract as justification for the unsupervised learning choice.
  • domain assumption Sample missingness interacts with causal direction identification in a manner that still permits useful ordering recovery.
    The abstract states that the authors study this interaction, implying it is treated as a manageable factor.

pith-pipeline@v0.9.0 · 5712 in / 1312 out tokens · 43360 ms · 2026-05-22T07:19:41.788115+00:00 · methodology

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