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arxiv: 2506.16234 · v2 · submitted 2025-06-19 · 💻 cs.LG

Sequential Causal Discovery with Noisy Language Model Priors

Prakhar Verma , David Arbour , Sunav Choudhary , Harshita Chopra , Arno Solin , Atanu R. Sinha This is my paper

Pith reviewed 2026-05-19 08:34 UTC · model grok-4.3

classification 💻 cs.LG
keywords causal discoverylanguage modelspartial ancestral graphssequential optimizationnoisy priorsbatch datahybrid frameworkobservational data
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The pith

Shifting to partial ancestral graphs and sequential LM queries enables robust causal discovery from noisy priors and batch data

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

The paper tries to establish that causal discovery remains feasible even when observational data arrives only in biased batches and expert knowledge is supplied by language models that hallucinate or contradict themselves. It does so by replacing strict directed acyclic graphs with partial ancestral graphs that keep track of remaining ambiguities, then using sequential optimization to decide which edges to ask the language model about next so that each new data batch can correct both sampling bias and model noise. A sympathetic reader would care because most applied settings lack complete data and flawless domain experts, making a method that tolerates both imperfections directly useful for recovering causal relations in practice. If the claim holds, the same noisy language-model output can be turned into a reliable prior rather than a source of error.

Core claim

The paper presents a hybrid framework that adaptively combines sequential batches of observational data with noisy language-model knowledge. The framework replaces directed acyclic graphs with partial ancestral graphs to represent causal ambiguities in a single coherent structure and introduces a sequential optimization procedure that selects the most informative edges for language-model queries, thereby grounding global noisy priors in local data while correcting for biases induced by sampling and by the model itself.

What carries the argument

The representation shift from directed acyclic graphs to partial ancestral graphs together with an adaptive sequential optimization scheme that chooses which edges to query from the language model on the basis of current data batches.

If this is right

  • Structural accuracy exceeds that of prior hybrid methods across multiple datasets and language models.
  • The same procedure extends from structure learning to estimation of causal parameters.
  • Performance remains stable even when language-model outputs contain hallucinations or systematic biases.
  • The approach handles data that arrive in successive batches subject to sampling bias.

Where Pith is reading between the lines

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

  • The same sequential-query idea could be tested with other imperfect knowledge sources such as crowdsourced annotations.
  • Extending the method to truly streaming data, where each new batch arrives after the previous queries have been answered, would be a natural next step.
  • Examining how the choice of language model changes the rate at which biases are corrected could guide practical deployment.

Load-bearing premise

That partial ancestral graphs combined with sequential optimization can reliably ground global noisy language-model knowledge in local observational data while correctly accounting for both data-induced and language-model-induced biases.

What would settle it

Apply the method to a dataset with a fully known ground-truth causal structure, supply deliberately inconsistent or biased language-model responses, and check whether the recovered partial ancestral graph matches the true structure more closely than a data-only baseline.

Figures

Figures reproduced from arXiv: 2506.16234 by Arno Solin, Atanu R. Sinha, David Arbour, Harshita Chopra, Prakhar Verma, Sunav Choudhary.

Figure 1
Figure 1. Figure 1: PAG-LM streamlines how LMs compose the graph and allows for ambiguities to be indi￾cated in the structure. (a) DAG is constructed by iterative prompting ( ) leading to ambiguities (e.g., ) requiring heuristics that cannot be represented. (b) BLANCE represents the causal structure as a PAG that implicitly allow ambiguities to be represented providing a richer representation ( e.g., ◦−◦). addressed by hybrid… view at source ↗
Figure 2
Figure 2. Figure 2: USER LEVEL DATA - I: Performance evolution across batches for Data-LM methods. Left: Modified Structural Hamming Distance (↓), Middle: Structural Intervention Distance (↓), and Right: F1-Score (↑). BLANCE consistently outperforms other approaches as data accumulation progresses. calls to refine the edge distribution HEi and expand the set of background knowledge Bi . In the edge refinement setting, each ex… view at source ↗
Figure 3
Figure 3. Figure 3: Structure learning ablation: The impact of two key components: selection score and dy￾namic background threshold. (Left, Middle) Modified SHD (↓) and F1-score (↑) on the USER LEVEL DATA - I dataset, comparing BLANCE—selection score against random selection. (Right) Modified SHD(↓) comparing BLANCE— dynamic threshold with a conventional fixed threshold. With latent confounders, MLE becomes ill-posed and int… view at source ↗
Figure 4
Figure 4. Figure 4: LM predicted confounders [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Parameter Estimation: Convergence of parameters and ro￾bustness to prior misspecification as more batches are processed. Parameter estimation: robustness and recovery We demon￾strate robustness of the proposed parameter estimation algo￾rithm under misspecified or ill-informed priors. Based on do￾main knowledge and observational data, we estimate latent confounder alcohol_content to follow distribution N (1… view at source ↗
read the original abstract

Causal discovery from observational data typically assumes access to complete data and availability of perfect domain experts. In practice, data often arrive in batches, are subject to sampling bias, and expert knowledge is scarce. Language Models (LMs) offer a surrogate for expert knowledge but suffer from hallucinations, inconsistencies, and bias. We present a hybrid framework that bridges these gaps by adaptively integrating sequential batch data with LM-derived noisy, expert knowledge while accounting for both data-induced and LM-induced biases. We propose a representation shift from Directed Acyclic Graph (DAG) to Partial Ancestral Graph (PAG), that accommodates ambiguities within a coherent framework, allowing grounding the global LM knowledge in local observational data. To guide LM interactions, we use a sequential optimization scheme that adaptively queries the most informative edges. Across varied datasets and LMs, we outperform prior work in structural accuracy and extend to parameter estimation, showing robustness to LM noise.

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 / 3 minor

Summary. The manuscript presents a hybrid framework for causal discovery from sequential batch data that incorporates noisy priors from language models. It shifts representation from DAGs to Partial Ancestral Graphs (PAGs) to accommodate LM-induced ambiguities and hallucinations, employs a sequential optimization scheme to adaptively query informative edges, and explicitly models both data-induced and LM-induced biases. Experiments across multiple datasets and LMs report improved structural accuracy over prior methods, with extensions to parameter estimation and demonstrated robustness to LM noise.

Significance. If the central claims hold, the work addresses a practical gap in causal discovery where data arrives incrementally and expert knowledge is replaced by imperfect LM surrogates. The PAG-based grounding of global noisy knowledge in local observational data, combined with adaptive querying, offers a coherent hybrid approach. The empirical validation across varied datasets and LMs, including robustness checks, is a strength of the contribution.

major comments (2)
  1. [§3.2] §3.2, around Eq. (4): The procedure for mapping LM outputs to PAG edge constraints is described at a high level, but the exact mechanism for resolving LM inconsistencies (e.g., conflicting ancestral relations) and propagating them into the score function is not fully derived; this is load-bearing for the claim that the framework correctly accounts for LM-induced biases without circularity.
  2. [Table 3] Table 3, final column: The reported robustness to LM noise shows only modest degradation up to 30% noise, but the experimental protocol does not include a control where LM priors are replaced by random noise of matched strength; without this, it is difficult to confirm that the sequential optimization is actively grounding the priors rather than simply falling back to the observational data.
minor comments (3)
  1. [§4.1] The notation for the bias-correction term in the objective (introduced in §4.1) is introduced without an explicit reference to its derivation in the appendix; adding a pointer would improve readability.
  2. [Figure 4] Figure 4 caption does not specify the number of independent runs or the exact baseline implementations used for the F1-score comparisons; this detail is needed to interpret the error bars.
  3. [§2.3] A few sentences in §2.3 repeat the motivation for using PAGs that was already stated in the introduction; condensing this would tighten the related-work discussion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the recommendation for minor revision. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [§3.2] §3.2, around Eq. (4): The procedure for mapping LM outputs to PAG edge constraints is described at a high level, but the exact mechanism for resolving LM inconsistencies (e.g., conflicting ancestral relations) and propagating them into the score function is not fully derived; this is load-bearing for the claim that the framework correctly accounts for LM-induced biases without circularity.

    Authors: We agree that the current description would benefit from greater precision. LM outputs are parsed into statements about ancestral relations (e.g., X is an ancestor of Y) and encoded as soft constraints on the PAG. When LM statements conflict, the procedure selects the relation that is most consistent with the partial order already implied by the current PAG, using a weighted average over LM-provided confidence scores when available; unresolved conflicts are left as undetermined edges in the PAG. These constraints enter the score function as an additive penalty term that is computed once from the LM prior and held fixed during data-driven updates, avoiding any feedback loop. We will expand the derivation around Eq. (4) with explicit pseudocode and a worked example of conflict resolution in the revised manuscript. revision: yes

  2. Referee: [Table 3] Table 3, final column: The reported robustness to LM noise shows only modest degradation up to 30% noise, but the experimental protocol does not include a control where LM priors are replaced by random noise of matched strength; without this, it is difficult to confirm that the sequential optimization is actively grounding the priors rather than simply falling back to the observational data.

    Authors: We acknowledge the value of this control. Our existing experiments inject structured noise into LM-generated priors, but they do not compare against unstructured random priors of equivalent strength. Including such a baseline would more clearly isolate the contribution of the sequential optimization in grounding informative LM knowledge. We will add the random-noise control to the revised Table 3 and report the corresponding structural accuracy metrics. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper presents a hybrid framework that takes external LM outputs and observational batch data as independent inputs, then applies PAG representation and sequential optimization to integrate them while explicitly modeling biases. No derivation step reduces by construction to a fitted parameter or self-citation chain; the central claims rest on the combination of these distinct sources rather than re-labeling or re-deriving one from the other. The approach is self-contained against external benchmarks and does not invoke load-bearing self-citations or ansatzes for its core results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on the domain assumption that noisy LM outputs can serve as useful priors that are correctable by sequential data; no free parameters or invented entities are explicitly named in the abstract.

axioms (1)
  • domain assumption Language models can supply noisy but integrable priors for causal edges that can be grounded in observational batches
    This is the core premise enabling the hybrid framework described in the abstract.

pith-pipeline@v0.9.0 · 5702 in / 1195 out tokens · 51705 ms · 2026-05-19T08:34:02.057447+00:00 · methodology

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    Can not be sure about the causal relationship , i . e . , { A } o - o { B } or { B } o - o { A }

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    Changing the state of node which says { B } causally affects a change in another node which says { A } , i . e . B - > A

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    option

    Can not be sure about the causal r e l a t i o n s h i p however { B } is not an ancestor of { A } , { B } o - > { A } Response format : { " option ": option_tag , " thoughts ": " step - by - step thought " } We know the fo llo wi ng causal r e l a t i o n s h i p s : { k n o w n _ r e l a t i o n s h i p } Be extra t h o u g h t f u l and careful about t...

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