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REVIEW 4 major objections 5 minor 17 references

Towards Probabilistic Question Answering Over Tabular Data

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper claims that combining automatically learned Bayesian networks with LLM-based query translation outperforms retrieval-only and SQL-based approaches on probabilistic table questions.

desk verdict LUCARIO is a genuinely new benchmark resource, but the headline results measure LLM query translation against the benchmark's own ground-truth BN, not probabilistic reasoning over the table. read the letter →

arxiv 2506.20747 v1 pith:Y64ZEF7F submitted 2025-06-25 cs.CL

Chen Shen , Sajjadur Rahman , Estevam Hruschka This is my paper
classification cs.CL
keywords probabilisticquestionansweringtabulardataBayesiannetworksneuro-symbolicreasoningLUCARIObenchmarkuncertaintyLLMquerytranslation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Most table-question-answering systems are built for factual retrieval: they find values, not likelihoods. This paper argues that probabilistic questions—'How likely is a delay given region A?'—need explicit reasoning under uncertainty. To make that measurable, it introduces LUCARIO, a benchmark of 1,570 probabilistic scenarios across 10 large real-world tables, with four linguistic variants per query. To answer them, it proposes Auto-BN, which automatically learns a Bayesian network from each table, translates a natural-language question into a probabilistic query with an LLM, and computes the answer by exact inference. The reported result is that Auto-BN beats LLM-only, SQL-based, and premise-retrieval baselines, with the largest gains on paraphrased 'natural' questions.

What carries the argument

The load-bearing object is the automatically learned Bayesian network over the table's columns, together with the premise and insight artifacts derived from it. A premise is a one-hop conditional statement, P(child | parents), covering one combination of node states; an insight is a small subset of premises ranked by KL divergence within the node's Markov blanket. The pipeline has four stages: learn the BN from the table; use the LLM to map the question to a target node and evidence node-state pairs; run exact inference (variable elimination) on the BN; and have the LLM verbalize the resulting probability. The BN carries the argument because all calibrated probability mass comes from exact symbolic inference, while the LLM is confined to the translation step, which the paper identifies as the main source of remaining errors.

What would settle it

Create a second version of a benchmark table whose ground-truth probabilities are computed from an independent source—say, a human-validated causal model or a network learned from a held-out portion of the rows—and run Auto-BN on the same questions. If most of its accuracy advantage over the baselines disappears, the edge came from sharing the same BN at benchmark construction and inference, not from probabilistic reasoning.

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Extended reading notes

Core claim

The paper's central claim is that a hybrid symbolic-neural pipeline—auto-learned Bayesian network induction plus LLM-based query translation—substantially outperforms neural-only and retrieval-only alternatives for probabilistic QA over large real-world tables. On LUCARIO, Auto-BN with GPT-4o reaches 38.2% Acc0.02 and a mean absolute error of 0.103, compared with 24.4% Acc0.02 for the best LLM+Table baseline, and it does so while evaluated only on the hardest 'natural' question type to prevent lexical shortcuts. The authors interpret this as evidence that deterministic SQL retrieval cannot express conditional uncertainty, that large premise sets overwhelm LLM reasoning, and that grounding the LLM's answer in exact inference is what drives accuracy.

Load-bearing premise

The evaluation assumes the auto-learned Bayesian network is the correct source of ground truth, because the same learned network is used both to build the benchmark answers and to run Auto-BN, so the non-circular skill being measured is mainly how well the LLM translates questions into that network's node-state vocabulary.

Editorial extensions

If this is right

  • Auto-BN can answer conditional-likelihood questions that NL2SQL systems cannot express, because deterministic SQL execution has no semantics for conditional uncertainty.
  • Distilling a large premise space into a few high-impact insights improves LLM accuracy more than retrieving many premises, suggesting that focused evidence beats exhaustive evidence for probabilistic reasoning.
  • Because Bayesian networks are learned automatically from data, the approach scales to tables with many columns and millions of rows without expert-curated structures.
  • The residual error rate is driven by the LLM's node-state translation step, so improving query translation—not the inference engine—is the clear next lever for accuracy.
  • LUCARIO's four question variants make benchmark scores robust to lexical shortcutting, since Auto-BN is only scored on the paraphrased Natural type.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the shared-BN circularity holds in practice, LUCARIO today measures question-to-vocabulary translation more than probability estimation; an external ground-truth source would certify the method's statistical claims.
  • The same grounding recipe could transfer to causal questions by replacing exact BN inference with an interventional or counterfactual engine, retaining the LLM only for query parsing.
  • The insight-distillation result suggests a cheap general recipe for retrieval-augmented LLM reasoning: rank a large rule base by divergence from the marginal distribution and prompt with the top few rules, instead of relying on retriever similarity alone.
  • A robustness probe: run Auto-BN with a different structure-learning algorithm or a human-validated network; if accuracy is stable across structures, the method is robust to structural uncertainty.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper introduces LUCARIO, a benchmark for probabilistic question answering over tabular data, built from 10 BIRD tables, with automatically learned Bayesian networks, premise and insight artifacts, and four linguistic question types. Ground-truth probabilities for each query are computed by exact inference over the Bayesian network induced from the corresponding table. The proposed Auto-BN framework learns a BN from the table, uses an LLM to translate natural-language questions into structured probabilistic queries, performs exact inference, and optionally verbalizes the result. Experiments report that Auto-BN with GPT-4o achieves 38.2% Acc0.02 and MAE 0.103, outperforming LLM+Table, NL2SQL, and premise-retrieval baselines, and the paper concludes that hybrid symbolic-neural reasoning is effective for probabilistic tabular QA.

Significance. If the evaluation were sound, the paper would address a real gap: a large-scale, data-driven benchmark for probabilistic QA over real-world tables, with linguistically varied questions and structured artifacts such as premises and insights. The authors deserve credit for assembling large tables, defining four question types, performing exact inference, and taking steps to avoid lexical leakage by restricting Auto-BN to the Natural question type. However, the central claim is not supported as stated. Because the benchmark's ground truth is generated by the same Bayesian network that Auto-BN uses for inference, the reported Acc0.02 and MAE values primarily measure how often the LLM translator recovers the hidden structured query, not how well the system performs probabilistic reasoning over the table's actual distribution. In addition, Auto-BN is evaluated only on the Natural question type while Table 4 appears to aggregate question types, and all results are single runs with no significance testing. The benchmark may still be a useful resource if its ground-truth validity is established independently, but the current evidence does not support the paper's headline claims.

major comments (4)
  1. [§3.4, Appendix D.1] Section 3.4 states that the ground-truth probability for each query is computed by exact inference over a Bayesian Network induced from the corresponding table, and Appendix D.1 states that "the same BN is used during both benchmark construction and inference." Therefore, whenever the LLM correctly translates the natural question into the intended target variable and evidence node-states, Auto-BN returns the benchmark's ground-truth probability by construction. Consequently, the headline numbers in §5.2 (38.2% Acc0.02, MAE 0.103) measure translation fidelity into the BN's node-state vocabulary, not the quality of probabilistic reasoning over the table's actual data distribution. This is a load-bearing issue for the central claim, and the paper's own Section 8 concedes that the auto-learned structures "may not represent ground truth." The authors should either construct ground truth from an independent source (for example, empirical conditional frequencies or an externally validated BN) or explicitly reframe the benchmark as measuring query-to-structured-query translation.
  2. [§5.1, §5.2, Table 4, Appendix E] Section 5.1 says Auto-BN is "evaluated exclusively on the most challenging 'natural' question type," while §5.2 says Table 4 reports metrics "computed per (question type, baseline) pair." Table 4, however, has no question-type dimension and lists Auto-BN alongside baselines without indicating that its row is Natural-only. Appendix E provides question-type-level results for the baselines but not for Auto-BN. If the baseline rows aggregate all four question types while the Auto-BN row reports only Natural questions, the comparison is not apples-to-apples and the claim that Auto-BN "substantially outperforms all baselines across all metrics besides error-rate" is not justified. The authors should report per-question-type results for every method or evaluate all methods on the same question types.
  3. [Appendix D.1, Section 4.2, Section 8] Appendix D.1 refers to "a modified structure learning algorithm" but never specifies the algorithm, its hyperparameters, or the discretization procedure, so the reader cannot assess the quality of the induced BNs. Moreover, no experiment compares BN-inferred marginal or conditional probabilities with direct empirical estimates from the same tables, and Section 8 explicitly warns that the learned structures "may not represent ground truth." Since the benchmark answers are defined as exact inferences over these very BNs, the validity of the benchmark itself is unestablished. At minimum, the authors should validate the learned BNs against empirical frequencies or an independent gold-standard structure and report sensitivity to the discretization and structure-learning hyperparameters.
  4. [Footnote 2, Table 4] Footnote 2 states that each result is a single run per method per dataset, and the standard deviations in Table 4 are computed across the 10 datasets, not across repeated runs. Several key comparisons differ by only a few percentage points in Acc0.02 or by roughly 0.02–0.05 in MAE, yet no significance tests or confidence intervals are reported. The claim in §5.2 that Auto-BN "substantially outperforms all baselines across all metrics besides error-rate" is therefore not statistically supported, especially because the error-rate for Auto-BN (6.5%) is not lower than all baselines and the differences may reflect run-to-run variability.
minor comments (5)
  1. [Table 4] The row label "LLM+Premise(Vector))" contains an extra closing parenthesis, and Table 4 uses "Mixtral-8x21B" while Appendix D.7 and the reference list use "Mixtral-8x22B"; these should be reconciled.
  2. [Appendix D.1] There is a typo in "grouth truth" that should read "ground truth," and the sentence "This conservative setup enforces a strict separation between the input modality and the inference mechanism" would benefit from a clearer statement of what exactly is being separated.
  3. [Table 1] Table 1 uses ✓ and ✗ symbols without a legend; the authors should state explicitly what each symbol means (e.g., "supported" vs. "not supported") and define abbreviations such as "Prob Artifacts (Insights)."
  4. [Appendix B] The linguistic-quality check uses only 10 randomly sampled premises and 10 questions per table, which is a small sample; the Grammarly score of 96 should be presented as anecdotal rather than as a rigorous evaluation of fluency.
  5. [§3.2] The phrase "contains 10 real-world large-scale tables (table SQLite file and description)" is grammatically awkward, and "The statistics of table source included" should be rephrased; also, the paper does not clearly explain how the "causal" edges in the auto-learned BNs were validated beyond the small expert sample in Appendix B.

Circularity Check

3 steps flagged · score 8.0 of 10

Ground-truth probabilities and Auto-BN inference come from the same auto-learned Bayesian network, so the reported gains reduce to LLM query-translation accuracy.

  1. self definitional [Section 3.4 (ground-truth definition) and Appendix D.1 (Auto-BN inference)]
    "Similar to existing benchmarks, the ground truth probability for each query is computed by performing exact inference over a Bayesian Network (induced from the corresponding table), based on a structured query derived from the natural language input. ... Because the same BN is used during both benchmark construction and inference, we take special care to prevent lexical leakage or shortcut exploitation."

    Auto-BN's only symbolic component is exact inference over the BN; the LLM merely translates the question into target and evidence node-state pairs. The benchmark's ground truth is defined as exact inference over that same BN from the same type of structured query. Therefore, whenever the LLM translation is correct, Auto-BN's output equals the ground truth by construction, and the probabilistic-inference part cannot fail. The measured Acc0.02/MAE thus quantify how often the LLM recovers the hidden structured query, not whether the system reasons correctly about the table's actual distribution.

  2. fitted input called prediction [Section 3.3 (BN artifact), Section 5.2 (main results), Table 4]
    "Bayesian Network (BN): A graphical model representing the dependencies and independencies among the table’s columns, automatically constructed based on the data distribution. ... Auto-BN substantially outperforms all baselines across all metrics besides error-rate."

    The BN is automatically fit to each table and then serves simultaneously as (a) the source of benchmark ground-truth probabilities and (b) Auto-BN's inference engine. The headline results (38.2% Acc0.02, MAE 0.103) therefore report how often the LLM maps natural language into the BN's node-state vocabulary, not how well either the learned BN or Auto-BN matches the table's true distribution. No comparison of BN-inferred probabilities to direct empirical estimates from the data is provided, so the learned structure is never externally validated.

1 more flagged steps
  1. other [Section 8 (Ethical Considerations)]
    "The learned structures reflect statistical estimations based solely on observed records, without incorporating broader world knowledge. As such, they may not represent ground truth and should not be used as generic justification or reliable decision making, such as investigations or healthcare applications."

    The paper itself concedes that the auto-learned Bayesian networks 'may not represent ground truth,' yet the benchmark defines its ground-truth answers as exact inference over those same networks. This makes the evaluation self-referential: Auto-BN is scored against the very model it uses, so a high score does not establish that either the BN or Auto-BN captures the true probabilities of the table. The concession highlights that the non-circular residual is only the LLM's query-to-node translation.

full rationale

The central evaluation is circular in a specific, quotable way. Section 3.4 defines every ground-truth probability as exact inference over a Bayesian Network induced from the corresponding table. Appendix D.1 explicitly states that the same BN is used during both benchmark construction and Auto-BN inference. Consequently, whenever the LLM translator correctly identifies the target variable and evidence node-states, Auto-BN returns the benchmark's ground-truth probability by construction; the symbolic probabilistic reasoning is guaranteed correct because it is the same computation that generated the label. The only non-circular competence being measured is natural-language-to-structured-query translation, and the paper provides no baseline that pairs the same translator with an independent probability estimator. The paper's own Section 8 further concedes that the learned structures 'may not represent ground truth,' undermining the use of those same structures as ground truth. This is not a case of mere self-citation; it is a reduction of the headline claim to a fit by construction. The score is 8 rather than 10 because a genuine, non-circular component remains: the LLM's ability to map paraphrased natural questions to the correct node-state pairs, which is exactly the error rate the authors observe.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the induced Bayesian network being the true model of each table, on the LLM translating questions into that network's node-state vocabulary, and on a set of unreported hyperparameters. The same network is used to create ground truths and to run Auto-BN, so the method's inference stage is not independently validated.

free parameters (5)
  • state_discretization_bins = not reported (states per node averages 4.94 in Table 3)
    Continuous columns are discretized into a small number of states before BN learning; bin boundaries determine the premises and all ground-truth probabilities but are not specified.
  • structure_learning_hyperparameters = not reported
    The 'modified structure learning algorithm' is never named, so score, search, and regularization choices that determine the BN are unknown.
  • premise_retrieval_top_k = 40
    Retrieval baselines use up to 40 premises per query (Appendix D.4); this cutoff affects baseline accuracy and is chosen by the authors.
  • insight_count = 20
    The insight-augmented baselines add exactly 20 high-impact insights selected by Markov blanket analysis; this number is selected by hand.
  • fallback_uniform_prior = 1/num_states
    When a model returns no valid probability, the evaluation substitutes a uniform prior over the target node's states (Section 3.6), affecting error rate and accuracy metrics.
assumptions (4)
  • domain assumption The auto-learned Bayesian network from each table is the correct probabilistic model for the benchmark questions.
    Ground truth is defined as exact inference over this network (Section 3.4), so the benchmark cannot distinguish correct data modeling from correct query translation.
  • domain assumption Each natural language question maps uniquely to node-state pairs of the induced BN.
    Auto-BN relies on the LLM to translate paraphrased Natural questions into a structured BN query (Section 4.2, D.1). Ambiguity would make both ground truth and prediction ill-defined.
  • domain assumption Learned edge directions can support the 'causal inference' query labels.
    Structure learning from observational data does not identify causal direction; the authors concede in Section 7 that edges may be correlations, yet the benchmark labels these queries causal.
  • standard math Standard Bayesian network factorization and exact variable elimination inference are valid.
    Used in Section 4.2 and D.1 for computing probabilities; this is textbook material from Pearl (1988).

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Cite this review

Pith. "Pith review of Towards Probabilistic Question Answering Over Tabular Data." pith.science (2026). https://pith.science/paper/Y64ZEF7F

@misc{pith2026250620747,
  author       = {Pith},
  title        = {Pith review of: Towards Probabilistic Question Answering Over Tabular Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Y64ZEF7F}},
  note         = {Machine review of arXiv:2506.20747}
}
read the original abstract

Current approaches for question answering (QA) over tabular data, such as NL2SQL systems, perform well for factual questions where answers are directly retrieved from tables. However, they fall short on probabilistic questions requiring reasoning under uncertainty. In this paper, we introduce a new benchmark LUCARIO and a framework for probabilistic QA over large tabular data. Our method induces Bayesian Networks from tables, translates natural language queries into probabilistic queries, and uses large language models (LLMs) to generate final answers. Empirical results demonstrate significant improvements over baselines, highlighting the benefits of hybrid symbolic-neural reasoning.

Figures

Figures reproduced from arXiv: 2506.20747 by the authors.

Figure 1
Figure 1. Probabilistic queries over tabular data integrates the output of probabilistic inference into the prompt of a large language model (LLM) to produce natural language answers ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Auto-Learned Bayesian Network Structure on [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Probabilistic Query Types 3.3 Benchmark Artifacts As mentioned before, for each table in the bench￾mark, besides for table SQLite file and correspond￾ing table description, the following artifacts ( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Benchmark Structure and Artifacts [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: Question Types in LUCARIO Real-world questions involving uncertainty are often expressed in diverse and nuanced ways. While many existing benchmarks for probabilistic reasoning primarily use formulations that closely mirror the symbolic representation of variables and …
Figure 7
Figure 7. Figure 7: Case Study for Factual Method on Prob. QA [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Performance of baselines by question type. Bars represent [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

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