LLM-Augmented Causal Discovery: Probabilistic Fusion of Edge Existence and Orientation

Neville K. Kitson; Anthony Constantinou

cs.AIAug 19, 2026

LLM-Augmented Causal Discovery: Probabilistic Fusion of Edge Existence and Orientation

Authors: Neville K. Kitson, Anthony Constantinou

Organizations: Machine Intelligence and Decision Systems (MInDS) Group, School of Electronic Engineering and Computer Science, Queen Mary University of London, London, United Kingdom, E1 4NS.

Abstract

Bayesian network structure learning (BNSL) from observational data struggles with orientation identifiability, while large language models (LLMs) offer broad but often unreliable causal knowledge. We propose combining these complementary sources through a novel representation, termed Probabilistic Dependency Graphs (PDGs). In a PDG, each edge is associated with a distribution over directed, undirected, and absent states, enabling fusion via weighted averaging. We evaluate this approach on 26 benchmark networks, combining ensembles of three BNSL algorithms (FGES, Tabu, PC) with three LLMs (Gemini, Claude, GPT) across multiple prompts and random seeds. A simple 50/50 fusion improves F1 over the better of either source alone in 22 of 26 networks, with a statistically significant mean improvement of $0.056$ $(p<0.001)$ . Analysis reveals that the two sources play complementary roles: BNSL contributes a high-recall edge skeleton (80% vs 60% for LLM), while LLM contributes accurate edge orientation (96% vs 77% for BNSL). Our results show that representing both sources as probabilistic uncertainty over edge existence and orientation is a practical and effective way to improve causal graph accuracy.

Figures & tables

Figure 1: Creating a causal DAG by fusing LLM knowledge and statistical learning. Maroon-coloured flows represent standard BNSL, grey flows are LLM interactions, and teal-coloured flows show the fusion of BNSL and LLM outputs to arrive at a final causal DAG. This is then evaluated against the original network definition.

Figure 2: Percentage of edges in agreement as regards existence and orientation for LLM and BNSL sources. The x-axis categorises the probability of the more likely outcome for each edge: whether the edge exists or not, and its direction. The y-axis shows the percentage of edges falling in each category.

Comparison	Wins	Losses	Mean $\Delta$ F1	$W$	$p$
Fusion vs. BNSL	23	3	+0.099	17.0	$<$ 0.001
Fusion vs. LLM	25	1	+0.188	3.0	$<$ 0.001
Fusion vs. best of either	22	4	+0.056	36.0	$<$ 0.001

Table 1: Summary of fusion improvement in F1 over BNSL and LLM alone (26 networks, 10K samples). Wilcoxon signed-rank two-sided test.

Figure 3: Change in F1 moving from the best of BNSL and LLM to the fused DAG plotted against number of variables in the network.

Figure 4: (A) Edge-recall (fraction of reference arcs detected at $p_{exist}\geq 0.3$ ) and (B) orientation accuracy (fraction of detected reference arcs correctly directed) for BNSL, LLM, and the fused PDG across 26 benchmark networks.

Ablation Type	Ablation 1	Ablation 2	Ablation 3	Diversity Gain
LLM Model	Gemini: 0.700	Claude: 0.683	GPT: 0.714	+0.046
BNSL Algorithm	FGES: 0.721	Tabu: 0.672	PC: 0.654	+0.039
LLM Repetition	First: 0.727	Second: 0.734	Third: 0.725	+0.026
Prompt Detail	Minimal: 0.696	Standard: 0.730	—	+0.030
Sample Size	1K: 0.674	1K+10K: 0.729	—	-0.031

Table 2: Ablation results (F1 score) for each diversity axis. All values use 10K data except for the sample size row, where 1K and 1K+10K are shown. For each axis, the best single ablation is bolded. Diversity gain is the difference between the main result (10K-only, F1=0.760) and the best ablation in each row.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

LLM	Mean	Max.	Mean	Max.	Mean	Max.	Mean	Max.
	Request Tokens		Response Tokens		Cost (US cents)		Latency (secs)
claude	964	3327	1680	5239	0.00	0.00	8.0	22.3
gemini	898	3136	2464	9132	0.00	0.00	37.9	122.9
gpt	850	3049	793	1913	0.16	0.41	12.5	55.3
All	904	3327	1646	9132	0.05	0.41	19.4	122.9

Appendix

Table 3: LLM request and response sizes, costs and latency over the 468 LLM requests in this study.

Network	Domain	Source	Variables	Arcs
alarm	patient monitoring	bnlearn	37	46
asia	respiratory diagnosis	bnlearn	8	8
barley	crop yield prediction	bnlearn	48	84
child	neonatal cardiology	bnlearn	20	25
constructionprod.	construction management	bnRep	18	19
corical	vaccine risk benefit analysis	bnRep	20	26

Appendix

Table 4: Benchmark networks used in the evaluation.

Network	Nodes	BNSL	LLM	Fusion	Fusion improvement over the better of BNSL and LLM
alarm	37	0.804	0.653	0.866	+0.062
asia	8	0.750	0.842	1.000	+0.158
barley	48	0.549	0.392	0.645	+0.096
child	20	0.902	0.702	0.923	+0.021
constructionproductivity	18	0.865	0.525	0.826	-0.039
corical	20	0.727	0.824	0.833	+0.010

Appendix

Table 5: Improvement in F1 attained by fusing BNSL and LLM over the better of BNSL and LLM alone.

Network	Nodes	BNSL	LLM	Fusion	Fusion DAG SHD change over the better of BNSL and LLM
alarm	37	12.000	33.000	11.000	-1.000
asia	8	2.000	3.000	0.000	-2.000
barley	48	59.000	87.000	50.000	-9.000
child	20	3.000	17.000	3.000	0.000
constructionproductivity	18	3.000	28.000	8.000	+5.000
corical	20	10.000	9.000	8.000	-1.000

Appendix

Table 6: Change in DAG SHD attained by fusing BNSL and LLM over the better of BNSL and LLM alone.

Network	Nodes	BNSL	LLM	Fusion	Fusion CPDAG SHD change over the better of BNSL and LLM
alarm	37	13.000	38.000	11.000	-2.000
asia	8	0.000	4.000	0.000	0.000
barley	48	69.000	91.000	59.000	-10.000
child	20	1.000	22.000	5.000	+4.000
constructionproductivity	18	1.000	33.000	11.000	+10.000
corical	20	13.000	15.000	15.000	+2.000

Appendix

Table 7: Change in CPDAG SHD attained by fusing BNSL and LLM over the better of BNSL and LLM alone.

Network	Nodes	50/50 Fusion	Oracle Fusion	Optimal BNSL Weight	Oracle vs 50/50	Oracle vs best of LLM and BNSL
alarm	37	0.866	0.884	0.55	+0.018	+0.080
asia	8	1.000	1.000	0.25	+0.000	+0.158
barley	48	0.645	0.645	0.50	+0.000	+0.096
child	20	0.923	0.941	0.55	+0.018	+0.039
constructionproductivity	18	0.826	0.919	0.90	+0.093	+0.054
corical	20	0.833	0.851	0.55	+0.018	+0.028

Appendix

Table 8: Improvement in F1 using an optimal weighting of BNSL to LLM rather than 50/50

Network	Nodes	Mean Indiv.	Ensemble	Gain
alarm	37	0.766	0.804	+0.038
asia	8	0.653	0.750	+0.097
barley	48	0.476	0.549	+0.073
child	20	0.791	0.902	+0.111
constructionproductivity	18	0.767	0.865	+0.098
corical	20	0.644	0.727	+0.084

Appendix

Table 9: BNSL ensemble effect per network: F1 of the mean individual algorithm runs vs. the merged three-algorithm ensemble (10K samples).

Score	Benchmark Identification	Causal Information Leakage
0	benchmark not identifiable	no causal information present
3	application domain recognisable but benchmark unknown	mild causal hints
5	plausible benchmark identification	several causal relationships inferable
8	strong benchmark match	most graph structure inferable
10	benchmark identifiable with high confidence	graph largely recoverable from context alone

Appendix

Table 10: Benchmark Identification and Causal Information Leakage Score Scales

		Obfuscated names		Benchmark names		Fusion gain in F1 over better of LLM/BNSL
blank line Network	blank Nodes	Minimal prompt	Standard prompt	Minimal prompt	Standard prompt
alarm	37	9	9	10	10	+0.062
asia	8	7	8	10	10	+0.158
barley	48	8	8	4	8	+0.096
child	20	9	8	9	9	+0.021
construct.	18	2	6	5	7	-0.039

Appendix

Table 11: Scores out of 10 for benchmark identification estimated by Claude Opus 4.5.

		Obfuscated names		Benchmark names		Fusion gain in F1 over better of LLM/BNSL
blank line Network	blank Nodes	Minimal prompt	Standard prompt	Minimal prompt	Standard prompt
alarm	37	4	4	4	4	+0.062
asia	8	4	6	4	7	+0.096
child	20	6	4	4	4	+0.021
construct.	18	4	4	4	4	-0.039
corical	20	7	7	7	7	+0.010

Appendix

Table 12: Scores out of 10 for causal information leakage estimated by Claude Opus 4.5.

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ABSOL: Aggregated Bayesian Subsampling Orchestrated with LLMs

Jackson Hassell, Chen Shen, Estevam Hruschka

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Graph Structure Learning Bayesian Network Structure Learning Bayesian Networks Probabilistic Graphical Models LLMs for Graph Learning

Open paper AskPDF arXiv

Large language models are increasingly used as natural-language interfaces to structured data, yet they remain unreliable when answers require consistent evidence conditioning, dependency-aware reasoning, and uncertainty estimation. Bayesian networks provide an explicit probabilistic reasoning layer, but learning useful structures from data remains costly and fragile at scale. We introduce ABSOL, a hybrid LLM-guided Bayesian network structure-learning framework that uses LLMs as bounded semantic guides. Across five discrete BN benchmarks spanning 27 to 1041 nodes, ABSOL is the only evaluated method to produce a viable graph on every benchmark, and achieves the highest Edge F_1 on every benchmark larger than 27 nodes with GPT-5.4. The four LLM augmentations, which contribute complementary semantic evidence to the statistical backbone, improve Edge F_1 over the non-LLM aggregation backbone by +0.23 on average. Complementary post-hoc refinement experiments suggest that these gains depend in part on limiting the LLM's authority over the final structure. Together, these results show that language-derived semantic knowledge can substantially improve scalable probabilistic structure learning when used as bounded guidance within a statistically grounded reasoning pipeline. The code for ABSOL is available at github.com/megagonlabs/absol-bn.

Abstract

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