Traceable Latent Variable Discovery Based on Multi-Agent Collaboration
Authors: Huaming Du, Tao Hu, Yijie Huang, Yu Zhao, Guisong Liu, Tao Gu, Gang Kou, Carl Yang
Organizations: Southwestern University of Finance and Economics, Chengdu, Sichuan, China · Hunan University of Technology and Business, Xiangjiang Laboratory, Hunan, China · Emory University, Atlanta, Georgia, United States
Revealing the underlying causal mechanisms in the real world is crucial for scientific and technological progress. Despite notable advances in recent decades, the lack of high-quality data and the reliance of traditional causal discovery algorithms (TCDA) on the assumption of no latent confounders, as well as their tendency to overlook the precise semantics of latent variables, have long been major obstacles to the broader application of causal discovery. To address this issue, we propose a novel causal modeling framework, TLVD, which integrates the metadata-based reasoning capabilities of large language models (LLMs) with the data-driven modeling capabilities of TCDA for inferring latent variables and their semantics. Specifically, we first employ a data-driven approach to construct a causal graph that incorporates latent variables. Then, we employ multi-LLM collaboration for latent variable inference, modeling this process as a game with incomplete information and seeking its Bayesian Nash Equilibrium (BNE) to infer the possible specific latent variables. Finally, to validate the inferred latent variables across multiple real-world web-based data sources, we leverage LLMs for evidence exploration to ensure traceability. We comprehensively evaluate TLVD on three de-identified real patient datasets provided by a hospital and two benchmark datasets. Extensive experimental results confirm the effectiveness and reliability of TLVD, with average improvements of 32.67% in Acc, 62.21% in CAcc, and 26.72% in ECit across the five datasets.
Figures & tables
Figure 1. A toy example of latent variable discovery using tabular data. figure1
Figure 2. The overview of TLVD framework. framework.
Figure 3. The train process of MALLM. Optimization Phase for Belief Network.
Figure 4. The reasoning process of MALLM. Optimization Phase for Belief Network.
Dataset
#Domain
#Sample
#Number of observed variables
#Number of latent variables
WCHSU-Cancer
Medical
200,000
12/22
6/4
WCHSU-Pain
Medical
1,568
16
4
Multitasking Behaviour Study
Social Science
202
9
4
Teacher’s Burnout Study
Social Science
599
32
11
Table 1. Statistics of datasets.
WCHSU-Cancer ( n=12 )
WCHSU-Cancer ( n=22 )
WCHSU-Pain
Methods
ACC
CAcc
ECit
ACC
CAcc
ECit
ACC
CAcc
ECit
GPT5
0.134 ± 0.067
0.100 ± 0.094
0.031 ± 0.029
0.150 ± 0.122
0.116 ± 0.039
0.079 ± 0.027
0.150 ± 0.122
0.095 ± 0.061
0.095 ± 0.061
Gemini-deepresearch
0.267 ± 0.081
0.286 ± 0.046
0.154 ± 0.024
0.300 ± 0.100
0.347 ± 0.042
0.236 ± 0.029
0.250 ± 0.000
0.338 ± 0.031
0.284 ± 0.026
OpenAI-deepresearch
0.433 ± 0.082
0.560 ± 0.049
0.215 ± 0.019
0.550 ± 0.100
0.214 ± 0.165
0.214 ± 0.089
0.550 ± 0.100
0.253 ± 0.050
0.200 ± 0.039
Qwen-deepresearch
0.200 ± 0.066
0.500 ± 0.000
0.077 ± 0.000
0.250 ± 0.000
0.271 ± 0.029
0.271 ± 0.029
0.300 ± 0.100
0.500 ± 0.158
0.105 ± 0.033
Doubao-deepresearch
0.000 ± 0.000
0.150 ± 0.050
0.038 ± 0.070
0.000 ± 0.000
0.000 ± 0.000
0.000 ± 0.000
0.150 ± 0.122
0.000 ± 0.000
0.000 ± 0.000
Table 2. Performance evaluation of different models.
WCHSU ( n=12 )
WCHSU ( n=22 )
WCHSU-Pain
Methods
ACC
CAcc
ECit
ACC
CAcc
ECit
ACC
CAcc
ECit
GPT5
0.120 ± 0.098
0.074 ± 0.042
0.074 ± 0.042
0.000 ± 0.000
0.111 ± 0.070
0.033 ± 0.021
0.133 ± 0.163
0.51 ± 0.0037
0.36 ± 0.0056
Gemini-deepresearch
0.240 ± 0.013
0.084 ± 0.042
0.084 ± 0.042
0.200 ± 0.163
0.160 ± 0.013
0.160 ± 0.013
0.266 ± 0.133
0.000 ± 0.000
0.000 ± 0.000
OpenAI-deepresearch
0.600 ± 0.126
0.388 ± 0.029
0.347 ± 0.026
0.667 ± 0.000
0.180 ± 0.016
0.180 ± 0.016
0.600 ± 0.134
0.318 ± 0.047
0.318 ± 0.047
Qwen-deepresearch
0.440 ± 0.080
0.225 ± 0.094
0.095 ± 0.039
0.200 ± 0.163
0.289 ± 0.089
0.087 ± 0.027
0.266 ± 0.133
0.000 ± 0.000
0.000 ± 0.000
Doubao-deepresearch
0.000 ± 0.000
0.000 ± 0.000
0.000 ± 0.000
0.133 ± 0.163
0.000 ± 0.000
0.000 ± 0.000
0.067 ± 0.133
0.000 ± 0.000
0.000 ± 0.000
Table 3. Performance evaluation of different models, where we randomly sample half of the original dataset.
WCHSU-Cancer ( n=12 )
WCHSU-Pain
Methods
ACC
CAcc
ECit
ACC
CAcc
ECit
Homo. (2 × LLaMA3.1 8B)
0.500
1.000
0.115
0.500
1.000
0.474
Homo. (2 × LLaMA3.1 70B)
0.833
1.000
0.462
0.850
1.000
0.737
Hetero. (LLaMA3.1 8B, Qwen2.5 7B)
0.333
1.000
0.346
0.250
1.000
0.421
Hetero. (LLaMA3.1 70B, Qwen2.5 72B)
0.500
1.000
0.346
0.750
1.000
0.632
TLVD
0.833
0.900
0.415
0.800
0.886
0.453
Table 4. Performance of different configurations.
Figure 5. Case study. figure-failure
Figure 6. Impact of data sources on model performance. figure-failure
Figure 7. Failure Attribution of Our Method. Note that the vertical axis represents specific failure modes, and the horizontal axis represents their respective proportions.
Appendix figures & tables6 assets
Supplementary material from the paper’s appendix.
Appendix
Multitasking Behaviour
Teacher’s Burnout Study
Methods
ACC
CAcc
ECit
ACC
CAcc
ECit
GPT5
0.250 ± 0.047
0.083 ± 0.053
0.083 ± 0.053
0.145 ± 0.045
0.069 ± 0.029
0.032 ± 0.013
Gemini-deepresearch
0.500 ± 0.000
0.657 ± 0.070
0.383 ± 0.041
0.364 ± 0.100
0.315 ± 0.038
0.146 ± 0.017
OpenAI-deepresearch
0.350 ± 0.122
0.150 ± 0.062
0.150 ± 0.062
0.564 ± 0.068
0.762 ± 0.049
0.354 ± 0.023
Qwen-deepresearch
0.050 ± 0.100
0.000 ± 0.000
0.000 ± 0.000
0.164 ± 0.068
0.154 ± 0.024
0.071 ± 0.011
Doubao-deepresearch
0.000 ± 0.000
0.000 ± 0.000
0.000 ± 0.000
0.127 ± 0.045
0.131 ± 0.039
0.061 ± 0.018
Appendix
Table 5. Performance comparison on benchmark datasets.
WCHSU-Cancer ( n=12 )
WCHSU-Pain
Methods
ACC
CAcc
ECit
ACC
CAcc
ECit
GPT5
0.200 ± 0.245
0.125 ± 0.065
0.125 ± 0.065
0.300 ± 0.187
0.100 ± 0.033
0.100 ± 0.033
Gemini-deepresearch
0.100 ± 0.200
0.000 ± 0.000
0.000 ± 0.000
0.100 ± 0.122
0.191 ± 0.021
0.163 ± 0.018
OpenAI-deepresearch
0.500 ± 0.316
0.250 ± 0.258
0.250 ± 0.135
0.450 ± 0.100
0.450 ± 0.041
0.200 ± 0.018
Qwen-deepresearch
0.200 ± 0.245
0.217 ± 0.027
0.208 ± 0.000
0.300 ± 0.100
0.443 ± 0.029
0.237 ± 0.018
Doubao-deepresearch
0.100 ± 0.200
0.208 ± 0.037
0.250 ± 0.113
0.150 ± 0.122
0.000 ± 0.000
0.000 ± 0.000
Appendix
Table 6. Performance comparison of models using the Hier. rank ( Huang et al., 2022 ) method.
WCHSU-Cancer ( n=12 )
WCHSU-Pain
Methods
ACC
CAcc
ECit
ACC
CAcc
ECit
Qwen3 235B
0.833
1.000
0.385
0.500
1.000
0.316
Llama 4 Maverick
0.500
0.750
0.115
0.750
1.000
0.474
GPT-oss-120B
0.667
1.000
0.269
1.000
1.000
0.632
DeepSeek-v3
0.833
1.000
0.385
0.750
0.857
0.368
Appendix
Table 7. Comparison of performance using different LLMs.
Figure 8. Performance of evaluation for ablation study on WCHSU-Cancer (n=12) and WCHSU-Pain. figure-failure
Figure 9. Performance comparison with different N and γ . WCHSU-parameter
Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan · Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan
Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China · Department of Applied Statistics, Beijing Technology and Business University, Beijing, China · College of Computer Science and Artificial Intelligence, Fudan University, Shanghai, China