BN Construction Methods Comparison

Summary

Three approaches to constructing a Bayesian network are compared on the Sleep Health and Lifestyle dataset: (I) human expert knowledge, (II) information-criteria-based structure learning (BIC/MIIC), and (III) LLM-based expert elicitation. BN III (LLM) achieves the lowest entropy, fewer logical inconsistencies, and strong SEM validation.

Overview

The paper frames the three BN construction strategies as:

Data → Stats. (BIC/MIIC) → BN II → Decision Support
     ↗ Expert knowledge   → BN I  ↗
     ↘ LLM elicitation    → BN III↗

All three BNs are constructed on the Sleep Health and Lifestyle Dataset (400 rows, 13 columns; variables: sleep duration, stress level, physical activity, BMI, occupation, gender, age, heart rate, quality of sleep, sleep disorder, daily steps).

BN I — Human Expert

Method: Researchers with limited domain knowledge manually specify edges based on common sense and existing literature.

Structure (10 nodes):

• Age, Gender → Occupation → Physical_Activity_Level → Stress_Level → Heart_Rate
• Daily_Steps → Physical_Activity_Level
• BMI_Category → Physical_Activity_Level
• Stress_Level → Sleep_Duration → Quality_of_Sleep

SEM Validation: All relationships statistically significant except:

• Physical_Activity → Stress_Level (p > 0.05)
• Stress_Level → Heart_Rate (p > 0.05)

Key problem: Human expert graph shows causal direction inconsistencies — e.g., graph indicates Stress_Level → Occupation, but logically occupation influences stress, not vice versa.

BN II — Information Criteria (BIC/MIIC)

Methods:

• MIIC (Multivariate Information-based Inductive Causation): identifies dependencies via conditional mutual information; good at finding latent confounders
• BIC (Bayesian Information Criterion): $\text{BIC}=-2\log L+k\log n$, where $L$ = likelihood, $k$ = free parameters, $n$ = data points. Scores candidate graphs by penalized likelihood.

Key problem: BIC graphs frequently misidentify causal directions (e.g., Occupation impacts Age and Gender, whereas these should be root causes). Statistical associations in the data do not guarantee correct causal directionality.

SEM validation: Most relationships significant, except Stress_Level → Occupation (p = 0.0708).

BN III — LLM Expert Elicitation

See LLM Expert Elicitation for Bayesian Networks for full methodology.

Structure highlights (Fig. 4):

• Gender → Sleep_Disorder, Occupation, Sleep_Duration
• Daily_Steps → Physical_Activity_Level → BMI_Category
• Occupation → Stress_Level; Sleep_Duration → Stress_Level
• Stress_Level → Quality_of_Sleep; Sleep_Duration → Quality_of_Sleep

SEM validation: All statistically significant except Physical_Activity → Quality_of_Sleep (p = 0.5989).

Advantage: Logically consistent causal directions; fewer backward edges; confounders identified.

Entropy Comparison

See Entropy-Based BN Evaluation for full entropy analysis. Summary:

Method	Mean $H$	Min $H$	Median $H$
LLM	1.42	0.89	1.29
BIC	1.48	0.91	1.32
Expert	1.48	0.93	1.21

Lower entropy = more structured, clearer dependencies. LLM wins on mean and min entropy.

Connections

• Provides context for LLM Expert Elicitation for Bayesian Networks (methodology of BN III)
• Quantitative evaluation in Entropy-Based BN Evaluation
• Application in LLM-BN Decision Support Application

See Also

• Shaposhnyk 2025 - Overview — paper context
• Entropy-Based BN Evaluation — quantitative comparison
• LLM Expert Elicitation for Bayesian Networks — full BN III methodology
• Directed Acyclic Graphs — the causal DAG theory that underpins BN structure and d-separation
• Causal Discovery - Overview — data-driven structure learning vs expert elicitation