Causal Preference Elicitation Methods

• Causal preference elicitation is a family of methods that extract, model, and update beliefs about causal structures using expert judgments and observed choices.
• State-of-the-art approaches, such as the CaPE framework, leverage Bayesian techniques, structural equation models, and active learning to efficiently concentrate posterior distributions over DAGs.
• Applications include expert-in-the-loop data science, econometric identification, and AI alignment, offering practical tools for robust causal discovery.

Causal preference elicitation refers to a family of methodologies for extracting, modeling, and updating beliefs about causal structures through informative queries or revealed preferences, incorporating both expert judgments and observed choices to resolve uncertainty about directed edge relations in causal graphs. State-of-the-art approaches leverage Bayesian frameworks, structural equation models, and active learning principles to efficiently concentrate posterior distributions over directed acyclic graphs (DAGs) or to identify subjective causal models from observed behavior. This field sits at the intersection of causal discovery, preference learning, and experimental design, with applications spanning expert-in-the-loop data science, econometric identification, and the alignment of machine learning systems with human values.

1. Bayesian Frameworks for Expert-in-the-Loop Causal Discovery

A canonical instantiation of causal preference elicitation is the Causal Preference Elicitation (CaPE) framework, a fully probabilistic, sequential Bayesian architecture for actively concentrating beliefs over DAGs through targeted queries to human experts (Bonilla et al., 1 Feb 2026). The CaPE framework starts from a prior $p(G)$ over DAGs %%%%1%%%% on $D$ nodes, frequently parameterized with a sparsity-controlling hyperparameter $\rho$ as

$$p(G) = \begin{cases} \frac{\rho^{|E(G)|} (1-\rho)^{\binom{D}{2}-|E(G)|}}{\sum_{G'} \rho^{|E(G')|} (1-\rho)^{\binom{D}{2}-|E(G')|}}, & G \text{ acyclic} \ 0, & \text{otherwise} \end{cases}$$

Given any black-box observational posterior $q_0(G)$ (e.g., from MCMC or bootstrap resampling), CaPE incorporates expert feedback as categorical judgments about local edge relations—whether $i \to j$, $j \to i$, or neither exists—modeled via a three-way conditional independent likelihood with parameters reflecting expert reliability and decisiveness.

Expert feedback is formally represented as a sequence of responses $$\mathcal D_{1:t} = \{(i_\tau, j_\tau, y_\tau)\}_{\tau=1}^t$$, and yields an updated posterior via importance weighting over sampled particles:

$$p\bigl(G\mid X, \mathcal D_{1:t}\bigr) \propto q_0(G) \prod_{\tau=1}^t p_\theta( y_\tau | (i_\tau, j_\tau), G )$$

where $p_\theta$ encodes the three-way likelihood over edge existence and direction, parameterized by $(\beta_{\mathrm{edge}}, \beta_{\mathrm{dir}})$.

2. Likelihood Modeling and Noisy Judgments

Likelihood modeling of expert feedback utilizes local summary scores for each candidate $G$, where $s_{i\to j}(G)$ captures a link-function-transformed edge weight plus optional structural features. The probability of edge existence and direction is computed as

$$p_{\mathrm{edge}}(G; i, j) = \sigma(\beta_{\mathrm{edge}} a_{ij}(G)), \quad p_{i\to j \mid \mathrm{edge}}(G; i, j) = \sigma(\beta_{\mathrm{dir}} d_{ij}(G))$$

with $a_{ij}(G) = \max\{ s_{i\to j}(G), s_{j\to i}(G) \}$ and $d_{ij}(G) = s_{i\to j}(G) - s_{j\to i}(G)$. The joint categorical response likelihood over $(i, j)$ then satisfies:

$$\begin{aligned} p_\theta\left( Y_{ij}=2|G \right) & = 1 - p_{\mathrm{edge}} \ p_\theta\left( Y_{ij}=1|G \right) & = p_{\mathrm{edge}} \cdot p_{i\to j\mid\mathrm{edge}} \ p_\theta\left( Y_{ij}=0|G \right) & = p_{\mathrm{edge}} \cdot (1 - p_{i\to j\mid\mathrm{edge}}) \end{aligned}$$

This construction enables robust modeling of both uncertainty and bias in expert judgments, and is essential for realistic posterior contraction in the presence of noisy or inconsistent responses.

3. Adaptive Query Selection via Information Gain

Active query policies in CaPE are driven by a BALD-style expected information gain (EIG) criterion, quantifying the mutual information between an expert's categorical response $Y_{ij}$ and the latent graph structure $G$ under the current posterior $q_t(G)$. For a candidate edge $(i,j)$, EIG is:

$$\mathrm{EIG}_t(i,j) = H_t^{ij} - \sum_{s=1}^S w_t^{(s)} H\left( p_\theta( \cdot | G^{(s)} ) \right)$$

where $H_t^{ij}$ is the entropy of the marginal predictive for $(i,j)$ across posterior particles, and the second term averages the conditional entropy under each particle $G^{(s)}$. In practice, EIG is computed only for a screened subset of candidate edge pairs with highest marginal uncertainty, ensuring computational tractability in high dimensions.

This adaptive selection provides a principled trade-off between exploration (querying highly uncertain edges) and exploitation (focusing on edges where the expert is maximally informative), yielding rapid posterior concentration even under tight query budgets.

4. Subjective Causality and Revealed Preference Identification

Beyond expert query frameworks, causal preference elicitation encompasses the identification of a decision maker's subjective causal model from revealed preferences over interventions or choices (Halpern et al., 2024, Ellis et al., 2021). In the axiomatic approach of Halpern & Piermont (Halpern et al., 2024), preferences over primitive and compound interventions on endogenous variables induce a unique (up to u-equivalence) recursive structural equation model $M = (U, V, F)$, a state distribution $\mu$, and a utility $u$ over outcomes. The key axioms (Cancellation, Model-Uniqueness, Definiteness, Centeredness, Recursivity) are necessary and sufficient for representing the agent’s behavior as expected utility maximization in a causal model.

Ellis & Thysen (Ellis et al., 2021) formalize revealed-causal-choice identification by linking an agent’s stochastic choice rule $\rho(a|q)$ to the underlying DAG $G$, the set of confounders, and active causal paths (minimal active paths—MAPs) used in her reasoning. Methodologies are provided to recover confounders and paths by constructing separating datasets and analyzing revealed choice probabilities, with formal identification results when data are exogenous or even generated endogenously by the agent’s own past decisions.

5. Causal Elicitation in Preference Learning and AI Alignment

In contemporary AI alignment and reward modeling, causal preference elicitation is foundational for robust generalization from noisy, heterogeneous, or confounded human feedback. A causal lens is indispensable for preference learning, as highlighted in recent work in LLM alignment (Kobalczyk et al., 6 Jun 2025). Here, each preference query is conceptualized as an interventional assignment, with latent user covariates $U$ and prompt/response features $(X,Y,Y')$ mediating confounding and reward heterogeneity.

Failure to address confounding, limited overlap, or preference heterogeneity yields causal misidentification (e.g., spurious correlations such as response length bias), undermining out-of-distribution robustness. Causally inspired solutions include stratified estimators for observed confounders, randomized prompt assignment, instrumental variables, latent-factor adjustment, and adversarial representation learning for deconfounding. These approaches explicitly model both the data-generating process and the conditions for identifiability of causal effects, providing modelers with theoretical and empirical guidelines for preference robustification.

6. Empirical Results and Performance Benchmarks

The effectiveness of causal preference elicitation frameworks such as CaPE has been substantiated on both synthetic and real-world benchmarks (Bonilla et al., 1 Feb 2026). On synthetic Erdős–Rényi graphs ($D=20$), CaPE’s EIG-based policy achieves a fivefold reduction in predictive entropy and a 40% reduction in structural Hamming distance compared to baselines, with sharply increased expected true-class probability. On biological networks such as Sachs protein signaling ($D=11$) and CRISPR gene perturbation ($D=50$), a few dozen targeted queries rapidly sharpen the posterior on edge existence and direction, outperforming static and uncertainty-sampling baselines on metrics such as AUPRC, SHD, and orientation F1.

These empirical results underscore the efficiency and scalability of active, expert-in-the-loop methods, as well as the value of targeted, causally meaningful interventions in data collection and experimental design.

7. Guidelines, Limitations, and Open Directions

Practical deployment of causal preference elicitation methods requires judicious modeling of expert reliability, careful decoupling of data-driven and expert-informed posteriors, robust particle approximations (with resampling and M-H rejuvenation), and selective query targeting via information gain. The identification of subjective causal models from revealed preferences depends critically on the richness of the variable space, support of the data, and validation of agent rationality via axiomatic consistency checks.

Open challenges include scaling to larger and structured variable domains, unsupervised identification of latent causal factors, principled integration of user rationales and meta-feedback, and rigorous active design for optimal preference elicitation under limited query budgets. In high-stakes applications such as AI alignment and policy evaluation, future work emphasizes compositional causal representation learning, causal verification under distribution shift, and the merging of expert, revealed, and observational sources of causal information.

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Summary Table: Representative Causal Preference Elicitation Approaches

Approach	Domain	Mechanism
CaPE (Bonilla et al., 1 Feb 2026)	Expert-in-the-loop	Bayesian particles + EIG queries
Revealed subjective (Halpern et al., 2024, Ellis et al., 2021)	Human choice / intervention	Axioms + preference identification
Causal RLHF (Kobalczyk et al., 6 Jun 2025)	LLM preference learning	Causal DAG, confounder control

These approaches collectively demonstrate the centrality of causal reasoning, active learning, and expert or agent interaction in the modern landscape of preference elicitation and causal discovery.