Causal Concept-Based Post-Hoc XAI Explained

• Causal concept-based post-hoc XAI is a framework that integrates human-interpretable semantic concepts with causal reasoning to provide counterfactual explanations.
• It employs structured causal models and quantitative estimands like ATE and DIE% to assess fairness, robustness, and interpretability with high fidelity.
• The approach advances beyond standard feature attribution by linking interventions in concept space to actionable recourse recommendations that enhance model transparency.

Causal concept-based post-hoc explainable artificial intelligence (XAI) integrates human-interpretable semantic concepts and causal reasoning into the analysis of black-box models. This paradigm provides explanations by intervening on high-level concepts within structured causal models (SCMs), quantifies the sufficiency and necessity of concept changes for decision outcomes, and enables actionable recourse while preserving model fidelity. It advances beyond standard feature-attribution methods by formally linking model behavior to interventions in a concept space, explicitly accounting for confounding, and supporting global, local, and contextual explanations.

1. Concept Layer and Structural Causal Models

Causal concept-based XAI introduces a concept layer comprising semantically interpretable variables (e.g., “Gray Hair”, “Suspicious Email”) and encodes the dependencies between these concepts using an SCM. Each concept variable $z_i$ is modeled via a structural equation $z_i \leftarrow f_i(\mathrm{pa}_i, u_i)$, with $\mathrm{pa}_i$ denoting the parent concepts and $u_i$ denoting exogenous noise. Explanations are obtained through counterfactual queries, such as $do(\bar z = \bar z')$, which represent interventions that set selected concepts to alternative values (Bjøru et al., 2 Dec 2025).

Mapping between concept space and data space is handled via (often invertible) decoders $\alpha: (z, w) \mapsto x$, with $w$ capturing remaining variation. Fidelity requires this decoder to be sufficiently high-performing so that counterfactuals only reflect intended concept changes, and that omitted factors $w$ remain independent of $z$. Violations may result in misleading explanations, especially under coarse or incomplete concept definitions or non-Markovian causal structures (Bjøru et al., 2 Dec 2025, Moreira et al., 16 Jan 2024).

2. Quantitative Causal Estimands and Hypothesis Testing

Explanations rely on formal causal quantities calculated with respect to concept interventions:

• Average Treatment Effect (ATE): $\mathrm{ATE} = E[O|do(T = t_1)] - E[O|do(T = t_0)]$ quantifies mean change in outcome $O$ under interventions on treatment concept $T$ (Lakkaraju et al., 7 Aug 2025).
• Deconfounded Impact Estimation (DIE%): $$\mathrm{DIE\%} = 100 \times | \mathrm{ATE}_{unadj} - \mathrm{ATE}_{deconf} |$$ measures change in causal effect after adjustment for confounders (typically protected attributes $Z$ via propensity score matching or G-computation).
• Probability of Sufficiency: $$P_{\mathrm{suff}}(do(z_i=1) \rightarrow y=1 \mid z_i=0, y=0)$$ is the probability that setting concept $z_i$ to a new value would flip the decision in a given context (Bjøru et al., 2 Dec 2025).
• Weighted Rejection Score (WRS): A group-level bias metric using weighted $t$-tests over outcome distributions by sensitive attributes (Lakkaraju et al., 7 Aug 2025).
• Contrastive Counterfactual Scores: Necessity and sufficiency scores, as in LEWIS, directly quantify “how likely would $O$ flip if $X$ were $x'$” in a specified context, supporting both direct and indirect causal influence (Galhotra et al., 2021).

These estimands support the evaluation of both individual and group-level explanations. They enable rigorous hypothesis testing regarding model fairness, robustness, or susceptibility to confounding, as demonstrated in financial risk and medical diagnosis case studies (Lakkaraju et al., 7 Aug 2025, Bjøru et al., 2 Dec 2025, Galhotra et al., 2021).

3. Algorithmic Workflows: Local and Global Explanations

Causal concept-based post-hoc XAI workflows typically consist of:

1. Stakeholder Query Selection: Mapping stakeholder questions to explanation modalities (instance-wise, group-level, bias/robustness).
2. Causal Graph Specification: Defining the SCM over concepts—either expert-driven or learned via constraint/score-based methods (e.g., FCI, PC, ICA-LiNGAM, NO-TEARS) (Sani et al., 2020, Moreira et al., 16 Jan 2024).
3. Estimand Calculation: Computing ATE, DIE%, WRS, counterfactual probabilities or attribution scores through abduction-action-prediction procedures, propensity-score methods, or do-calculus.
4. Baseline Generation: Constructing random and biased baselines for fairness and reliability assessment (biassed: predictions depend only on protected attribute; random: predictions from uniform/marginal distributions) (Lakkaraju et al., 7 Aug 2025).
5. Post-hoc Drill-Down: Employing standard XAI tools (e.g., SHAP, counterfactual simulation) for root cause analysis on flagged instances or subpopulations.
6. Recourse Optimization: Solving minimal-cost actionable concept interventions subject to sufficiency thresholds, typically via efficient integer programming (Galhotra et al., 2021).

This iterative, interactive process adapts explanation granularity and modality to each stakeholder’s context, exemplified in H-XAI’s multi-method workflow (Lakkaraju et al., 7 Aug 2025).

4. Faithfulness, Alignment, and Interpretability Criteria

Explanatory fidelity in causal concept-based XAI requires alignment between model representations, human concept vocabularies, and the true causal structure (Marconato et al., 2023). Alignment is defined as a bijective or surjective mapping between machine representations $Z$ and human-understood generative factors $G$, operationalized via:

• Disentanglement (EMPIDA score): Ensuring each machine concept $M_j$ depends on exactly one human factor $G_i$, invariant under interventions on others.
• Monotonicity: Concept activation maps exhibit monotonic (in expectation) responses to interventions, supporting robust symbolic communication.
• Content-Style Separation and Concept Leakage: Interpretable representations must insulate content (meaningful concepts) from style or confounded factors, quantified via information-theoretic bounds on leakage (Marconato et al., 2023).

Algorithmically, this is achieved by collecting annotated concept datasets, training encoders (e.g., VAEs, bottleneck models), estimating alignment via intervention experiments and monotonic regression, and extracting probes or surrogates faithful to both human and model semantics (Bjøru et al., 2 Dec 2025, Marconato et al., 2023).

5. Baseline Construction, Bias Auditing, and Robustness Assessments

Causal concept-based post-hoc XAI frameworks include baseline comparisons and bias auditing as central elements. Random and biased baselines are constructed synthetically:

Baseline Type	Construction	Diagnostic Interpretation
Random	Predictions sampled i.i.d. from uniform/marginal	Reveals model reliability
Biased	Predictions function only of protected attribute Z	Reveals model fairness

If a model’s RDE score matches the biased baseline, fairness concerns arise; similarity to random baseline suggests unreliability (Lakkaraju et al., 7 Aug 2025). These baselines contextualize causal scores and support automatic, hypothesis-driven bias flagging. Robustness to perturbations or missing data is assessed by evaluating residual errors under $do$-interventions on input perturbations and by causal estimation of impact across sensitive groups (Lakkaraju et al., 7 Aug 2025).

6. Limitations, Extensions, and Comparison to Standard XAI

Key limitations of causal concept-based XAI are:

• Complete and correct specification of SCMs can be challenging, especially in high-dimensional or poorly understood domains; generator fidelity (e.g., StarGAN) may be insufficient to isolate concept changes (Bjøru et al., 2 Dec 2025, Moreira et al., 16 Jan 2024).
• Selection and annotation of semantically complete concept sets is non-trivial; missing concepts or unmeasured confounders bias estimands (Moreira et al., 16 Jan 2024).
• Computational costs scale with the number of concept interventions and SCM complexity.
• Aggregative metrics (ATE, WRS) can mask subgroup heterogeneity (Lakkaraju et al., 7 Aug 2025).

Contrasted with correlation-based post-hoc methods such as SHAP or LIME, which are limited to feature-attribution and do not support causal reasoning, concept-based causal frameworks offer:

• Causal, counterfactual answerability—quantifying the probability that interventions would flip outcomes.
• Formal adjustment for confounding, supporting fair and reliable explanations.
• Recourse recommendations and hypothesis-driven audits (Galhotra et al., 2021, Moreira et al., 16 Jan 2024).

Extensions involve adoption of higher-fidelity causal generators, automated concept discovery, strengthening of SCM specification via expert-data fusion, and integration with recourse and fairness tooling (Bjøru et al., 2 Dec 2025, Moreira et al., 16 Jan 2024).

7. Empirical Evaluation and Benchmarking

Empirical studies in the literature validate causal concept-based post-hoc XAI across image (CelebA, CUB-200), tabular (credit, fraud), and medical datasets. DiConStruct is shown to achieve higher fidelity to black-box models (up to 99% in local variants) while maintaining concept accuracy, outperforming joint/distill CBMs (Moreira et al., 16 Jan 2024). Probability-of-sufficiency and contrastive scores reliably identify actionable concepts and drivers of prediction in tasks from face attribute classification to fraud detection and medical risk stratification (Bjøru et al., 2 Dec 2025, Lakkaraju et al., 7 Aug 2025, Galhotra et al., 2021).

This body of research demonstrates the potential for structured, causal concept-based explanations to advance AI interpretability, fairness, and stakeholder trust by delivering transparent and actionable insights into complex model behavior.