Contrastive Causal Explanations

• Contrastive causal explanations are methods that determine why outcome Y occurs rather than Y' by identifying specific variable changes within an explicit causal framework.
• They integrate counterfactual reasoning with structured causal models like Pearl's SCM to distinguish between predictive contrasts and genuine causal interventions.
• Empirical studies and computational approaches highlight divergence between predictive flips and intervention-based explanations, emphasizing challenges in practical application.

Contrastive causal explanations are explanations that answer questions of the form “Why outcome $Y$ rather than $Y'$?” by identifying the variable changes that would have produced the alternative outcome under an explicit causal account of the system or world. In machine learning and allied areas, they sit at the intersection of counterfactual explanation, actual causality, and interventionist explanation. A central distinction running through the literature is the difference between a predictive contrast—what would flip a model’s output—and a causal contrast—what intervention would change the outcome under the relevant causal structure. Several recent works argue that these notions often diverge, so a counterfactual that is close in feature space or effective for a predictor need not be a valid contrastive causal explanation (Smith, 2023, White et al., 2021, Galhotra et al., 2021).

1. Conceptual foundations

The topic is grounded in the observation that human explanations are often contrastive: they answer not an indeterminate “Why?”, but “Why $P$, rather than $Q$?”. In rule-based systems this is operationalized through the distinction between a fact and a foil; in maritime autonomy it is formulated as “Why did the collision avoidance system choose maneuver $\tau^*$ rather than maneuver $\tau'$?”; and in black-box prediction it is treated as a question about which macro-level features are causal “difference-makers” for $\hat Y$ (Herbold et al., 2024, Jose et al., 9 Apr 2026, Sani et al., 2020). Across these settings, the explanatory target is not merely an observed outcome but the difference between the actual outcome and a salient alternative.

The formal backbone of many accounts is the structural-model framework. In Halpern and Pearl’s structural-model approach, a causal model is built from exogenous variables, endogenous variables, and structural equations; counterfactuals are evaluated by intervening on variables and solving the modified system. Their definition of actual cause is organized by AC1, AC2, and AC3: factivity, counterfactual dependence under a contingency, and minimality (Halpern et al., 2013). Woodward’s interventionist schema similarly treats causal explanation as requiring an invariant generalization $Y = G(X)$ together with counterfactual information about how $Y$ would change under interventions on $X$ (White et al., 2021).

A recurrent theme is that contrastive explanation becomes causally substantive only when it is tied to interventions rather than correlations. One paper states that a satisfactory explanation must consist of both counterfactual instances and a causal equation or system of equations, because counterfactual instances by themselves “explain little” (White et al., 2021). Another stresses that most AI systems estimate a predictive function $Y'$0 with no underlying theoretical causal model, while users are naturally predisposed to interpret “if $Y'$1 had been different, $Y'$2 would have changed” statements causally (Tesic et al., 2022). This suggests that contrastive causal explanation is both a formal problem and a communicative one: it concerns how alternatives are generated, and what kind of causal claim those alternatives license.

2. Formalizations and explanation objects

A prominent formalization uses Pearl’s structural causal models and Pearl’s Counterfactual Method. In this framework each endogenous variable is generated by

$Y'$3

and individual-level counterfactuals take the form $Y'$4, “the value of $Y'$5 if we were to set $Y'$6 for an individual with exogenous variables $Y'$7”. The operational procedure is abduction, action, and prediction: infer the exogenous variables from the factual observation, apply a $Y'$8-intervention, and recompute the counterfactual outcome with the same background factors held fixed (Smith, 2023). In this setting, a contrastive causal explanation compares factual $Y'$9 with counterfactual $P$0 for the same individual.

A second formalization is probabilistic and explicitly contrastive. LEWIS defines three central scores: necessity,

$P$1

sufficiency,

$P$2

and necessity-and-sufficiency,

$P$3

These are probabilities of contrastive counterfactual dependence under a probabilistic causal model, and they are intended to answer questions such as why an individual received an undesirable decision rather than a favorable one, or what intervention would provide recourse (Galhotra et al., 2021).

Formal XAI and logic-based approaches define explanation objects through minimality. In the ASP-based framework for classification, a counterfactual intervention is a set of feature-value replacements that flips the label from 1 to 0, a causal explanation is the corresponding set of original feature values, and a c-explanation is a $P$4-minimal causal explanation. Explanatory responsibility for a value-explanation is

$P$5

so responsibility increases as the minimal explanation shrinks (Bertossi, 2020). In recent vision work, analogous minimality notions appear as minimal sufficient, contrastive, and complete feature sets for image classifiers, and as concept-based abductive and contrastive explanations where interventions are performed by concept erasure in internal representation space (Kelly et al., 31 Jul 2025, Canizales et al., 7 May 2026).

These families differ in explanatory object—counterfactual outcomes, probabilistic causal scores, minimal feature sets, minimal concept sets—but they share two constraints. First, the explanation is defined relative to an alternative outcome. Second, explanatory relevance is secured by intervention or intervention-like manipulation, not by association alone.

3. Computational paradigms

One computational paradigm begins with standard model-based counterfactual explanations and then evaluates them causally. In the DiCE and Wachter-style setup, a counterfactual explanation is generated by optimizing for a small perturbation $P$6 that flips the learned predictor $P$7, for example through the Wachter loss

$P$8

The critique is that $P$9 “does not necessarily take into account causal relationships in the data”, so the resulting counterfactual answers “What minimal change to the input would flip the model prediction?” rather than “What minimal intervention in the world would change the outcome?” (Smith, 2023).

A second paradigm is declarative search over interventions. In the ASP framework, entities and domains are represented symbolically, the classifier is accessed through an external predicate $Q$0, intervention rules non-deterministically generate feature changes, stopping rules detect outcome reversal, and weak constraints minimize the number of changed features. This yields c-explanations and maximum-responsibility explanations while allowing domain-specific semantic knowledge—such as age constraints or one-hot encoding constraints—to be imposed directly in the program (Bertossi, 2020).

A third paradigm learns a causal graph over interpretable features and model outputs. In “Explaining the Behavior of Black-Box Prediction Algorithms with Causal Learning”, the analyst observes macro-level features $Q$1 and the black-box output $Q$2, then uses FCI to estimate a partial ancestral graph over $Q$3 that allows arbitrary unmeasured confounding. Directed edges into $Q$4 mark definite causal drivers, bidirected edges indicate purely associated features due to latent confounding, and partially oriented edges encode ambiguity (Sani et al., 2020). This does not immediately generate local counterfactuals, but it identifies which variables can legitimately serve as difference-makers in later contrastive explanations.

A fourth paradigm models the internal computation of a trained neural network causally. TRACER treats a DNN as a deterministic structural causal system, intervenes on input features, records the effect on internal activations, groups functionally similar layers into layer groups using CKA, and assigns Average Causal Effect scores to those groups. It then generates target-class counterfactuals with a conditional GAN plus autoencoder, so that explanations contrast the observed input and causal pathway with a counterfactual input and its causal pathway (Diallo et al., 2024).

A fifth paradigm works through a causal generative model of latent factors. In visual models, the Distributional Causal Graph approach defines an SCM over latent image factors, samples counterfactual factor configurations under interventions, and then requires a counterfactual image generator to map those interventions back to pixels. The authors argue that existing image generative models are limited for this purpose because adversarial realism and reconstruction objectives suppress rare but causally meaningful counterfactual configurations such as low-probability attribute combinations (Parafita et al., 2019).

4. Domain-specific realizations

In robotics, contrastive causal explanation has been instantiated as nearest-success reasoning over a learned causal Bayesian network. For robot failures in stacking cubes and dropping spheres into containers, the system learns a Bayesian network from randomized simulation data, discretizes continuous variables into intervals, and uses breadth-first search over the discretized parameter space to find the closest configuration whose predicted success probability exceeds a threshold. The explanation is then the difference between the failed state and that nearest successful state, verbalized as statements such as “too high” or “too far to the right” (Diehl et al., 2022).

In recommendation, the explanatory unit is an item in a user’s interaction history. A VAE generates perturbed yet plausible histories, the black-box recommender is queried on those histories, and a causal rule-mining model estimates whether a history item $Q$5 increases the probability of the recommended item $Q$6 under the contrast $Q$7 versus $Q$8. The resulting explanation has the form “Because you purchased $Q$9, the model recommends you $\tau^*$0” (Xu et al., 2020).

In autonomous navigation, the contrast is between trajectories rather than labels. A collision avoidance system chooses

$\tau^*$1

with a linearly additive cost

$\tau^*$2

A fact is the chosen trajectory $\tau^*$3, a foil is either the nominal trajectory or the best trajectory satisfying a selected maneuver characteristic, and the explanation is built from the cost components where the fact is strictly better than the foil: $\tau^*$4 The explanation module then selects the single most salient improvement and maps it to nautical semantics such as CPA distance or COLREG rule compliance (Jose et al., 9 Apr 2026).

In rule-based smart environments, the fact is a fired action, no action, or an error, and the foil is a predicted user-expected rule. Candidate foil rules are ranked by a TOPSIS procedure over factors including Jaccard precondition similarity, ownership, frequency, and prior explanation occurrence. The final explanation uses one of three templates: “$\tau^*$5 occurred instead of $\tau^*$6 because $\tau^*$7”, “$\tau^*$8 did not occur because $\tau^*$9”, or “$\tau'$0 did not occur because error $\tau'$1 occurred” (Herbold et al., 2024).

In concept-based vision analysis, the explanatory variables are high-level concepts rather than pixels. A concept strength vector is built from CLIP-derived concept vectors, concept erasure defines interventions in representation space, and minimal concept sets are computed that are sufficient to preserve a prediction or necessary in the sense that erasing them changes the prediction. These explanations can then be aggregated over collections of images to characterize shared behaviors such as systematic misclassification patterns (Canizales et al., 7 May 2026).

5. Empirical findings and evaluation

Empirical work repeatedly shows that predictive counterfactuals and causal contrasts diverge. In a study evaluating DiCE explanations against Pearl’s counterfactual method on simulated chain, fork, and collider structures, 30 counterfactual explanations were tested and “out of 30 different results, 10 (33\%) showed conflict between the CE output and the PCM output.” The conflicts were 3/10 for the chain, 2/10 for the fork, and 5/10 for the collider structure, with the collider case especially problematic because predictive models can exploit non-causal associations introduced by conditioning on a collider (Smith, 2023).

Robotics results show that causal models can support operational explanations outside static prediction tasks. The learned Bayesian networks for cube stacking and sphere dropping reached sim2real accuracy of approximately 70% and 72%, respectively, and were sufficient to produce explanations like “the upper cube was stacked too high and too far to the right of the lower cube” or “the container was too small and too high” on real robots (Diehl et al., 2022). In recommendation, causal explanations were validated by checking whether $\tau'$2; the reported percentage of reliable explanations exceeded 90% across datasets and backbone recommenders, while explanation fidelity approached 95–100% and substantially exceeded that of association-rule baselines (Xu et al., 2020).

Image-classification work has produced quantitatively tractable black-box causal explanations. One paper reports that its algorithms for sufficient, contrastive, and complete causal explanations take on average 6 seconds per image on a ResNet50 model, require no model internals or gradients, and reveal that different models exhibit different patterns of sufficiency, contrastiveness, and completeness (Kelly et al., 31 Jul 2025). TRACER, which builds causal maps over internal layer groups, reports that about 85% of MNIST samples can be explained by a causal mechanism with just 2 intermediate causal nodes, about 99% by 3 nodes, and 100% by 4 nodes; the compressed C1 model then achieves 99.48% accuracy versus 99.64% for AlexNet, with about 99.42% reduction in parameters and about 4× faster inference (Diallo et al., 2024).

Human-subject evaluations suggest that contrastive causal explanations can improve understanding while also introducing new demands. In maritime collision avoidance, an exploratory user study with four experienced marine officers found generally positive ratings for usefulness and understanding of the system’s reasoning, especially for the availability of an alternative maneuver and the corresponding comparison. At the same time, participants reported that the additional explanatory information could increase workload, particularly when explanations were always present rather than demand-driven (Jose et al., 9 Apr 2026).

6. Limits, misconceptions, and future directions

A persistent limitation is epistemic: the true causal structure is often unknown. In the DiCE-versus-SCM evaluation, the SCM is ground truth by construction because data are simulated from it, and the author explicitly notes the small sample of explanations, the simplified causal structures, and the assumption that all features are actionable and all counterfactual values are plausible (Smith, 2023). Related work on causal learning for black-box prediction likewise depends on assumptions such as faithfulness, sufficient data for FCI, and usable macro-level variables, while concept-based explanation depends on the linear representation hypothesis, vocabulary completeness, and the quality of concept erasure (Sani et al., 2020, Canizales et al., 7 May 2026).

A second limitation is semantic scope. Several papers stress that the causal claims are often model-internal rather than claims about the external world. TRACER is explicit that it estimates the causal mechanisms of the trained DNN, not the true causal structure of the data-generating process (Diallo et al., 2024). The causal image-generation paper similarly emphasizes that valid contrastive explanations require a causal model over latent factors and a generator capable of rendering low-probability but causally meaningful alternatives, a requirement that current image generators do not reliably satisfy (Parafita et al., 2019).

A third issue is interpretive risk. Experiments on lay users show that counterfactual explanations of AI predictions can unjustifiably increase people’s beliefs that the cited factors are causal in the real world. In two experiments with total $\tau'$3, counterfactual explanations increased “Action” ratings—willingness to recommend intervening on the factor—even when they did not further increase “Expectation” ratings about predictive association; a short warning that AI systems capture correlations and not necessarily causal relationships attenuated this effect (Tesic et al., 2022). This supports the broader claim that counterfactual instances, without causal equations or structural models, “explain little” and can be epistemically misleading (White et al., 2021).

Current research directions therefore converge on a few themes. One is to integrate causal structure directly into explanation generation rather than only into evaluation, using SCMs or causal discovery to constrain feasible interventions (Smith, 2023). Another is to provide richer but selective foil selection, whether through user-chosen alternatives in maritime supervision, context-aware predicted foils in rule-based systems, or behavior-level concept aggregation in vision (Jose et al., 9 Apr 2026, Herbold et al., 2024, Canizales et al., 7 May 2026). A further direction is empirical validation through actual interventions in deployed systems, which several authors describe as difficult but crucial for establishing whether a purported contrastive causal explanation tracks real recourse rather than model-specific sensitivity (Diehl et al., 2022, Xu et al., 2020).

In this body of work, contrastive causal explanations emerge not as a single algorithmic family but as a unifying criterion: an explanation is strongest when it identifies the variables, concepts, rules, or objectives that are genuine difference-makers for “$\tau'$4 rather than $\tau'$5” under an explicit intervention semantics.