Source-linked AI summary
Contrastive Explanation: A Structural-Model Approach
Tim Miller
TL;DR
AI explanation research lacks a general, consistent account of contrastive questions, including why an outcome occurred rather than another outcome or occurred this time but not another time. The paper extends structural causal models to define contrastive causes and explanations for counterfactual and bi-factual questions. It shows the model is internally consistent and aligned with accepted and alternative properties of contrastive explanation, while demonstrating it on classification and planning.
Problem
Explainable AI lacks a clear, consistent understanding of contrastive explanation, including bi-factual questions comparing outcomes across similar cases or different situations.
Method
The paper extends Halpern and Pearl’s structural-causal-model account to define contrastive causes and explanations for counterfactual and bi-factual questions.
Results
The model is internally consistent and agrees with well-accepted and alternative properties of contrastive explanation, with demonstrations in classification and goal-directed planning.
Takeaways & Limitations
A single structural-causal model can provide a general framework for understanding contrastive explanation across artificial-intelligence subfields.
Takeaways & Limitations
The structural-model examples can represent correlational machine-learning predictors rather than causes in the real world, although real-world causal models may offer better explanations.
Abstract
from arXiv · showhide
This paper presents a model of contrastive explanation using structural casual models. The topic of causal explanation in artificial intelligence has gathered interest in recent years as researchers and practitioners aim to increase trust and understanding of intelligent decision-making. While different sub-fields of artificial intelligence have looked into this problem with a sub-field-specific view, there are few models that aim to capture explanation more generally. One general model is based on structural causal models. It defines an explanation as a fact that, if found to be true, would constitute an actual cause of a specific event. However, research in philosophy and social sciences shows that explanations are contrastive: that is, when people ask for an explanation of an event -- the fact -- they (sometimes implicitly) are asking for an explanation relative to some contrast case; that is, "Why P rather than Q?". In this paper, we extend the structural causal model approach to define two complementary notions of contrastive explanation, and demonstrate them on two classical problems in artificial intelligence: classification and planning. We believe that this model can help researchers in subfields of artificial intelligence to better understand contrastive explanation.
1 Introduction
The paper motivates contrastive explanation as explaining an event relative to a contrast case, addressing limits in causal explanations for AI decisions. It extends structural-causal-model explanations to counterfactual and bi-factual questions and demonstrates the model in classification and planning.
- Explainable AI research seeks greater trust and understanding of decisions, partly because users distrust black-box algorithms and worry about their ethical and societal implications.
- Explanations are often contrastive: people ask why P rather than an explicit or implicit Q, with P the fact and Q the contrast case.
- Contrastive explanations fit the questioner’s uncertainty and can be simpler by identifying only information needed relative to the contrast case.
- The paper extends structural-causal-model explanations to counterfactual questions involving hypothetical foils and bi-factual questions contrasting actual events across situations.
- The model defines causes and explanations for both question types, shows internal consistency, and demonstrates them on classification and goal-directed planning.
2 Related Work
Related work treats contrastive explanation as selecting causal differences relative to a contrast case, but explainable AI lacks a consistent general account, especially for bi-factual questions.
- Contrastive explanations explain events relative to contrast cases, which may be implicit and determine the explanatory context.
- Philosophical accounts characterize relevant explanations as causal differences between the fact and its contrast, rather than exhaustive lists of causes.
- The paper distinguishes P-contrast, captured by counterfactual explanations, from O-contrast and T-contrast, captured by bi-factual explanations.
- Explainable AI lacks consistent terminology and understanding because many why-not approaches are counterfactual rather than explicitly contrastive.
- Bi-factual questions remain underaddressed, despite requests to compare similar cases with different outcomes and show the differences between them.
- The proposed general model aims to map across AI subfields and address gaps such as the lack of bi-factual explanation.
3 Structural Models
The paper represents AI decision processes with structural causal models and uses causal formulas to reason about counterfactual interventions. An illustrative arthropod classifier maps feature variables to outputs, including correlated prediction settings.
- The approach builds contrastive explanations on Halpern and Pearl’s structural models, whose counterfactual semantics are represented through structural equations.
- A structural causal model contains exogenous and endogenous variables, value ranges, and functions determining endogenous values from other model variables.
- Counterfactual models override selected endogenous variables with specified values, producing a modified model for evaluating hypothetical cases.
- Causal formulas express Boolean events under interventions, allowing the model to state what would hold if selected variables received specified values.
- The illustrative arthropod model uses legs, stinger, eyes, compound eyes, wings, and output variables to classify inputs among arthropod types.
- Structural causal models can represent correlative machine-learning predictors by modeling physical features as causes of the algorithm’s output, not necessarily real-world causes.
4 Contrastive ‘Why’ Questions
Contrastive why-questions ask why a fact occurred relative to a foil or surrogate, rather than simply asking why the fact occurred. The paper distinguishes counterfactual questions, involving hypothetical incompatible foils, from bi-factual questions, involving actual events in different situations.
- Contrastive why-questions: Contrastive why-questions ask why a fact occurred rather than, or in contrast with, another event or outcome.The contrast case may be implicit and identifies the comparison relevant to the explanation.
- Bi-factual explananda: Bi-factual explananda ask why a fact occurred in one situation while a surrogate occurred in another, with both events actually occurring.The two situations can represent different inputs, executions, or models, including an updated model compared with its predecessor.
- Counterfactual explananda: Counterfactual explananda ask why fact φ occurred instead of hypothetical foil ψ in the same situation.The paper assumes φ and ψ are incompatible for this type of question.
- Counterfactual explananda: A ‘rather than’ explanation identifies a causal difference between the fact and foil, without requiring knowledge of every cause of either event.The arthropod example explains Bee rather than Fly using the observed difference in wing count.
- Structural-model treatment: The paper models the two contrastive question types using structural causal models, then defines contrastive causes and explanations for them.Bi-factual questions can compare different outcomes across situations, or ask why outcomes remained the same despite situational differences.
5 Contrastive Cause
The paper defines contrastive causes as paired causes that capture differences between a fact and a foil, extending actual-cause reasoning to counterfactual and bi-factual questions. It formalizes these notions and illustrates them with structural-model examples from classification and model changes.
- Definition: Contrastive causes pair a cause of the fact with a corresponding cause of the foil, capturing what distinguishes the two outcomes.This extends ordinary actual-cause analysis, where causes are conjunctions of primitive events and actual causes are minimal sufficient causes.
- Framework: The framework evaluates contrastive differences within the relevant history: one structural-model situation for counterfactual questions and two situations for bi-factual questions.The explanandum is a fact–foil pair rather than a single event, and the corresponding causes are paired as well.
- Counterfactual Causes: A contrastive counterfactual cause consists of partial causes whose difference identifies the changes needed to make the hypothetical foil true.Its first component must be a partial cause of the fact, while the full definition imposes additional contrastive conditions.
- Counterfactual Causes: In the arthropod example, stinger presence and four wings distinguish Bee from Fly, whereas leg count is excluded because it fails the difference condition.The explanation contrasts the actual features with the Fly requirements of no stinger and two wings.
- Bi-factual Causes: The framework also handles bi-factual cases across models, including changes in structural functions and additional causes, and establishes equivalence results under stated assumptions.Theorem 4 connects an actual cause under an exclusive fact–foil assumption to a counterfactual contrastive cause; Theorem 5 gives the corresponding bi-factual relation.
6 Constrastive Explanation
The paper extends structural-causal-model explanations to contrastive questions by defining contrastive causes and explanations for counterfactual and bi-factual cases. It formalizes these notions relative to an agent’s knowledge and demonstrates them in classification and goal-directed planning.
- Contrastive explanation extends Halpern and Pearl’s causal-explanation framework by replacing standard actual causes with contrastive causes.The explanation identifies information sufficient to establish causation relative to a contrast case.
- Counterfactual contrastive explanation: Counterfactual contrastive explanations answer “Why P rather than Q?” with a pair of assignments that causally distinguishes the fact from a hypothetical foil.The pair must satisfy acceptance, sufficiency, minimality, and meaningful-information conditions relative to epistemic state K.
- Counterfactual contrastive explanation: The alternative counterfactual definition treats an explanation as partial explanations of each event whose assignments satisfy the difference condition and are maximal.The paper proves this alternative is equivalent to the original definition.
- Bi-factual contrastive explanation: Bi-factual contrastive explanations use the same difference condition while comparing two actual situations, so no hypothetical foil situation is needed.The paper defines bi-factual explanations through partial explanations and proves equivalence between its two formulations.
- Goal-directed planning: In planning, the contrastive cause for A2 instead of A1 swaps goals G1 and G2, but the explanation retains only ⟨(¬G2, G2)⟩ because G1 is already known.Minimality and meaningfulness exclude the known G1 component.
- Goal-directed planning: When the explainee can infer preconditions from known goals and actions, the model yields no explanation because its meaningful-information condition is not satisfied.In the planning example, the agent can already infer P1 and P2.
- Goal-directed planning: A missing causal-graph edge can itself support a contrastive explanation by contrasting action functions with and without the relevant precondition.For A2, the explanation contrasts FA2 without P2 against a function including P2.
7 Conclusion
The paper proposes a general structural-causal model of contrastive explanation for counterfactual and bi-factual why-questions. It argues that the model is consistent with established properties and alternative definitions, addressing a gap in treatments that often provide separate full explanations rather than their contrastive difference.
- The model defines contrastive causes and explanations for both counterfactual “rather than” and bi-factual “but” questions.
- The authors report consistency with well-accepted properties of contrastive explanation and with alternative definitions.
- The work targets the limited treatment of bi-factual questions and of the difference condition in explainable artificial intelligence.Some existing approaches consider contrastive questions but provide two full explanations instead of the contrastive explanation itself.