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Algorithmic Recourse: from Counterfactual Explanations to Interventions

Amir-Hossein Karimi, Bernhard Schölkopf, Isabel Valera

arXiv:2002.06278v4cs.LGcs.AIstat.ML

TL;DR

The paper addresses the gap between explaining what feature values would yield a favorable prediction and recommending how an individual can achieve them. It uses causal reasoning to formulate recourse as minimal interventions that account for downstream effects. The resulting framework distinguishes these interventions from nearest counterfactual explanations and identifies conditions under which CFE-based actions can fail or be suboptimal.

  • Problem

    Counterfactual explanations often indicate where an individual needs to get but do not specify how to get there, while direct translations to actions can ignore causal dependencies.

  • Method

    The paper models recourse actions as interventions in a structural causal model and minimizes their cost while accounting for downstream effects.

  • Results

    The proposed minimal-intervention formulation produces structural counterfactuals that favorably change the model output, whereas CFE-based actions may be suboptimal or infeasible.

  • Takeaways & Limitations

    Recourse should focus on causal recommendations for how to act rather than relying solely on explanations of desirable feature values.

  • Takeaways & Limitations

    CFE-based recourse may require enforcing an independent post-intervention model even when the true structural causal model contains dependent features.

Abstract

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As machine learning is increasingly used to inform consequential decision-making (e.g., pre-trial bail and loan approval), it becomes important to explain how the system arrived at its decision, and also suggest actions to achieve a favorable decision. Counterfactual explanations -- "how the world would have (had) to be different for a desirable outcome to occur" -- aim to satisfy these criteria. Existing works have primarily focused on designing algorithms to obtain counterfactual explanations for a wide range of settings. However, one of the main objectives of "explanations as a means to help a data-subject act rather than merely understand" has been overlooked. In layman's terms, counterfactual explanations inform an individual where they need to get to, but not how to get there. In this work, we rely on causal reasoning to caution against the use of counterfactual explanations as a recommendable set of actions for recourse. Instead, we propose a shift of paradigm from recourse via nearest counterfactual explanations to recourse through minimal interventions, moving the focus from explanations to recommendations. Finally, we provide the reader with an extensive discussion on how to realistically achieve recourse beyond structural interventions.

1 INTRODUCTION

Counterfactual explanations help describe desirable model outcomes, but translating them directly into recourse actions can ignore causal dependencies and produce costly or ineffective recommendations. The paper therefore reformulates recourse around minimal causal interventions that account for downstream effects.

  • Counterfactual explanations describe how features would need to differ for an individual to receive a desirable prediction.
  • Existing approaches may treat nearest counterfactual instances as recommendations without specifying how individuals can realize those feature values.
  • In the loan example, a 14% salary increase to $85,000 automatically produces $3,000 in additional savings under the stated savings relationship.
  • Directly derived actions can demand excessive effort or fail to produce the desired outcome when they ignore causal relationships governing the world.The paper illustrates these problems with salary and bank-balance changes, and with agricultural yield affected by altitude-linked temperature changes.
  • The proposed reformulation treats recourse actions as causal interventions whose downstream effects can produce favorable structural counterfactuals.

2 ALGORITHMIC RECOURSE VIA COUNTERFACTUAL EXPLANATIONS

Nearest counterfactual explanations identify similar feature values associated with a desired prediction, but do not by themselves specify feasible actions for reaching them. CFE-based recourse adds action costs and feasibility constraints, while remaining distinct from the causal-intervention formulation developed later.

  • Nearest counterfactual explanations minimize feature changes under a context-dependent dissimilarity metric while achieving the desired prediction.
  • Counterfactual instances may be drawn from a dataset or generated by an algorithm.
  • Existing methods solve the counterfactual-explanation optimization problem using varied distance functions, predictive models, and plausibility constraints.
  • Nearest counterfactual explanations explain which feature values would yield a desired prediction but leave uncertain how an individual can realize them.
  • CFE-based recourse minimizes a user-specified action cost subject to feasibility and plausibility constraints.Feasibility constraints can exclude recommendations such as changing gender or reducing age.

3 A CAUSAL PERSPECTIVE OF ALGORITHMIC RECOURSE

The paper recasts recourse actions as structural interventions in a causal model, exposing when counterfactual-explanation-based actions reproduce the desired counterfactual. These actions are reliable only under restrictive causal conditions, motivating causal counterfactual analysis of recourse.

  • Assumptions: CFE-based recourse assumes that feature-wise differences directly translate into minimal actions producing the nearest counterfactual.It also assumes a one-to-one relationship between feature distance and action cost.
  • Actions as Interventions: Structural causal models represent observed variables, exogenous variables, and structural equations capturing inter-variable causal dependencies.Structural interventions replace selected equations and sever graph edges incident on intervened variables.
  • Actions as Interventions: Structural counterfactuals evaluate how an individual’s feature vector changes after an intervention and whether the predictive output changes favorably.The post-intervention model captures effects on the world, while structural counterfactuals capture the effect on the individual.
  • Limitations of CFE-based recourse: CFE-based actions guarantee recourse if and only if the intervened variables have no descendants.If descendants exist, their values depend on changed parent values, so the structural counterfactual can differ from the nearest counterfactual explanation.
  • Limitations of CFE-based recourse: In an independent causal world, CFE-based actions always guarantee recourse because all observed features are root nodes.The independent-world case makes the descendant set empty.
  • Limitations of CFE-based recourse: The independent-world assumption is unrealistic and can require costly interventions on descendants to preserve counterfactual feature values.Such interventions may conflict with the distance-cost assumption and can unnecessarily restrict an individual’s agency.

4 ALGORITHMIC RECOURSE VIA MINIMAL INTERVENTIONS

The paper reformulates recourse as finding the minimally costly feasible interventions whose causal consequences produce a favorable prediction, rather than independently shifting features toward a nearest counterfactual. The formulation supports structural counterfactual computation and is illustrated theoretically and on synthetic and German credit settings.

  • MINT minimizes the cost of feasible actions whose resulting structural counterfactual receives a favorable prediction.The resulting instance need not be the nearest counterfactual explanation.
  • For a known causal model and feasible interventions, the optimal MINT action is no more costly than any feasible CFE-based action that achieves recourse.
  • Structural counterfactuals are computed through abduction, action, and prediction in an additive noise model, with interventions modifying the structural causal model.The formulation generalizes to other DAGs under invertibility, which makes exogenous variables identifiable during abduction.
  • In the synthetic example, MINT increases salary from $75,000 to $85,000, induces balance of $28,000, and costs about half the nearest-CFE action.The nearest CFE instead increases balance to $30,000; the reported comparison is cost(δ*; xF) ≈ 2 cost(A*; xF).
  • In the German credit example, MINT recommends age 33 and $1,138 credit instead of waiting six years, reducing individual effort by 42%.Across 50 negatively affected individuals, prior actions were 39% ± 24% more costly for logistic regression and 65% ± 8% more costly for a decision tree.
  • The demonstrations support the theoretical claim that MINT actions are less costly than CFE-based actions because they use causal relations between variables.

5 TOWARDS REALISTIC INTERVENTIONS

Realistic recourse must model how interventions interact with causal mechanisms, distinguish intervention types and variable agency, and separate feasibility from plausibility. The paper extends the framework beyond hard interventions while noting that real-world actions may affect multiple model variables.

  • Structural interventions sever all incoming edges to an intervened node, whereas additive interventions preserve existing causal relations while changing a variable.The appropriate intervention type depends on the variable’s semantic meaning and should be chosen before optimization.
  • Real-world recourse actions must follow the world’s causal rules, which determine whether an intervention cancels or complements existing mechanisms.
  • Some settings constrain intervention choices: adding insulin cannot disable existing mechanisms, whereas treating malignancy may require structural amputation.
  • Variables span immutable, mutable-but-non-actionable, and actionable categories, rather than a simple actionable-versus-immutable distinction.A credit score may change through salary or savings interventions even though it is not directly intervenable.
  • Action feasibility can depend on pre- and post-intervention values of the intervened variable and other variables.
  • Feasibility restricts actions an individual can perform, while plausibility concerns how likely the resulting counterfactual instance is.A higher credit score may be plausible in observed data but directly changing it is not feasible.
  • The framework assumes a one-to-one mapping between real-world actions and interventions on endogenous variables, although some actions may intervene on multiple variables.Finding a higher-paying job could simultaneously affect income and employment length.

6 DISCUSSION

The discussion argues that causal reasoning is necessary for realistic algorithmic recourse: counterfactual explanations can support auditing, but do not generally guarantee feasible actions. The paper instead proposes minimal interventions while acknowledging dependence on a true causal model and the need for further work on realistic constraints.

  • 6 DISCUSSION: Counterfactual explanations may fail to provide feasible or effective recourse because they do not model causal relations and downstream effects.The paper characterizes many existing approaches as contrastive rather than genuinely counterfactual in their treatment of causality.
  • 6 DISCUSSION: The paper reformulates recourse as cost-minimizing interventions in a structural causal model, yielding minimal interventions intended to change the model output favorably.The formulation models actions through physical laws represented by a structural causal model.
  • 6 DISCUSSION: The proposed formulation relies on availability of the true causal model, while future work considers learning partial or complete world models and handling imperfect causal knowledge.The authors identify inefficiencies from partial or imperfect causal models as an open question.
  • 6 DISCUSSION: Counterfactual explanations remain useful for guided data audits and evaluating properties such as robustness and fairness, even though they do not by themselves imply recourse.The paper presents minimal interventions as complementary to these uses.
  • 6 DISCUSSION: Future research should combine intervention-based recourse with sequential planning and better define variables, permissible interventions, and recourse cost functions.These issues are especially relevant when constraints depend on context, individuals, or multiple intervention stages.

A.1 Proof of Proposition 3.1

The proof shows that CFE-based actions generally guarantee recourse only when intervened variables have no descendants, because interventions otherwise alter downstream variables and separate the structural counterfactual from the CFE.

  • A.1 Proof of Proposition 3.1: CFE-based actions guarantee recourse if and only if the set of descendants of the intervened variables is empty.The proof assumes a causal graph with known parent sets and partitions variables into intervened, non-descendant, and descendant sets.
  • A.1 Proof of Proposition 3.1: The proof permits intervention on an arbitrary subset of observed variables, provided it includes every variable assigned a nonzero CFE change.This condition links the CFE perturbation to the intervention index set.
  • A.1 Proof of Proposition 3.1: Structural interventions leave non-descendant variables unaffected, which supports equality between the structural counterfactual and CFE when no descendants exist.The proof establishes the two directions of the proposition using this invariance.
  • A.1 Proof of Proposition 3.1: When an intervention changes a variable with descendants, at least one descendant generally changes, so the structural counterfactual differs from the nearest CFE.The proof excludes rare piecewise-constant cases where a descendant remains invariant.

A.2 Proof of Corollary 3.1

The corollary identifies independence as a special case in which CFE-based actions always guarantee recourse.

  • A.2 Proof of Corollary 3.1: If all observed features are root nodes in the true world, CFE-based actions always guarantee recourse.All variables then have empty descendant sets, so the result follows from Proposition 3.1.

A.3 Proof of Proposition 4.1

The proof establishes that, whenever a feasible CFE-based action achieves recourse, the optimized intervention solution has no greater cost.

  • A.3 Proof of Proposition 4.1: cost(A∗; xF) ≤ cost(ACFE; xF) whenever both actions are feasible and the CFE-based action achieves recourse.The inequality follows directly from A∗ being optimal under the feasible-action constraint.
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