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Recourse under Model Multiplicity via Argumentative Ensembling (Technical Report)

Junqi Jiang, Antonio Rago, Francesco Leofante, Francesca Toni

TL;DR

This work addresses recourse in settings with model multiplicity ($MM$), where multiple equally accurate predictors can yield conflicting outcomes for the same input. It formalizes Recourse-Aware Ensembling (RAE) and argues that naive extensions to handle counterfactual explanations (CEs) fail to satisfy key properties. The authors propose argumentative ensembling, grounded in a bipolar argumentation framework with model preferences, to guarantee CE validity and coherence while incorporating user priorities. Theoretical analysis shows favorable properties (non-emptiness, validity, coherence) and a trade-off with majority voting, while empirical evaluation on three real-world datasets demonstrates robust CE provision without degrading accuracy and highlights the practical value of preferences. The approach provides a scalable, explainable, and user-aligned mechanism for recourse under MM and opens avenues for richer argumentation-based explainability in ML systems.

Abstract

Model Multiplicity (MM) arises when multiple, equally performing machine learning models can be trained to solve the same prediction task. Recent studies show that models obtained under MM may produce inconsistent predictions for the same input. When this occurs, it becomes challenging to provide counterfactual explanations (CEs), a common means for offering recourse recommendations to individuals negatively affected by models' predictions. In this paper, we formalise this problem, which we name recourse-aware ensembling, and identify several desirable properties which methods for solving it should satisfy. We show that existing ensembling methods, naturally extended in different ways to provide CEs, fail to satisfy these properties. We then introduce argumentative ensembling, deploying computational argumentation to guarantee robustness of CEs to MM, while also accommodating customisable user preferences. We show theoretically and experimentally that argumentative ensembling satisfies properties which the existing methods lack, and that the trade-offs are minimal wrt accuracy.

Recourse under Model Multiplicity via Argumentative Ensembling (Technical Report)

TL;DR

This work addresses recourse in settings with model multiplicity (), where multiple equally accurate predictors can yield conflicting outcomes for the same input. It formalizes Recourse-Aware Ensembling (RAE) and argues that naive extensions to handle counterfactual explanations (CEs) fail to satisfy key properties. The authors propose argumentative ensembling, grounded in a bipolar argumentation framework with model preferences, to guarantee CE validity and coherence while incorporating user priorities. Theoretical analysis shows favorable properties (non-emptiness, validity, coherence) and a trade-off with majority voting, while empirical evaluation on three real-world datasets demonstrates robust CE provision without degrading accuracy and highlights the practical value of preferences. The approach provides a scalable, explainable, and user-aligned mechanism for recourse under MM and opens avenues for richer argumentation-based explainability in ML systems.

Abstract

Model Multiplicity (MM) arises when multiple, equally performing machine learning models can be trained to solve the same prediction task. Recent studies show that models obtained under MM may produce inconsistent predictions for the same input. When this occurs, it becomes challenging to provide counterfactual explanations (CEs), a common means for offering recourse recommendations to individuals negatively affected by models' predictions. In this paper, we formalise this problem, which we name recourse-aware ensembling, and identify several desirable properties which methods for solving it should satisfy. We show that existing ensembling methods, naturally extended in different ways to provide CEs, fail to satisfy these properties. We then introduce argumentative ensembling, deploying computational argumentation to guarantee robustness of CEs to MM, while also accommodating customisable user preferences. We show theoretically and experimentally that argumentative ensembling satisfies properties which the existing methods lack, and that the trade-offs are minimal wrt accuracy.
Paper Structure (16 sections, 10 theorems, 1 figure, 6 tables)

This paper contains 16 sections, 10 theorems, 1 figure, 6 tables.

Key Result

Theorem 1

Augmented ensembling satisfies non-emptiness, model agreement, majority vote and counterfactual coherence. It satisfies non-triviality if $|\mathcal{M}| \!>\! 2$. It does not satisfy counterfactual validity.

Figures (1)

  • Figure 1: BAF for Example \ref{['ex:arg']} where: models' predictions for the input $\mathbf{x}$ are given as superscripts, e.g. $M_1(\mathbf{x}) = 0$ but $M_4(\mathbf{x}) = 1$; reciprocal supports are represented by dual-headed green arrows labelled with $+$ and standard (reciprocal) attacks are represented by single-headed (dual-headed, resp.) red arrows labelled with $-$.

Theorems & Definitions (35)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Definition 8
  • Example 1
  • Theorem 1
  • ...and 25 more