Optimal Transport Group Counterfactual Explanations

• URL: http://arxiv.org/abs/2601.20692v1
• Date: Wed, 28 Jan 2026 15:22:20 GMT
• Title: Optimal Transport Group Counterfactual Explanations
• Authors: Enrique Valero-Leal, Bernd Bischl, Pedro Larrañaga, Concha Bielza, Giuseppe Casalicchio,
• Abstract summary: Group counterfactual explanations find a set of counterfactual instances to explain a group of input instances contrastively.<n>We learn an explicit optimal transport map that sends any group instance to its counterfactual without re-optimization.<n>Experiments show that they accurately generalize, preserve group geometry and incur only negligible additional transport cost.
• Score: 15.277896909284296
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Group counterfactual explanations find a set of counterfactual instances to explain a group of input instances contrastively. However, existing methods either (i) optimize counterfactuals only for a fixed group and do not generalize to new group members, (ii) strictly rely on strong model assumptions (e.g., linearity) for tractability or/and (iii) poorly control the counterfactual group geometry distortion. We instead learn an explicit optimal transport map that sends any group instance to its counterfactual without re-optimization, minimizing the group's total transport cost. This enables generalization with fewer parameters, making it easier to interpret the common actionable recourse. For linear classifiers, we prove that functions representing group counterfactuals are derived via mathematical optimization, identifying the underlying convex optimization type (QP, QCQP, ...). Experiments show that they accurately generalize, preserve group geometry and incur only negligible additional transport cost compared to baseline methods. If model linearity cannot be exploited, our approach also significantly outperforms the baselines.

Related papers

• Equivariance by Contrast: Identifiable Equivariant Embeddings from Unlabeled Finite Group Actions [18.11344454990819]
  We learn equivariant embeddings from observation pairs $(mathbfy, g cdot mathbfy)$, where $g$ is drawn from a finite group acting on the data.<n>Our method jointly learns a latent space and a group representation in which group actions correspond to invertible linear maps.
  arXiv  Detail & Related papers  (2025-10-24T17:59:46Z)
• Project-Probe-Aggregate: Efficient Fine-Tuning for Group Robustness [61.45587642780908]
  We propose a three-step approach for parameter-efficient fine-tuning of image-text foundation models.<n>Our method improves its two key components: minority samples identification and the robust training algorithm.<n>Our theoretical analysis shows that our PPA enhances minority group identification and is Bayes optimal for minimizing the balanced group error.
  arXiv  Detail & Related papers  (2025-03-12T15:46:12Z)
• S-CFE: Simple Counterfactual Explanations [22.262567049579648]
  We tackle the problem of finding manifold-aligned counterfactual explanations for sparse data.<n>Our approach effectively produces sparse, manifold-aligned counterfactual explanations.
  arXiv  Detail & Related papers  (2024-10-21T07:42:43Z)
• Discovering Abstract Symbolic Relations by Learning Unitary Group Representations [7.303827428956944]
  We investigate a principled approach for symbolic operation completion (SOC) SOC poses a unique challenge in modeling abstract relationships between discrete symbols. We demonstrate that SOC can be efficiently solved by a minimal model - a bilinear map - with a novel factorized architecture.
  arXiv  Detail & Related papers  (2024-02-26T20:18:43Z)
• Generating collective counterfactual explanations in score-based classification via mathematical optimization [4.281723404774889]
  A counterfactual explanation of an instance indicates how this instance should be minimally modified so that the perturbed instance is classified in the desired class. Most of the Counterfactual Analysis literature focuses on the single-instance single-counterfactual setting. By means of novel Mathematical Optimization models, we provide a counterfactual explanation for each instance in a group of interest.
  arXiv  Detail & Related papers  (2023-10-19T15:18:42Z)
• Lie Group Decompositions for Equivariant Neural Networks [12.139222986297261]
  We show how convolution kernels can be parametrized to build models equivariant with respect to affine transformations. We evaluate the robustness and out-of-distribution generalisation capability of our model on the benchmark affine-invariant classification task.
  arXiv  Detail & Related papers  (2023-10-17T16:04:33Z)
• Modeling the Q-Diversity in a Min-max Play Game for Robust Optimization [61.39201891894024]
  Group distributionally robust optimization (group DRO) can minimize the worst-case loss over pre-defined groups. We reformulate the group DRO framework by proposing Q-Diversity. Characterized by an interactive training mode, Q-Diversity relaxes the group identification from annotation into direct parameterization.
  arXiv  Detail & Related papers  (2023-05-20T07:02:27Z)
• Examining and Combating Spurious Features under Distribution Shift [94.31956965507085]
  We define and analyze robust and spurious representations using the information-theoretic concept of minimal sufficient statistics. We prove that even when there is only bias of the input distribution, models can still pick up spurious features from their training data. Inspired by our analysis, we demonstrate that group DRO can fail when groups do not directly account for various spurious correlations.
  arXiv  Detail & Related papers  (2021-06-14T05:39:09Z)
• Commutative Lie Group VAE for Disentanglement Learning [96.32813624341833]
  We view disentanglement learning as discovering an underlying structure that equivariantly reflects the factorized variations shown in data. A simple model named Commutative Lie Group VAE is introduced to realize the group-based disentanglement learning. Experiments show that our model can effectively learn disentangled representations without supervision, and can achieve state-of-the-art performance without extra constraints.
  arXiv  Detail & Related papers  (2021-06-07T07:03:14Z)
• GroupifyVAE: from Group-based Definition to VAE-based Unsupervised Representation Disentanglement [91.9003001845855]
  VAE-based unsupervised disentanglement can not be achieved without introducing other inductive bias. We address VAE-based unsupervised disentanglement by leveraging the constraints derived from the Group Theory based definition as the non-probabilistic inductive bias. We train 1800 models covering the most prominent VAE-based models on five datasets to verify the effectiveness of our method.
  arXiv  Detail & Related papers  (2021-02-20T09:49:51Z)
• Invariant Feature Coding using Tensor Product Representation [75.62232699377877]
  We prove that the group-invariant feature vector contains sufficient discriminative information when learning a linear classifier. A novel feature model that explicitly consider group action is proposed for principal component analysis and k-means clustering.
  arXiv  Detail & Related papers  (2019-06-05T07:15:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.