mlsanityData to 14 Oct 2026

Generating Likely Counterfactuals Using Sum-Product Networks

arXiv 2401.14086 ↗First posted 25 Jan 2024cs.AI cs.LG math.OCcited by 6

Not on the map. Why?

Abstract (arXiv)

The need to explain decisions made by AI systems is driven by both recent regulation and user demand. The decisions are often explainable only post hoc. In counterfactual explanations, one may ask what constitutes the best counterfactual explanation. Clearly, multiple criteria must be taken into account, although "distance from the sample" is a key criterion. Recent methods that consider the plausibility of a counterfactual seem to sacrifice this original objective. Here, we present a system that provides high-likelihood explanations that are, at the same time, close and sparse. We show that the search for the most likely explanations satisfying many common desiderata for counterfactual explanations can be modeled using Mixed-Integer Optimization (MIO). We use a Sum-Product Network (SPN) to estimate the likelihood of a counterfactual. To achieve that, we propose an MIO formulation of an SPN, which can be of independent interest. The source code with examples is available at https://github.com/Epanemu/LiCE.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 31 of its 73 references that are in the map. First posted on arXiv 25 Jan 2024.

Builds on

31 of 73 references.

References · 31

  1. 2017Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPRcited by 1,089
  2. 2019Explaining Machine Learning Classifiers through Diverse Counterfactual Explanationscited by 614
  3. 2018Actionable Recourse in Linear Classificationcited by 328
  4. 2020Algorithmic Recourse: from Counterfactual Explanations to Interventionscited by 250
  5. 2019FACE: Feasible and Actionable Counterfactual Explanationscited by 233
  6. 2020A Survey on the Explainability of Supervised Machine Learningcited by 227
  7. 2021Trustworthy AI: From Principles to Practicescited by 207
  8. 2019Learning Model-Agnostic Counterfactual Explanations for Tabular Datacited by 146
  9. 2019Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifierscited by 144
  10. 2021Benchmarking and Survey of Explanation Methods for Black Box Modelscited by 136
  11. 2020A survey of algorithmic recourse: definitions, formulations, solutions, and prospectscited by 118
  12. 2019Efficient Search for Diverse Coherent Explanationscited by 111
19 more
  1. 2021CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithmscited by 86
  2. 2021Evaluating Robustness of Counterfactual Explanationscited by 41
  3. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  4. 2021Optimal Counterfactual Explanations in Tree Ensemblescited by 36
  5. 2022OMLT: Optimization & Machine Learning Toolkitcited by 35
  6. 2020Convex Density Constraints for Computing Plausible Counterfactual Explanationscited by 32
  7. 2022Diffeomorphic Counterfactuals with Generative Modelscited by 29
  8. 2019SPFlow: An Easy and Extensible Library for Deep Probabilistic Learning using Sum-Product Networkscited by 26
  9. 2019Bayesian Learning of Sum-Product Networkscited by 24
  10. 2022Formalising the Robustness of Counterfactual Explanations for Neural Networkscited by 24
  11. 2020Scaling Guarantees for Nearest Counterfactual Explanationscited by 22
  12. 2023Provably Robust and Plausible Counterfactual Explanations for Neural Networks via Robust Optimisationcited by 20
  13. 2023Finding Regions of Counterfactual Explanations via Robust Optimizationcited by 19
  14. 2019Deep Structured Mixtures of Gaussian Processescited by 16
  15. 2022Keep Your Friends Close and Your Counterfactuals Closer: Improved Learning From Closest Rather Than Plausible Counterfactual Explanations in an Abstract Settingcited by 11
  16. 2023Achieving Diversity in Counterfactual Explanations: a Review and Discussioncited by 11
  17. 2023CeFlow: A Robust and Efficient Counterfactual Explanation Framework for Tabular Data using Normalizing Flowscited by 8
  18. 2017Nonconvex piecewise linear functions: Advanced formulations and simple modeling toolscited by 7
  19. 2019On the Sample Complexity of Learning Sum-Product Networkscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 3.

6 papers.

  1. 2026PAR: Plausibility-aware Amortized Recourse Generationcited by 2
  2. 2025Counterfactual Explanations in Medical Imaging: Exploring SPN-Guided Latent Space Manipulationcited by 0
  3. 2025Constraint-Reduced MILP with Local Outlier Factor Modeling for Plausible Counterfactual Explanations in Credit Approvalcited by 0
  4. 2025Tractable Probabilistic Models for Investment Planningcited by 0
  5. 2026Diverse and Plausible Algorithmic Recourse via Tractable Recourse Distributionscited by 0
  6. 2026A Compositional Theory of Curvature in Probabilistic Circuitscited by 0