Scope-Restricted Backtracking Counterfactuals

Johan de Aguas, Martin Jullum
Proceedings of the 13th International Conference on Probabilistic Graphical Models, PMLR 343:274-305, 2026.

Abstract

Interventional counterfactuals evaluate statements such as "had $A$ been $a$" by replacing the assignment for $A$ while keeping the unit’s exogenous background fixed. Backtracking counterfactuals reverse this logic: they preserve the structural assignments and instead vary background conditions across worlds. This semantics is natural for diagnostic explanation, but full backtracking may be too permissive because every exogenous coordinate can vary. We introduce scope-restricted backtracking counterfactuals, in which the modeler specifies which coordinates may vary while the remainder are shared across worlds. The scope determines the admissible carriers of the contrast, while a cross-world kernel governs the plausibility of their alternative values. We present model-based inference for general scope-restricted backtracking counterfactuals, derive sharp marginal bounds for a specified explanatory query, and establish frontier and compatibility conditions under which this explanatory query admits a modified-value policy representation. A linear-Gaussian example distinguishes local-noise, ancestor, irrelevant-noise, and infeasible explanations across scopes, while an application to the UCI Adult benchmark illustrates kernel specification, sensitivity, and how much of the explanation is carried by the cross-world coupling itself.

Cite this Paper

BibTeX
@InProceedings{pmlr-v343-de-aguas26a, title = {Scope-Restricted Backtracking Counterfactuals}, author = {{de Aguas}, Johan and Jullum, Martin}, booktitle = {Proceedings of the 13th International Conference on Probabilistic Graphical Models}, pages = {274--305}, year = {2026}, editor = {Camps-Valls, Gustau and Leonelli, Manuele and Varando, Gherardo}, volume = {343}, series = {Proceedings of Machine Learning Research}, month = {09--11 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v343/main/assets/de-aguas26a/de-aguas26a.pdf}, url = {https://proceedings.mlr.press/v343/de-aguas26a.html}, abstract = {Interventional counterfactuals evaluate statements such as "had $A$ been $a$" by replacing the assignment for $A$ while keeping the unit’s exogenous background fixed. Backtracking counterfactuals reverse this logic: they preserve the structural assignments and instead vary background conditions across worlds. This semantics is natural for diagnostic explanation, but full backtracking may be too permissive because every exogenous coordinate can vary. We introduce scope-restricted backtracking counterfactuals, in which the modeler specifies which coordinates may vary while the remainder are shared across worlds. The scope determines the admissible carriers of the contrast, while a cross-world kernel governs the plausibility of their alternative values. We present model-based inference for general scope-restricted backtracking counterfactuals, derive sharp marginal bounds for a specified explanatory query, and establish frontier and compatibility conditions under which this explanatory query admits a modified-value policy representation. A linear-Gaussian example distinguishes local-noise, ancestor, irrelevant-noise, and infeasible explanations across scopes, while an application to the UCI Adult benchmark illustrates kernel specification, sensitivity, and how much of the explanation is carried by the cross-world coupling itself.} }
Endnote
%0 Conference Paper %T Scope-Restricted Backtracking Counterfactuals %A Johan de Aguas %A Martin Jullum %B Proceedings of the 13th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2026 %E Gustau Camps-Valls %E Manuele Leonelli %E Gherardo Varando %F pmlr-v343-de-aguas26a %I PMLR %P 274--305 %U https://proceedings.mlr.press/v343/de-aguas26a.html %V 343 %X Interventional counterfactuals evaluate statements such as "had $A$ been $a$" by replacing the assignment for $A$ while keeping the unit’s exogenous background fixed. Backtracking counterfactuals reverse this logic: they preserve the structural assignments and instead vary background conditions across worlds. This semantics is natural for diagnostic explanation, but full backtracking may be too permissive because every exogenous coordinate can vary. We introduce scope-restricted backtracking counterfactuals, in which the modeler specifies which coordinates may vary while the remainder are shared across worlds. The scope determines the admissible carriers of the contrast, while a cross-world kernel governs the plausibility of their alternative values. We present model-based inference for general scope-restricted backtracking counterfactuals, derive sharp marginal bounds for a specified explanatory query, and establish frontier and compatibility conditions under which this explanatory query admits a modified-value policy representation. A linear-Gaussian example distinguishes local-noise, ancestor, irrelevant-noise, and infeasible explanations across scopes, while an application to the UCI Adult benchmark illustrates kernel specification, sensitivity, and how much of the explanation is carried by the cross-world coupling itself.
APA
de Aguas, J. & Jullum, M.. (2026). Scope-Restricted Backtracking Counterfactuals. Proceedings of the 13th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 343:274-305 Available from https://proceedings.mlr.press/v343/de-aguas26a.html.

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