Tractable Shapley Values and Interactions via Tensor Networks

Farzaneh Heidari, Chao Li, Guillaume Rabusseau
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:3043-3051, 2026.

Abstract

We show how to replace the $O(2^n)$ coalition enumeration over $n$ features behind Shapley values and Shapley-style interaction indices with a \emph{few-evaluation} scheme on a tensor-network (TN) surrogate: TN-SHAP. The key idea is to represent a predictor’s local behavior as a factorized multilinear map, so that coalitional quantities become \emph{linear probes} of a coefficient tensor. TN-SHAP replaces exhaustive coalition sweeps with just a small number of targeted evaluations to extract order$-k$ Shapley interactions. In particular, both order-1 (single-feature) and order-2 (pairwise) computations have cost $O\!\big(n\,\mathrm{poly}(\chi) + n^2\big)$, where $\chi$ is the TN’s maximal cut rank. We provide theoretical guarantees on the approximation error and tractability of TN-SHAP. On UCI datasets, our method matches enumeration on the fitted surrogate while reducing evaluation by orders of magnitude and achieves \textbf{25–1000$\times$} wall-clock speedups over KernelSHAP-IQ at comparable accuracy, while amortizing training across local cohorts.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-heidari26a, title = { Tractable Shapley Values and Interactions via Tensor Networks }, author = {Heidari, Farzaneh and Li, Chao and Rabusseau, Guillaume}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {3043--3051}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/heidari26a/heidari26a.pdf}, url = {https://proceedings.mlr.press/v300/heidari26a.html}, abstract = { We show how to replace the $O(2^n)$ coalition enumeration over $n$ features behind Shapley values and Shapley-style interaction indices with a \emph{few-evaluation} scheme on a tensor-network (TN) surrogate: TN-SHAP. The key idea is to represent a predictor’s local behavior as a factorized multilinear map, so that coalitional quantities become \emph{linear probes} of a coefficient tensor. TN-SHAP replaces exhaustive coalition sweeps with just a small number of targeted evaluations to extract order$-k$ Shapley interactions. In particular, both order-1 (single-feature) and order-2 (pairwise) computations have cost $O\!\big(n\,\mathrm{poly}(\chi) + n^2\big)$, where $\chi$ is the TN’s maximal cut rank. We provide theoretical guarantees on the approximation error and tractability of TN-SHAP. On UCI datasets, our method matches enumeration on the fitted surrogate while reducing evaluation by orders of magnitude and achieves \textbf{25–1000$\times$} wall-clock speedups over KernelSHAP-IQ at comparable accuracy, while amortizing training across local cohorts. } }
Endnote
%0 Conference Paper %T Tractable Shapley Values and Interactions via Tensor Networks %A Farzaneh Heidari %A Chao Li %A Guillaume Rabusseau %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-heidari26a %I PMLR %P 3043--3051 %U https://proceedings.mlr.press/v300/heidari26a.html %V 300 %X We show how to replace the $O(2^n)$ coalition enumeration over $n$ features behind Shapley values and Shapley-style interaction indices with a \emph{few-evaluation} scheme on a tensor-network (TN) surrogate: TN-SHAP. The key idea is to represent a predictor’s local behavior as a factorized multilinear map, so that coalitional quantities become \emph{linear probes} of a coefficient tensor. TN-SHAP replaces exhaustive coalition sweeps with just a small number of targeted evaluations to extract order$-k$ Shapley interactions. In particular, both order-1 (single-feature) and order-2 (pairwise) computations have cost $O\!\big(n\,\mathrm{poly}(\chi) + n^2\big)$, where $\chi$ is the TN’s maximal cut rank. We provide theoretical guarantees on the approximation error and tractability of TN-SHAP. On UCI datasets, our method matches enumeration on the fitted surrogate while reducing evaluation by orders of magnitude and achieves \textbf{25–1000$\times$} wall-clock speedups over KernelSHAP-IQ at comparable accuracy, while amortizing training across local cohorts.
APA
Heidari, F., Li, C. & Rabusseau, G.. (2026). Tractable Shapley Values and Interactions via Tensor Networks . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:3043-3051 Available from https://proceedings.mlr.press/v300/heidari26a.html.

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