Tractable Shapley Values and Interactions via Tensor Networks
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| Format: | Preprint |
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2025
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| _version_ | 1866916071137607680 |
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| author | Heidari, Farzaneh Li, Chao Rabusseau, Guillaume |
| author_facet | Heidari, Farzaneh Li, Chao Rabusseau, Guillaume |
| contents | We show how to replace the O(2^n) coalition enumeration over n features behind Shapley values and Shapley-style interaction indices with a 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 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(n*poly(chi) + n^2), 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 25-1000x wall-clock speedups over KernelSHAP-IQ at comparable accuracy, while amortizing training across local cohorts. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_22138 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tractable Shapley Values and Interactions via Tensor Networks Heidari, Farzaneh Li, Chao Rabusseau, Guillaume Machine Learning We show how to replace the O(2^n) coalition enumeration over n features behind Shapley values and Shapley-style interaction indices with a 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 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(n*poly(chi) + n^2), 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 25-1000x wall-clock speedups over KernelSHAP-IQ at comparable accuracy, while amortizing training across local cohorts. |
| title | Tractable Shapley Values and Interactions via Tensor Networks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.22138 |