TT-FSI: Scalable Faithful Shapley Interactions via Tensor-Train

TL;DR

TT-FSI introduces a tensor-train based method to compute Faithful Shapley Interactions efficiently, significantly reducing computational time and memory usage, enabling scalability to higher dimensions.

Contribution

The paper develops TT-FSI, a novel tensor-train approach that exploits algebraic structure for scalable computation of Faithful Shapley Interactions, with theoretical guarantees and practical efficiency.

Findings

Achieves up to 280× speedup over baseline methods

Reduces memory usage by 85× compared to SHAP-IQ

Scales to 20-dimensional problems where others fail

Abstract

The Faithful Shapley Interaction (FSI) index uniquely satisfies the faithfulness axiom among Shapley interaction indices, but computing FSI requires $O(d^\ell \cdot 2^d)$ time and existing implementations use $O(4^d)$ memory. We present TT-FSI, which exploits FSI's algebraic structure via Matrix Product Operators (MPO). Our main theoretical contribution is proving that the linear operator $v \mapsto \text{FSI}(v)$ admits an MPO representation with TT-rank $O(\ell d)$, enabling an efficient sweep algorithm with $O(\ell^2 d^3 \cdot 2^d)$ time and $O(\ell d^2)$ core storage an exponential improvement over existing methods. Experiments on six datasets ($d=8$ to $d=20$) demonstrate up to 280$\times$ speedup over baseline, 85$\times$ over SHAP-IQ, and 290$\times$ memory reduction. TT-FSI scales to $d=20$ (1M coalitions) where all competing methods fail.