shap-weighted reconstruction

This paper addresses the weak interpretability, lack of mathematical unification, and absence of theoretical stability guarantees for SHAP values in discrete or multi-valued input spaces. To resolve these issues, we establish a rigorous theoretical framework grounded in generalized Fourier spectral analysis. We first embed the SHAP attribution system into the spectral domain, introducing a generalized Fourier expansion under a tensor-product orthogonal basis and revealing a linear mapping between SHAP values and Fourier coefficients. Under both deterministic and probabilistic settings, we derive stability estimates and convergence theorems with explicit error bounds. Theoretical analysis leverages Lipschitz continuity, Gaussian process limits, and concentration inequalities, and establishes convergence for both Fourier truncation and infinite-width neural networks. Numerical experiments validate the theoretical results on real-world clinical imbalanced datasets.

Industrial deployment of intelligent fault diagnosis (IFD) is hindered by weak temporal attribution capability of existing post-hoc explanation methods and prohibitively high computational cost of SHAP—exacerbated by domain transformations that cause explosive feature dimensionality. Method: This paper proposes SHEP, an efficient posterior attribution method. Its core innovation is a novel patch-level local attribution mechanism, integrating SHAP subset sampling approximation with gradient-assisted stability calibration to enable linear-complexity SHAP estimation within a time-frequency fused feature space—reducing complexity from exponential to linear. Contribution/Results: Evaluated on multi-condition bearing and gearbox datasets, SHEP achieves 98.7% SHAP fidelity while accelerating inference by 126×, enabling millisecond-scale online explanation. The implementation is open-sourced and has become a benchmark tool for explainability in IFD.

This work addresses the longstanding challenge of jointly optimizing model interpretability and predictive performance in machine learning. We propose a SHAP-driven regularized training framework, whose core innovation is the first direct incorporation of TreeSHAP attribution values into the loss function via a novel joint regularization term based on the entropy of the attribution distribution. This term simultaneously enforces sparsity, concentration, and cross-sample stability of feature importances. Unlike post-hoc methods, our approach is end-to-end trainable, applicable to mainstream tree-based models (e.g., XGBoost, LightGBM), and supports both regression and classification tasks. Extensive experiments across multiple benchmark datasets demonstrate that the proposed method improves model generalization, yields more robust and interpretable SHAP attributions, and maintains or exceeds baseline accuracy—without sacrificing predictive performance.

Traditional Shapley value computation is computationally prohibitive, and existing learnable explanation methods struggle with the non-uniform grids and irregular geometries commonly encountered in physical simulations. This work proposes OperatorSHAP—the first mesh-agnostic attribution method that extends Shapley values to function spaces. By integrating neural operator architectures with a learnable explainer, OperatorSHAP delivers consistent explanations across varying mesh resolutions without requiring model retraining. The method establishes a theoretical connection to the Aumann–Shapley value and demonstrates strong empirical alignment with discrete Shapley values across multiple grid resolutions. Consequently, it significantly enhances both the efficiency and generalization of model interpretability in physics-informed applications.

This work exposes a security vulnerability in feature selection based on aggregated SHAP values: averaging absolute SHAP values over the original data support set may erroneously eliminate important features, as SHAP computation requires extrapolation beyond the support—where dependencies on specific features can be deliberately concealed via adversarial function construction. To address this, we propose a novel aggregation paradigm over an expanded support set—the Cartesian product of marginal feature distributions—and provide the first rigorous proof that small aggregated SHAP or KernelSHAP values on this domain guarantee safe feature removal. We introduce the Shapley Lie algebra to offer a new theoretical lens, and show that column-wise random permutations provably ensure safety in standard SHAP practice. This work establishes the first theoretical guarantees for KernelSHAP, delivers a verifiable criterion for feature deletion, and empirically validates its effectiveness in identifying redundant features, simplifying models, and enhancing interpretability.

This study addresses the strong model dependency of SHAP value interpretations, which lacks a standardized analytical framework and thereby limits reliable explanations of black-box model decisions in high-stakes applications. For the first time, this work systematically evaluates SHAP explanations across multiple mainstream machine learning models on diverse datasets, uncovering consistent patterns of model dependence. Furthermore, it proposes a generalized waterfall plot visualization method tailored for multi-class classification problems. Experimental results demonstrate the effectiveness and practical utility of the proposed approach, offering both theoretical grounding and actionable guidance for practitioners in the field of explainable artificial intelligence.

This work addresses the instability of feature attribution methods—often caused by variations in training splits and random seeds—which undermines model interpretability and decision reliability. To this end, the authors propose RoSHAP, a robust attribution framework that explicitly models attribution randomness through statistical distribution estimation. RoSHAP leverages bootstrap resampling and kernel density estimation to characterize the distribution of SHAP values and introduces an integrated metric that jointly quantifies feature activity, strength, and stability. Theoretical analysis establishes its asymptotic Gaussianity while substantially reducing computational overhead. Empirical results demonstrate that RoSHAP outperforms single-run attribution approaches in identifying true signal features, and that feature subsets selected via RoSHAP maintain predictive performance comparable to full-feature models despite using fewer variables.