Predominately in explainable artificial intelligence (XAI) research, the Shapley value (SV) is applied to determine feature attributions for any black box model. Shapley interaction indices extend the SV to define any-order feature interactions. Defining a unique Shapley interaction index is an open research question and, so far, three definitions have been proposed, which differ by their choice of axioms. Moreover, each definition requires a specific approximation technique. Here, we propose SHAPley Interaction Quantification (SHAP-IQ), an efficient sampling-based approximator to compute Shapley interactions for arbitrary cardinal interaction indices (CII), i.e. interaction indices that satisfy the linearity, symmetry and dummy axiom.

Predominately in explainable artificial intelligence (XAI) research, the Shapley value (SV) is applied to determine feature attributions for any black box model. Shapley interaction indices extend the SV to define any-order feature interactions. Defining a unique Shapley interaction index is an open research question and, so far, three definitions have been proposed, which differ by their choice of axioms. Moreover, each definition requires a specific approximation technique. Here, we propose SHAPley Interaction Quantification (SHAP-IQ), an efficient sampling-based approximator to compute Shapley interactions for arbitrary cardinal interaction indices (CII), i.e. interaction indices that satisfy the linearity, symmetry and dummy axiom. SHAP-IQ is based on a novel representation and, in contrast to existing methods, we provide theoretical guarantees for its approximation quality, as well as estimates for the variance of the point estimates. For the special case of SV, our approach reveals a novel representation of the SV and corresponds to Unbiased KernelSHAP with a greatly simplified calculation. We illustrate the computational efficiency and effectiveness by explaining language, image classification and high-dimensional synthetic models.

With the rapid growth of large-scale machine learning models in genomics, Shapley values have emerged as a popular method for model explanations due to their theoretical guarantees. While Shapley values explain model predictions locally for an individual input query sequence, extracting biological knowledge requires global explanation across thousands of input sequences. This demands exponential model evaluations per sequence, resulting in significant computational cost and carbon footprint. Herein, we develop SHAP zero, a method that estimates Shapley values and interactions with a near-zero marginal cost for future queried sequences after paying a one-time fee for model sketching. SHAP zero achieves this by establishing a surprisingly underexplored connection between the Shapley values and interactions and the Fourier transform of the model. Explaining two genomic models, one trained to predict guide RNA binding and the other to predict DNA repair outcome, we demonstrate that SHAP zero achieves orders of magnitude reduction in amortized computational cost compared to state-of-the-art algorithms, revealing almost all predictive motifs -- a finding previously inaccessible due to the combinatorial space of possible interactions.

Predominately in explainable artificial intelligence (XAI) research, the Shapley value (SV) is applied to determine feature attributions for any black box model. Shapley interaction indices extend the SV to define any-order feature interactions. Defining a unique Shapley interaction index is an open research question and, so far, three definitions have been proposed, which differ by their choice of axioms. Moreover, each definition requires a specific approximation technique. Here, we propose SHAPley Interaction Quantification (SHAP-IQ), an efficient sampling-based approximator to compute Shapley interactions for arbitrary cardinal interaction indices (CII), i.e. interaction indices that satisfy the linearity, symmetry and dummy axiom. SHAP-IQ is based on a novel representation and, in contrast to existing methods, we provide theoretical guarantees for its approximation quality, as well as estimates for the variance of the point estimates.

Predominately in explainable artificial intelligence (XAI) research, the Shapley value (SV) is applied to determine feature attributions for any black box model. Shapley interaction indices extend the SV to define any-order feature interactions. Defining a unique Shapley interaction index is an open research question and, so far, three definitions have been proposed, which differ by their choice of axioms. Moreover, each definition requires a specific approximation technique. Here, we propose SHAPley Interaction Quantification (SHAP-IQ), an efficient sampling-based approximator to compute Shapley interactions for arbitrary cardinal interaction indices (CII), i.e. interaction indices that satisfy the linearity, symmetry and dummy axiom. SHAP-IQ is based on a novel representation and, in contrast to existing methods, we provide theoretical guarantees for its approximation quality, as well as estimates for the variance of the point estimates. For the special case of SV, our approach reveals a novel representation of the SV and corresponds to Unbiased KernelSHAP with a greatly simplified calculation. We illustrate the computational efficiency and effectiveness by explaining language, image classification and high-dimensional synthetic models.

Abstract: Predominately in explainable artificial intelligence (XAI) research, the Shapley value (SV) is applied to determine feature importance scores for any black box model. Shapley interaction indices extend the Shapley value to define any-order feature interaction scores. Defining a unique Shapley interaction index is an open research question and, so far, three definitions have been proposed, which differ by their choice of axioms. Moreover, each definition requires a specific approximation technique. We, however, propose SHAPley Interaction Quantification (SHAP-IQ), an efficient sampling-based approximator to compute Shapley interactions for all three definitions, as well as all other that satisfy the linearity, symmetry and dummy axiom.