Amortized SHAP values via sparse Fourier function approximation

Ali Gorji, Andisheh Amrollahi, Andreas Krause

Keywords: interpretability, explainability, shap values

TL;DR: Computing SHAP values for black boxes and trees, orders of magnitudes faster than other methods

Abstract:

SHAP values -- a.k.a.~SHapley Additive exPlanations -- are a popular local feature-attribution method widely used in interpretable and explainable AI. We tackle the problem of efficiently computing these values. We cover both the model-agnostic (black-box) setting, where one only has query access to the model and also the case of (ensembles of) trees where one has access to the structure of the tree. For both the black-box and the tree setting we propose a two-stage approach for estimating SHAP values.

Our algorithm's first step harnesses recent results showing that many real-world predictors have a spectral bias that allows us to either exactly represent (in the case of ensembles of decision trees), or efficiently approximate them (in the case of neural networks) using a compact Fourier representation.
For the case of trees, given access to the tree structure, one can extract the Fourier representation using a simple recursive algorithm.
For the black-box setting, given query access to the black-box function, we utilize a sparse Fourier approximation algorithm to efficiently extract its compact Fourier approximation.

In the second step of the algorithm, we use the Fourier representation to exactly compute SHAP values. The second step is computationally very cheap because firstly, the representation is compact and secondly, we prove that there exists a closed-form expression for SHAP values for the Fourier basis functions. Furthermore, the expression we derive effectively ``linearizes'' the computation into a simple summation and is amenable to parallelization on multiple cores or a GPU. Since the function approximation (first step) is only done once, it allows us to produce Shapley values in an amortized way. We show speedups compared to relevant baseline methods equal levels of accuracy for both the tree and black-box settings. Moreover, this approach introduces a reliable and fine-grained continuous trade-off between computation and accuracy through the sparsity of the Fourier approximation, a feature previously unavailable in all black-box methods.

Primary Area: interpretability and explainable AI

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Submission Number: 7817