Shapley Value Computation via Functional Decomposition
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Solution Overview
Problem
Computing Shapley values for machine learning models is computationally expensive, and existing approximation methods often produce results far from the true values.
Innovation Solution
The proposed solution involves computing Shapley values exactly for certain SHAP definitions that satisfy additivity and dummy assumptions by leveraging model structure information, such as known functional decompositions or model orders, and using iterative methods to approximate values when the order is unknown.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If sampling methods are used to approximate Shapley values, then computational cost is reduced, but accuracy of results deteriorates significantly
Solution Approach 1:
The patent segments the model into functional components through fANOVA decomposition, breaking down the complex model into additive terms of different orders. This segmentation allows efficient computation of Shapley values for each component separately while maintaining exact accuracy, avoiding the need for sampling approximations.
Solution Approach 2:
The patent changes the parameter of model representation from black-box to structured functional decomposition. By transforming the model into a sum of functional components with known structures, the computation can exploit this structural information to calculate exact Shapley values efficiently without relying on sampling methods.
2Measurement precision
If exact Shapley values are computed using traditional methods, then accuracy is maintained, but computational complexity increases exponentially
Solution Approach 1:
The patent divides the computation into segments corresponding to different functional components of the model. Instead of computing Shapley values for the entire model at once (which requires 2^p evaluations), it computes Shapley values for each low-order functional component separately and sums them, reducing complexity from exponential to polynomial.
Solution Approach 2:
The patent performs preliminary functional decomposition of the model before computing Shapley values. By pre-processing the model into a structured form with known functional components, it creates a foundation that enables efficient subsequent computation, avoiding the need for exhaustive evaluations.
3Productivity
If functional decomposition is used to speed up computation, then computational efficiency improves, but requirement for model structure information increases
Solution Approach 1:
The patent makes the computational method self-adaptive by automatically performing fANOVA decomposition when functional structure is unknown. The system can autonomously analyze the model and determine its functional components without requiring external specification, making the method universally applicable while maintaining efficiency.
Solution Approach 2:
The patent creates a universal computational framework that handles multiple cases: models with known functional decomposition, models where decomposition can be automatically derived, and general cases using iterative approximation. This multi-functional approach maintains high efficiency across different model types without requiring specialized handling for each case.
Data Source
AI summary
Systems, apparatuses, methods, and computer program products are disclosed for computing a Shapley additive explanation (SHAP) value ϕi using model structure information. An example method includes receiving a model ƒ(x) that uses a vector of features x as input, where the model has a known functional decomposition and generating, using the known functional decomposition, a set of lower order terms ƒv(xv), where a lower order term from the set of lower order terms takes a subset of the features as input, where a sum of the set of lower order terms equals the model ƒ(x). The example method further includes computing a set of lower-order SHAP values ϕi(ƒv) for the set of lower order terms and computing the SHAP value ϕi for the model based on a sum of the set of lower-order SHAP values.