This paper applies Sobol indices to compute the contribution of each feature, enabling the method to capture higher-order interactions between features. Existing methods typically use the loss function to measure the difference between the original output and the perturbed output. For example, in classification problems, cross-entropy is commonly applied as follows :

Si=cross_entropy(f(x),f(x−i)), S_i = \text{cross\_entropy}(f(\mathbf{x}), f(\mathbf{x}_{-i})),

where SiS_i represents the importance scores of the ii-th feature. In contrast, this paper computes SiS_i based on Sobol indices.

The perturbation function is as follows :

Φ(x,M)=x⊙M+(1−M)⊙0 \Phi(\mathbf{x}, \mathbf{M}) = \mathbf{x} \odot \mathbf{M} + (1 - \mathbf{M}) \odot 0

In this paper, the function is defined similarly to existing literature but is referred to as Inpainting perturbation.