This paper define the importance score of an image patch as the dependence between the perturbation $M_i$ and the output $y$. The greater the dependence of $y$ on $M_i$, the more important the corresponding image patch $x_i$ is.
To compute the dependence between two random variables, they introduce the Hilbert-Schmidt Independence Criterion along with a computationally efficient estimation method for HSIC.
The algorithm is defined as follows:
References
- A. Gretton, O. Bousquet, A. Smola, and B. Schölkopf. Measuring statistical dependence with hilbert-schmidt norms. In Proceedings of the 16th International Conference on Algorithmic Learning Theory, ALT’05, page 63–77, Berlin, Heidelberg, 2005. Springer-Verlag
- Novello, P., Fel, T. and Vigouroux, D., 2022. Making sense of dependence: Efficient black-box explanations using dependence measure. Advances in Neural Information Processing Systems, 35, pp.4344-4357.