In this document we provide the detailed proofs of results presented in the main manuscript. We also provide the Hoeffding decomposition for the bootstrap in Proposition A.4. In Section B we provide all results needed for a complete proof of Theorem 1. In Sections B.1, B.2, and B.3 we provide the proof of Theorem 1, the adaptation of high dimensional CLT of [8] to our setting and all supporting lemmas, respectively. In Section C we provide all details of the proof of the Bootstrap consistency, i.e.

An Zhang and Leheng Sheng contribute equally to this work. Zhibo Cai is the corresponding author.

Moreover,10 we will add one more predictiveperformance measure: F1 score. If the attribution map accurately represents the importance of the pixels, the20 classifier must havelower predictiveperformance. In [4], the authors introduce attention map transfer and gradient transfer. The function of the loss functions34 are different. The intent behind our stochastic matching regularizer is to facilitate42 the transfer of relevant information and prevent overfitting.