Rectify Heterogeneous Models with Semantic Mapping.

This is the supplementary material for the paper “Rectify Heterogeneous Model with Semantic Mapping”, which contains four parts. First, we give a detailed proof of the sample complexity theorem for homogeneous model reuse case in our paper. Then, the concrete derivation of Bregman ADMM solver for REFORM implementation is presented. Next is an illustration of the EMIT strategy to generate feature meta representations, together with discussions on EMIT and REFORM. Finally are descriptions of experimental settings and additional investigation results. 1. Proof of Theorem 1 In this section, we give proof of theorem 1 in our paper. A C-class dataset D = {(xi,yi)}i=1 is sampled from the latent distributionZ = X ×Y , withX and Y corresponding to the instance and label distribution, respectively. In each pair, instance xi ∈ R, and label vector yi ∈ {−1, 1} . The position of the value 1 in yi denotes the class label. In this theoretical analysis, we assume all the instances are in the homogeneous form without loss of generality. In other words, there is a constant value 1 at the end of each instance representation (so we do not need to consider the bias in the classifier). In addition, we can bound each instance by ‖xi‖ ≤ χ for i = 1, . . . , N . χ is a positive scalar. Consider the linear classifier W ∈ Rd×C , which can be learned by the following form: