2e9f978b222a956ba6bdf427efbd9ab3-Supplemental.pdf

B.3 Derivations of Eq. (19) Similar to derivation above, we give the gradient with respect to weight vector w RM+, which is given by wDKL = w log Z(U,w) wEU,w (log pθ(X |z))T1N + wEU,w (log pθ(U |z))Tw . The learning rate of each stochastic gradient descent step is γt t 1, where t {1,,T}denotes the iteration for optimization. We already report the t-SNE visualization of ByPE-VAE and standard VAE in Figure. Here we give more t-SNE visualization results. First, we randomly sample from ByPE-VAEs trained on different datasets, namely, MNIST, Fashion MNIST, and Celeba, as shown in Fig.7.