Exercises
579
19.4 (? ?) Evaluate the Kullback–Leibler divergence term in (19.14). Hence, show how the gradients of this term with respect to w and φ can be evaluated for training the encoder and decoder networks. 19.5 (?) We have seen that the ELBO given by (19.11) can be written in the form (19.14). Show that it can also be written as Z Ln (w, φ) = q(zn |xn , φ) ln {p(xn |zn , w)p(zn )} dzn Z − q(zn |xn , φ) ln q(zn |xn , φ) dzn . (19.24) 19.6 (?) Show that the ELBO given by (19.11) can be written in the form Z Ln (w, φ) = q(zn |xn , φ) ln p(zn ) dzn Z p(xn |zn , w) + q(zn |xn , φ) ln dzn . q(zn |xn , φ)
(19.25)