  In this paper, we develop the notion of evidence lower bound difference
(ELBD), based on which an efficient score algorithm is presented to implement
feature selection on latent variables of VAE and its variants. Further, we
propose weak convergence approximation algorithms to optimize VAE related
models through weighing the ``more important" latent variables selected and
accordingly increasing evidence lower bound. We discuss two kinds of different
Gaussian posteriors, mean-filed and full-covariance, for latent variables, and
make corresponding theoretical analyses to support the effectiveness of
algorithms. A great deal of comparative experiments are carried out between our
algorithms and other 9 feature selection methods on 7 public datasets to
address generative tasks. The results provide the experimental evidence of
effectiveness of our algorithms. Finally, we extend ELBD to its generalized
version, and apply the latter to tackling classification tasks of 5 new public
datasets with satisfactory experimental results.
