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We consider a variational autoencoder (VAE) for binary data. Our maininnovations are an interpretable lower bound for its training objective, amodified initialization and architecture of such a VAE that leads to fastertraining, and a decision support for finding the appropriate dimension of thelatent space via using a PCA. Numerical examples illustrate our theoreticalresult and the performance of the new architecture.

A lower bound for the ELBO of the Bernoulli Variational Autoencoder