  Deep Generative Networks (DGNs) with probabilistic modeling of their output
and latent space are currently trained via Variational Autoencoders (VAEs). In
the absence of a known analytical form for the posterior and likelihood
expectation, VAEs resort to approximations, including (Amortized) Variational
Inference (AVI) and Monte-Carlo (MC) sampling. We exploit the Continuous
Piecewise Affine (CPA) property of modern DGNs to derive their posterior and
marginal distributions as well as the latter's first moments. These findings
enable us to derive an analytical Expectation-Maximization (EM) algorithm that
enables gradient-free DGN learning. We demonstrate empirically that EM training
of DGNs produces greater likelihood than VAE training. Our findings will guide
the design of new VAE AVI that better approximate the true posterior and open
avenues to apply standard statistical tools for model comparison, anomaly
detection, and missing data imputation.
