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Although variational autoencoders (VAE) are successfully used to obtainmeaningful low-dimensional representations for high-dimensional data, thecharacterization of critical points of the loss function for generalobservation models is not fully understood. We introduce a theoreticalframework that is based on a connection between $\beta$-VAE and generalizedlinear models (GLM). The equality between the activation function of a$\beta$-VAE and the inverse of the link function of a GLM enables us to providea systematic generalization of the loss analysis for $\beta$-VAE based on theassumption that the observation model distribution belongs to an exponentialdispersion family (EDF). As a result, we can initialize $\beta$-VAE nets bymaximum likelihood estimates (MLE) that enhance the training performance onboth synthetic and real world data sets. As a further consequence, weanalytically describe the auto-pruning property inherent in the $\beta$-VAEobjective and reason for posterior collapse.

A Generalised Linear Model Framework for $\beta$-Variational Autoencoders based on Exponential Dispersion Families