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  4. A Generalised Linear Model Framework for v-Variational Autoencoders based on Exponential Dispersion Families
 
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2021
Journal Article
Title

A Generalised Linear Model Framework for v-Variational Autoencoders based on Exponential Dispersion Families

Abstract
Although variational autoencoders (VAE) are successfully used to obtain meaningful low-dimensional representations for high-dimensional data, the characterization of critical points of the loss function for general observation models is not fully understood. We introduce a theoretical framework that is based on a connection between v-VAE and generalized linear models (GLM). The equality between the activation function of a v-VAE and the inverse of the link function of a GLM enables us to provide a systematic generalization of the loss analysis for v-VAE based on the assumption that the observation model distribution belongs to an exponential dispersion family (EDF). As a result, we can initialize v-VAE nets by maximum likelihood estimates (MLE) that enhance the training performance on both synthetic and real world data sets. As a further consequence, we analytically describe the auto-pruning property inherent in the v-VAE objective and reason for posterior collapse.
Author(s)
Sicks, Robert
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM  
Korn, Ralf
Department of Financial Mathematics TU Kaiserslautern
Schwaar, Stefanie  
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM  
Journal
Journal of Machine Learning Research  
Link
Link
Language
English
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM  
Keyword(s)
  • variational autoencoders

  • ML-estimation

  • EDF observation models

  • loss analysis

  • posterior collapse

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