Variational Mixture of Normalizing Flows

3 March 2020

Guilherme Grijó Pires Instituto de Telecomunicações/IST

In the past few years, deep generative models, such as generative adversarial networks, variational autoencoders, and their variants, have seen wide adoption for the task of modelling complex data distributions. In spite of the outstanding sample quality achieved by those methods, they model the target distributions implicitly, in the sense that the probability density functions induced by them are not explicitly accessible. This fact renders those methods unfit for tasks that require, for example, scoring new instances of data with the learned distributions. Normalizing flows overcome this limitation by leveraging the change-of-variables formula for probability density functions, and by using transformations designed to have tractable and cheaply computable Jacobians. Although flexible, this framework lacked (until the publication of recent work) a way to introduce discrete structure (such as the one found in mixtures) in the models it allows to construct, in an unsupervised scenario. The present work overcomes this by using normalizing flows as components in a mixture model, and devising a training procedure for such a model. This procedure is based on variational inference, and uses a variational posterior parameterized by a neural network. As will become clear, this model naturally lends itself to (multimodal) density estimation, semi-supervised learning, and clustering.

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Variational Mixture of Normalizing Flows banner Guilherme is a ML Engineer / Data Scientist, and recent graduate from IST's MSc program in Electrical and Computer Engineering. Having worked at Jungle (, he developed an interest for the application of machine learning and data-driven techniques to the modelling of dynamical systems, such as power transformers, wind turbines, industrial components. Presently a consultant with DareData (, he has had the chance to work on a broad set of data-problems. He is currently trying to kickstart an academic research career, and he is interested in a probabilistic view of machine learning, generative models, and more recently in dynamical systems and causality.