A RAD approach to deep mixture models

TL;DR

This paper introduces the RAD normalizing flow architecture that combines continuous and discrete latent variables through domain partitioning, enabling effective modeling of complex data with both types of structures while maintaining key flow properties.

Contribution

It proposes a novel RAD approach that integrates discrete and continuous variables in flow models, overcoming limitations of traditional flow architectures.

Findings

Retains exact sampling and inference capabilities.

Allows modeling of discrete structures alongside continuous data.

Demonstrates effectiveness on complex data distributions.

Abstract

Flow based models such as Real NVP are an extremely powerful approach to density estimation. However, existing flow based models are restricted to transforming continuous densities over a continuous input space into similarly continuous distributions over continuous latent variables. This makes them poorly suited for modeling and representing discrete structures in data distributions, for example class membership or discrete symmetries. To address this difficulty, we present a normalizing flow architecture which relies on domain partitioning using locally invertible functions, and possesses both real and discrete valued latent variables. This Real and Discrete (RAD) approach retains the desirable normalizing flow properties of exact sampling, exact inference, and analytically computable probabilities, while at the same time allowing simultaneous modeling of both continuous and discrete structure in a data distribution.