A RAD approach to deep mixture models
This addresses a problem for researchers and practitioners in machine learning who need to model mixed continuous-discrete data distributions, representing an incremental improvement over existing flow-based methods.
The paper tackles the limitation of existing flow-based models in handling discrete structures in data distributions by introducing a Real and Discrete (RAD) normalizing flow architecture. The result is a model that retains exact sampling, inference, and probability computation while enabling simultaneous modeling of continuous and discrete data.
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.