Deep Density Destructors

We propose a unified framework for deep density models by formally defining density destructors. A density destructor is an invertible function that transforms a given density to the uniform density—essentially destroying any structure in the original density. This destructive transformation generalizes Gaussianization via ICA and more recent autoregressive models such as MAF and Real NVP. Informally, this transformation can be seen as a generalized whitening procedure or a multivariate generalization of the univariate CDF function. Unlike Gaussianization, our destructive transformation has the elegant property that the density function is equal to the absolute value of the Jacobian determinant. Thus, each layer of a deep density can be seen as a shallow density—uncovering a fundamental connection between shallow and deep densities. In addition, our framework provides a common interface for all previous methods enabling them to be systematically combined, evaluated and improved. Leveraging the connection to shallow densities, we also propose a novel tree destructor based on tree densities and an image-specific destructor based on pixel locality. We illustrate our framework on a 2D dataset, MNIST, and CIFAR-10. Code is available on first author’s website.