NICE: Non-linear Independent Components Estimation
This provides a method for density estimation and generative modeling in machine learning, with incremental improvements in tractability and sampling.
The paper tackles the problem of modeling complex high-dimensional densities by proposing NICE, a deep learning framework that learns a non-linear transformation to map data to a latent space with independent variables, resulting in good generative models on four image datasets and applications like inpainting.
We propose a deep learning framework for modeling complex high-dimensional densities called Non-linear Independent Component Estimation (NICE). It is based on the idea that a good representation is one in which the data has a distribution that is easy to model. For this purpose, a non-linear deterministic transformation of the data is learned that maps it to a latent space so as to make the transformed data conform to a factorized distribution, i.e., resulting in independent latent variables. We parametrize this transformation so that computing the Jacobian determinant and inverse transform is trivial, yet we maintain the ability to learn complex non-linear transformations, via a composition of simple building blocks, each based on a deep neural network. The training criterion is simply the exact log-likelihood, which is tractable. Unbiased ancestral sampling is also easy. We show that this approach yields good generative models on four image datasets and can be used for inpainting.