NICE: Non-linear Independent Components Estimation

TLDR

A good representation is one in which the data distribution is easy to model. The authors propose NICE, a deep learning framework for modeling complex high‑dimensional densities. NICE learns a non‑linear deterministic transformation that maps data to a latent space with independent variables, using neural‑network‑based building blocks that allow trivial Jacobian computation and exact log‑likelihood training. The method enables unbiased ancestral sampling and achieves strong generative performance on four image datasets, also supporting inpainting.

Abstract

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.