NICE: Non-linear Independent Components Estimation

TL;DR

NICE introduces a deep learning framework that models complex high-dimensional densities by transforming data into a space with independent components, enabling efficient density estimation and sampling.

Contribution

It presents a novel non-linear transformation with tractable Jacobian and inverse, allowing effective density modeling and sampling in high-dimensional spaces.

Findings

Achieves good generative performance on four image datasets.

Enables efficient ancestral sampling and inpainting.

Uses a simple training criterion based on exact log-likelihood.

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.