# NICE: Non-linear Independent Components Estimation

arXiv: https://arxiv.org/abs/1410.8516 · HTML: https://mlsanity.com/paper/1410.8516/

## Key facts

- Cited by 1,058 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2014.

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## Abstract (arXiv)

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.