NICE: Non-linear Independent Components Estimation. 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.

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  1. Celledoni, E.; Ehrhardt, M. J.; Etmann, C.; McLachlan, R. I.; Owren, B.; Schonlieb, C.-B.; Sherry, F.: Structure-preserving deep learning (2021)
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  3. Arenz, Oleg; Zhong, Mingjun; Neumann, Gerhard: Trust-region variational inference with Gaussian mixture models (2020)
  4. Brehmer, Johann; Louppe, Gilles; Pavez, Juan; Cranmer, Kyle: Mining gold from implicit models to improve likelihood-free inference (2020)
  5. Jin, Pengzhan; Zhang, Zhen; Zhu, Aiqing; Tang, Yifa; Karniadakis, George Em: Sympnets: intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems (2020)
  6. Simon Badger, Joseph Bullock: Using neural networks for efficient evaluation of high multiplicity scattering amplitudes (2020) arXiv
  7. Sil C. van de Leemput; Jonas Teuwen; Bram van Ginneken; Rashindra Manniesing: MemCNN: A Python/PyTorch package for creating memory-efficient invertible neural networks (2019) not zbMATH
  8. Wu, Ying Nian; Gao, Ruiqi; Han, Tian; Zhu, Song-Chun: A tale of three probabilistic families: discriminative, descriptive, and generative models (2019)
  9. Zhang, Shiliang; Jiang, Hui; Dai, Lirong: Hybrid orthogonal projection and estimation (HOPE): a new framework to learn neural networks (2016)
  10. Mathieu Germain, Karol Gregor, Iain Murray, Hugo Larochelle: MADE: Masked Autoencoder for Distribution Estimation (2015) arXiv