NICE swMATH ID: 29631 Software Authors: Laurent Dinh, David Krueger, Yoshua Bengio Description: 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. Homepage: https://arxiv.org/abs/1410.8516 Source Code: https://github.com/laurent-dinh/nice Related Software: Glow; Adam; ImageNet; Python; torchdiffeq; AlexNet; Wasserstein GAN; PyTorch; StackGAN; CIFAR; TensorFlow; MADE; i-RevNet; WaveGlow; WaveNet; Flow-GAN; darch; PixelCNN++; LR-GAN; Flow++ Cited in: 18 Publications all top 5 Cited by 54 Authors 2 Marino, Joseph 2 Tang, Yifa 2 Wan, Xiaoliang 2 Wei, Shuangqing 2 Zabaras, Nicholas J. 2 Zhu, Aiqing 1 Abbasnejad, M. Ehsan 1 An, Senjian 1 Arenz, Oleg 1 Brehmer, Johann 1 Celledoni, Elena 1 Chen, Lei 1 Cranmer, Kyle 1 Dai, Lirong 1 Ehrhardt, Matthias Joachim 1 Etmann, Christian 1 Gao, Huanhuan 1 Gao, Ruiqi 1 Guo, Ling 1 Han, Tian 1 He, Jiawei 1 Isomura, Takuya 1 Jiang, Hui 1 Jin, Pengzhan 1 Karniadakis, George Em 1 Li, Ling 1 Li, Tingting 1 Liang, Zhangyong 1 Liu, Jian 1 Liu, Lingqiao 1 Liu, Wanquan 1 Louppe, Gilles 1 Mandt, Stephan 1 McLachlan, Robert I. 1 Neumann, Gerhard 1 Owren, Brynjulf 1 Padmanabha, Govinda Anantha 1 Pavez, Juan 1 Schönlieb, Carola-Bibiane 1 Sherry, Ferdia 1 Shi, Javen 1 Toyoizumi, Taro 1 van den Hengel, Anton 1 Wang, Ruhua 1 Wu, Hao 1 Wu, Yingnian 1 Xia, Yingzhi 1 Zhang, Jiawei 1 Zhang, Shiliang 1 Zhang, Zhen 1 Zhong, Mingjun 1 Zhou, Tao 1 Zhu, Beibei 1 Zhu, Song-Chun all top 5 Cited in 13 Serials 4 Journal of Computational Physics 2 Neural Computation 2 Journal of Machine Learning Research (JMLR) 1 Acta Mechanica 1 Journal of Computational and Applied Mathematics 1 Quarterly of Applied Mathematics 1 Neural Networks 1 European Journal of Applied Mathematics 1 Machine Learning 1 Proceedings of the National Academy of Sciences of the United States of America 1 International Journal of Computer Vision 1 Communications in Computational Physics 1 Mathematical Foundations of Computing all top 5 Cited in 13 Fields 14 Computer science (68-XX) 7 Statistics (62-XX) 5 Numerical analysis (65-XX) 2 Probability theory and stochastic processes (60-XX) 2 Geophysics (86-XX) 2 Biology and other natural sciences (92-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year