Neural Autoregressive Distribution Estimation

Benigno Uria, Marc-Alexandre Côté, Karol Gregor, Iain Murray, Hugo Larochelle

Research output: Contribution to journalArticlepeer-review


We present Neural Autoregressive Distribution Estimation (NADE) models, which are neural network architectures applied to the problem of unsupervised distribution and density estimation. They leverage the probability product rule and a weight sharing scheme inspired from restricted Boltzmann machines, to yield an estimator that is both tractable and has good generalization performance. We discuss how they achieve competitive performance in modeling both binary and real-valued observations. We also present how deep NADE models can be trained to be agnostic to the ordering of input dimensions used by the autoregressive product rule decomposition. Finally, we also show how to exploit the topological structure of pixels in images using a deep convolutional architecture for NADE.
Original languageEnglish
Pages (from-to)1-37
Number of pages37
JournalJournal of Machine Learning Research
Issue number205
Publication statusPublished - 1 Sep 2016


  • deep learinng
  • neural networks
  • density modeling
  • unsupervised learning

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