1.) Dropout.<p>Gal and Ghahramani &quot;We show that a neural network with arbitrary depth and non-linearities, with dropout applied before every weight layer, is mathematically equivalent to an approximation to the probabilistic deep Gaussian process&quot; <a href="http:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;1506.02142.pdf" rel="nofollow">http:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;1506.02142.pdf</a><p>2.) Deep.<p>There have been many hierarchical networks in Bayesian statistics. Hierarchical Dirichlet Process, hierarchical beta process, Pitman-Yor process, Gaussian process, nested, dependent, translated, generalized versions of the Chinese Restaurant process, or the Indian Buffet one. The deep part isn&#x27;t new.<p>3.) Auto-encoders.<p>People seem to talk about auto-encoders a lot. Its very definition introduces hidden variables about which very little is defined. It corresponds with some kind of prior on what representation should be used by the network. This is studied in Bayesian compressive sensing. <a href="http:&#x2F;&#x2F;machinelearning.wustl.edu&#x2F;mlpapers&#x2F;paper_files&#x2F;icml2007_JiC07.pdf" rel="nofollow">http:&#x2F;&#x2F;machinelearning.wustl.edu&#x2F;mlpapers&#x2F;paper_files&#x2F;icml20...</a><p>4.) Layered training.<p>Layers are trained one by one. Doesn&#x27;t really ring a bell. Maybe it corresponds to some MCMC method I&#x27;m not aware of. There are often inner and outer loops in MCMC and I guess something fundamental can be told about the right moments to switch from inner to outer. However, that does not correspond to learning low-level features first.