Discussion of "The Neural Autoregressive Distribution Estimator"

The Restricted Boltzmann Machine (Smolensky, 1986; Hinton et al., 2006) has inspired much research in recent years, in particular as a building block for deep architectures (see Bengio (2009) for a review). The Restricted Boltzmann Machine (RBM) is an undirected graphical model with latent variables, exact inference, rather simple sampling procedures (block Gibbs), and several successful learning algorithms based on approximations of the log-likelihood gradient. However, when it comes to actually computing the distribution or density function, it is intractable, except when either the number of inputs or latent variables is very small (about 25 binary hidden units with current computers and about an hour of computing, on MNIST).