  Renormalization group (RG) methods, which model the way in which the
effective behavior of a system depends on the scale at which it is observed,
are key to modern condensed-matter theory and particle physics. We compare the
ideas behind the RG on the one hand and deep machine learning on the other,
where depth and scale play a similar role. In order to illustrate this
connection, we review a recent numerical method based on the RG---the
multiscale entanglement renormalization ansatz (MERA)---and show how it can be
converted into a learning algorithm based on a generative hierarchical Bayesian
network model. Under the assumption---common in physics---that the distribution
to be learned is fully characterized by local correlations, this algorithm
involves only explicit evaluation of probabilities, hence doing away with
sampling.
