  Conditional belief networks introduce stochastic binary variables in neural
networks. Contrary to a classical neural network, a belief network can predict
more than the expected value of the output $Y$ given the input $X$. It can
predict a distribution of outputs $Y$ which is useful when an input can admit
multiple outputs whose average is not necessarily a valid answer. Such networks
are particularly relevant to inverse problems such as image prediction for
denoising, or text to speech. However, traditional sigmoid belief networks are
hard to train and are not suited to continuous problems. This work introduces a
new family of networks called linearizing belief nets or LBNs. A LBN decomposes
into a deep linear network where each linear unit can be turned on or off by
non-deterministic binary latent units. It is a universal approximator of
real-valued conditional distributions and can be trained using gradient
descent. Moreover, the linear pathways efficiently propagate continuous
information and they act as multiplicative skip-connections that help
optimization by removing gradient diffusion. This yields a model which trains
efficiently and improves the state-of-the-art on image denoising and facial
expression generation with the Toronto faces dataset.
