Latent Optimal Paths by Gumbel Propagation for Variational Bayesian
  Dynamic Programming
Xinlei Niu Christian Walder Jing Zhang Charles Patrick Martin
We propose a unified approach to obtain structured sparse optimal paths in
the latent space of a variational autoencoder (VAE) using dynamic programming
and Gumbel propagation. We solve the classical optimal path problem by a
probability softening solution, called the stochastic optimal path, and
transform a wide range of DP problems into directed acyclic graphs in which all
possible paths follow a Gibbs distribution. We show the equivalence of the
Gibbs distribution to a message-passing algorithm by the properties of the
Gumbel distribution and give all the ingredients required for variational
Bayesian inference. Our approach obtaining latent optimal paths enables
end-to-end training for generative tasks in which models rely on the
information of unobserved structural features. We validate the behavior of our
approach and showcase its applicability in two real-world applications:
text-to-speech and singing voice synthesis.