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arXiv · 2306.02568

Latent Optimal Paths by Gumbel Propagation for Variational Bayesian Dynamic Programming

Xinlei Niu·Christian Walder·Jing Zhang·Charles Patrick Martin
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Abstract

We propose the stochastic optimal path which solves the classical optimal path problem by a probability-softening solution. This unified approach transforms a wide range of DP problems into directed acyclic graphs in which all 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 of a latent path, namely Bayesian dynamic programming (BDP). We demonstrate the usage of BDP in the latent space of variational autoencoders (VAEs) and propose the BDP-VAE which captures structured sparse optimal paths as latent variables. This enables end-to-end training for generative tasks in which models rely on unobserved structural information. At last, we validate the behavior of our approach and showcase its applicability in two real-world applications: text-to-speech and singing voice synthesis. Our implementation code is available at \url{https://github.com/XinleiNIU/LatentOptimalPathsBayesianDP}.

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Xinlei Niu, Christian Walder, Jing Zhang, Charles Patrick Martin. 2023-06-05. Latent Optimal Paths by Gumbel Propagation for Variational Bayesian Dynamic Programming. https://arxiv.org/abs/2306.02568

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