Latent Optimal Paths by Gumbel Propagation for Variational Bayesian Dynamic Programming

• URL: http://arxiv.org/abs/2306.02568v3
• Date: Tue, 25 Jun 2024 06:13:38 GMT
• Title: Latent Optimal Paths by Gumbel Propagation for Variational Bayesian Dynamic Programming
• Authors: Xinlei Niu, Christian Walder, Jing Zhang, Charles Patrick Martin,
• Abstract summary: We show the equivalence of the Gibbs distribution to a message-passing algorithm by the properties of the Gumbel distribution. We propose the BDP-VAE which captures structured sparse optimal paths as latent variables.
• Score: 12.249274845167415
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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