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Latent Optimal Paths by Gumbel Propagation for Variational Bayesian Dynamic Programming

arXiv 2306.02568 ↗First posted 5 Jun 2023stat.ML cs.LGcited by 0

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Abstract (arXiv)

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 urlhttps://github.com/XinleiNIU/LatentOptimalPathsBayesianDP.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 31 of its 48 references that are in the map. First posted on arXiv 5 Jun 2023.

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References · 31

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19 more
  1. 2021Diff-TTS: A Denoising Diffusion Model for Text-to-Speechcited by 156
  2. 2021DiffSinger: Singing Voice Synthesis via Shallow Diffusion Mechanismcited by 154
  3. 2014A* Samplingcited by 150
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  17. 2021VAENAR-TTS: Variational Auto-Encoder based Non-AutoRegressive Text-to-Speech Synthesiscited by 7
  18. 2021Leveraging Recursive Gumbel-Max Trick for Approximate Inference in Combinatorial Spacescited by 7
  19. 2020Exact, Parallelizable Dynamic Time Warping Alignment with Linear Memorycited by 3

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