Relative entropy-regularized optimal transport on a graph: a new algorithm and an experimental comparison

Courtain, Sylvain; Guex, Guillaume; Kivimäki, Ilkka; Saerens, Marco

doi:10.1007/s13042-022-01704-6

Cited by 2 publications

(2 citation statements)

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“…Hence it was proposed in [ 19 , 45 , 46 ] to use biased gradient estimates which neglect the terms resorting to a REINFORCE gradient estimate. Unfortunately, as established by Corenflos et al [ 47 ], this can introduce some very substantial bias. To address this problem, differentiable resampling procedures have been introduced; e.g.…”

Section: Further Extensionsmentioning

confidence: 99%

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Differentiable samplers for deep latent variable models

Doucet

Moulines

Thin

2023

Phil. Trans. R. Soc. A.

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Latent variable models are a popular class of models in statistics. Combined with neural networks to improve their expressivity, the resulting deep latent variable models have also found numerous applications in machine learning. A drawback of these models is that their likelihood function is intractable so approximations have to be carried out to perform inference. A standard approach consists of maximizing instead an evidence lower bound (ELBO) obtained based on a variational approximation of the posterior distribution of the latent variables. The standard ELBO can, however, be a very loose bound if the variational family is not rich enough. A generic strategy to tighten such bounds is to rely on an unbiased low-variance Monte Carlo estimate of the evidence. We review here some recent importance sampling, Markov chain Monte Carlo and sequential Monte Carlo strategies that have been proposed to achieve this. This article is part of the theme issue ‘Bayesian inference: challenges, perspectives, and prospects’.

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Section: Further Extensionsmentioning

confidence: 99%

“…To address this problem, differentiable resampling procedures have been introduced; e.g. [ 47 , 48 ]. In these approaches, resampling is replaced by solving a regularized optimal transport problem.…”

Section: Further Extensionsmentioning

confidence: 99%