mlsanityData to 14 Oct 2026

Bounding Evidence and Estimating Log-Likelihood in VAE

arXiv 2206.09453 ↗First posted 19 Jun 2022cs.LG cs.AI stat.MLcited by 6

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Abstract (arXiv)

Many crucial problems in deep learning and statistical inference are caused by a variational gap, i.e., a difference between model evidence (log-likelihood) and evidence lower bound (ELBO). In particular, in a classical VAE setting that involves training via an ELBO cost function, it is difficult to provide a robust comparison of the effects of training between models, since we do not know a log-likelihood of data (but only its lower bound). In this paper, to deal with this problem, we introduce a general and effective upper bound, which allows us to efficiently approximate the evidence of data. We provide extensive theoretical and experimental studies of our approach, including its comparison to the other state-of-the-art upper bounds, as well as its application as a tool for the evaluation of models that were trained on various lower bounds.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 14 of its 37 references that are in the map. First posted on arXiv 19 Jun 2022.

Builds on

14 of 37 references.

References · 14

  1. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 7,005
  2. 2013Auto-Encoding Variational Bayescited by 4,053
  3. 2014Deep Learning Face Attributes in the Wildcited by 3,693
  4. 2018Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Reviewcited by 482
  5. 2015Importance Weighted Autoencoderscited by 456
  6. 2016R'enyi Divergence Variational Inferencecited by 104
  7. 2017Filtering Variational Objectivescited by 91
  8. 2018Tighter Variational Bounds are Not Necessarily Bettercited by 76
  9. 2019The Thermodynamic Variational Objectivecited by 26
  10. 2018Leveraging the Exact Likelihood of Deep Latent Variable Modelscited by 23
  11. 2015Sandwiching the marginal likelihood using bidirectional Monte Carlocited by 20
  12. 2021Mind the Gap when Conditioning Amortised Inference in Sequential Latent-Variable Modelscited by 14
2 more
  1. 2019Stochastic Variational Inference via Upper Boundcited by 8
  2. 2021Improving Actor-Critic Reinforcement Learning via Hamiltonian Monte Carlo Methodcited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 1; 2025: 1; 2026: 2.

6 papers.

  1. 2023Are Ensembles Getting Better all the Time?cited by 6
  2. 2023Forward chi2 Divergence Based Variational Importance Samplingcited by 4
  3. 2026TUBE: Tangent Upper Bound on Evidence for Discrete Diffusion Language Modelscited by 2
  4. 2024A Conditional Diffusion Model for Electrical Impedance Tomography Image Reconstructioncited by 1
  5. 2025Tight Bounds for Jensen's Gap with Applications to Variational Inferencecited by 0
  6. 2026Quasi Monte Carlo methods enable extremely low-dimensional deep generative modelscited by 0