mlsanityData to 14 Oct 2026

Statistical Guarantees for Variational Autoencoders using PAC-Bayesian Theory

arXiv 2310.04935 ↗First posted 7 Oct 2023cs.LG stat.MLcited by 16

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Abstract (arXiv)

Since their inception, Variational Autoencoders (VAEs) have become central in machine learning. Despite their widespread use, numerous questions regarding their theoretical properties remain open. Using PAC-Bayesian theory, this work develops statistical guarantees for VAEs. First, we derive the first PAC-Bayesian bound for posterior distributions conditioned on individual samples from the data-generating distribution. Then, we utilize this result to develop generalization guarantees for the VAE's reconstruction loss, as well as upper bounds on the distance between the input and the regenerated distributions. More importantly, we provide upper bounds on the Wasserstein distance between the input distribution and the distribution defined by the VAE's generative model.

Key facts. Cited by 16 papers in the map (data through 14 Oct 2026). Builds on 28 of its 61 references that are in the map. First posted on arXiv 7 Oct 2023.

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28 of 61 references.

References · 28

  1. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,054
  2. 2020NVAE: A Deep Hierarchical Variational Autoencodercited by 637
  3. 2015Generating Sentences from a Continuous Spacecited by 612
  4. 2014Semi-Supervised Learning with Deep Generative Modelscited by 496
  5. 2017Wasserstein Auto-Encoderscited by 373
  6. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 293
  7. 2021User-friendly introduction to PAC-Bayes boundscited by 239
  8. 2018Sorting out Lipschitz function approximationcited by 213
  9. 2017Generalization and Equilibrium in Generative Adversarial Nets (GANs)cited by 166
  10. 2019A Primer on PAC-Bayesian Learningcited by 132
  11. 2020Tighter risk certificates for neural networkscited by 112
  12. 2016PAC-Bayesian Theory Meets Bayesian Inferencecited by 88
16 more
  1. 2020Lipschitz constant estimation of Neural Networks via sparse polynomial optimizationcited by 87
  2. 2017Entropy-SGD optimizes the prior of a PAC-Bayes bound: Generalization properties of Entropy-SGD and data-dependent priorscited by 81
  3. 2018How Well Generative Adversarial Networks Learn Distributionscited by 78
  4. 2017Meta-Learning by Adjusting Priors Based on Extended PAC-Bayes Theorycited by 76
  5. 2020PAC-Bayes Analysis Beyond the Usual Boundscited by 63
  6. 2016A Strongly Quasiconvex PAC-Bayesian Boundcited by 54
  7. 2017On the Discrimination-Generalization Tradeoff in GANscited by 48
  8. 2020Some Theoretical Insights into Wasserstein GANscited by 28
  9. 2020Statistical guarantees for generative models without dominationcited by 27
  10. 2018Nonparametric Density Estimation under Adversarial Lossescited by 26
  11. 2022Online PAC-Bayes Learningcited by 22
  12. 2022On PAC-Bayesian reconstruction guarantees for VAEscited by 20
  13. 2017PAC-Bayes and Domain Adaptationcited by 16
  14. 2021Certifiably Robust Variational Autoencoderscited by 14
  15. 2023PAC-Bayesian Generalization Bounds for Adversarial Generative Modelscited by 13
  16. 2021Statistical Regeneration Guarantees of the Wasserstein Autoencoder with Latent Space Consistencycited by 3

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Citing papers per year: 2023: 2; 2024: 3; 2025: 7; 2026: 4.

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  1. 2023A Note on the Convergence of Denoising Diffusion Probabilistic Modelscited by 9
  2. 2024Statistical Guarantees for Lifelong Reinforcement Learning using PAC-Bayes Theorycited by 7
  3. 2025Generalization in VAE and Diffusion Models: A Unified Information-Theoretic Analysiscited by 3
  4. 2023Variational excess risk bound for general state space modelscited by 2
  5. 2024A Markov Random Field Multi-Modal Variational AutoEncodercited by 2
  6. 2025Multi-Component VAE with Gaussian Markov Random Fieldcited by 2
  7. 2026Bound to Disagree: Generalization Bounds via Certifiable Surrogatescited by 2
  8. 2024Multi-View Majority Vote Learning Algorithms: Direct Minimization of PAC-Bayesian Boundscited by 1
  9. 2025Multiview Representation Learning via Distributed Joint Latent Space Structuringcited by 1
  10. 2026PAC-Bayesian Reconstruction Guarantees for Time Series Variational Autoencoderscited by 1
  11. 2025Information-theoretic Generalization Analysis for VQ-VAEs: A Role of Latent Variablescited by 0
  12. 2025Deep Actor-Critics with Tight Risk Certificatescited by 0
4 more
  1. 2025Understanding Cross-Domain Adaptation in Low-Resource Topic Modelingcited by 0
  2. 2025Nonlinear Dimensionality Reduction Techniques for Bayesian Optimizationcited by 0
  3. 2026Can Generative Artificial Intelligence Survive Data Contamination? Theoretical Guarantees under Contaminated Recursive Trainingcited by 0
  4. 2026Latent Inference-Time Guidance of Time Series Foundation Modelscited by 0