# PAC-Bayesian Reconstruction Guarantees for Time Series Variational Autoencoders

arXiv: https://arxiv.org/abs/2609.05212 · HTML: https://mlsanity.com/paper/2609.05212/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 63 references that are in the map.
- First posted on arXiv 4 Sep 2026.

## Builds on (most cited first, 30 of 48)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [TabICL: A Tabular Foundation Model for In-Context Learning on Large Data](https://mlsanity.com/paper/2502.05564/) (2025)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation](https://mlsanity.com/paper/2111.08095/) (2021)
- [A Primer on PAC-Bayesian Learning](https://mlsanity.com/paper/1901.05353/) (2019)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Tighter risk certificates for neural networks](https://mlsanity.com/paper/2007.12911/) (2020)
- [Entropy-SGD optimizes the prior of a PAC-Bayes bound: Generalization properties of Entropy-SGD and data-dependent priors](https://mlsanity.com/paper/1712.09376/) (2017)
- [PAC-Bayes Analysis Beyond the Usual Bounds](https://mlsanity.com/paper/2006.13057/) (2020)
- [Generalization Bounds: Perspectives from Information Theory and PAC-Bayes](https://mlsanity.com/paper/2309.04381/) (2023)
- [Simpler PAC-Bayesian Bounds for Hostile Data](https://mlsanity.com/paper/1610.07193/) (2016)
- [Causal Recurrent Variational Autoencoder for Medical Time Series Generation](https://mlsanity.com/paper/2301.06574/) (2023)
- [PAC-Bayes unleashed: generalisation bounds with unbounded losses](https://mlsanity.com/paper/2006.07279/) (2020)
- [Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder](https://mlsanity.com/paper/2102.01331/) (2021)
- [Dichotomize and Generalize: PAC-Bayesian Binary Activated Deep Neural Networks](https://mlsanity.com/paper/1905.10259/) (2019)
- [Differentiable PAC-Bayes Objectives with Partially Aggregated Neural Networks](https://mlsanity.com/paper/2006.12228/) (2020)
- [PAC-Bayes Generalisation Bounds for Heavy-Tailed Losses through Supermartingales](https://mlsanity.com/paper/2210.00928/) (2022)
- [Non-Vacuous Generalisation Bounds for Shallow Neural Networks](https://mlsanity.com/paper/2202.01627/) (2022)
- [On PAC-Bayesian reconstruction guarantees for VAEs](https://mlsanity.com/paper/2202.11455/) (2022)
- [On Margins and Derandomisation in PAC-Bayes](https://mlsanity.com/paper/2107.03955/) (2021)
- [Online Variational Filtering and Parameter Learning](https://mlsanity.com/paper/2110.13549/) (2021)

## Built on by (most cited first, 1 of 1)

- [Latent Inference-Time Guidance of Time Series Foundation Models](https://mlsanity.com/paper/2609.38058/) (2026)

## Abstract (arXiv)

Forecasting time series accurately is critical for applications with complex data ranging from energy systems to healthcare and finance. Among current state of the art models, generative latent variable models are increasingly implemented; yet principled generalisation guarantees for modern latent variable models remain limited. In particular, while Variational AutoEncoders are widely used for sequential data, their theoretical analysis is largely restricted to i.i.d. settings. In this work, we develop a PAC-Bayesian framework for latent variables models applied to time series. Building on reconstruction-based bounds, we extend PAC-Bayesian guarantees to Markovian latent structures, capturing temporal dependencies through a sequential generative process. These guarantees do not grow with the length of the trajectory. Our bounds depend on assumptions which are common in the literature; we provide an example framework where they would be verified to show that they are not as restrictive as they may seem.