PAC-Bayesian Reconstruction Guarantees for Time Series Variational Autoencoders
Abstract
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.
Related
- Enhanced Uncertainty Quantification Variational Autoencoders for the Solution of Bayesian Inverse Problems
- Improving the Last-Iterate Guarantees of Anytime Algorithms for Stochastic Monotone Variational Inequalities
- Sharp Reconstruction Bounds for Autoencoders Using the Same Forward Map
- Risk-Averse Bayesian Games with an Unknown Type Distribution: Bayesian Learning, Equilibrium Analysis, and Finite-Sample Guarantees
- Asymptotically Valid Laplace Variational Inference for Bayesian Nonparametric Clustering of Marked Point Patterns
BibTeX
@misc{hashimotocullen2026pacbayesian,
title = {{PAC-Bayesian Reconstruction Guarantees for Time Series Variational Autoencoders}},
author = {Chloé Hashimoto-Cullen and Ghislain Agoua and Benjamin Guedj and Sylvain Le Corff},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05212},
eprint = {2609.05212},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05740628v1},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - PAC-Bayesian Reconstruction Guarantees for Time Series Variational Autoencoders
AU - Chloé Hashimoto-Cullen
AU - Ghislain Agoua
AU - Benjamin Guedj
AU - Sylvain Le Corff
PY - 2026
DA - 2026/09/04
PB - HAL
DO - 10.48550/arxiv.2609.05212
UR - https://hal.science/hal-05740628v1
AB - 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.
ER -