arXiv Machine Learning
Aug 31

Prequential posteriors

The paper introduces prequential posteriors, a Bayesian approach that uses a predictive‑sequential loss function to update deep generative forecasting models (DGFMs) when new data arrive. By adopting a consistency notion suitable for model misspecification, the authors prove that both the loss minimizer and the posterior concentrate on parameters with optimal predictive performance. Scalable inference is achieved with parallelisable waste‑free sequential Monte Carlo samplers that employ preconditioned gradient kernels, and the method is validated on synthetic and real meteorological time‑series data.

By Shreya Sinha-Roy, Richard G. Everitt, Christian P. Robert, Ritabrata Dutta
arXiv Machine Learning
Sep 7

PAC-Bayesian Reconstruction Guarantees for Time Series Variational Autoencoders

The paper presents PAC‑Bayesian reconstruction guarantees for Variational Autoencoders applied to time‑series data. It extends existing bounds, which were limited to i.i.d. settings, to Markovian latent structures, allowing temporal dependencies to be captured without the bounds growing with trajectory length. The authors also provide an example framework showing that the required assumptions are not overly restrictive.

By Chlo\'e Hashimoto-Cullen, Ghislain Agoua, Benjamin Guedj, Sylvain Le Corff
arXiv Machine Learning
Sep 16

Stable by Construction: Variational Latent Markov Operators for Long-Horizon PDE Prediction

The paper introduces a variational framework called VAMO that incorporates latent Markov dynamics for neural PDE solvers, aiming to improve long‑horizon predictions by mitigating error accumulation. By representing physical states as latent distributions and evolving them through probabilistic transitions, the method aligns learned dynamics with a spectral geometry induced by structured Gaussian perturbations. Experiments on fluid‑dynamics benchmarks show that VAMO reduces error growth and enhances rollout stability compared to deterministic and noise‑injection baselines.

By Junyi Liao, Johann Guilleminot, Vahid Tarokh