PAC-Bayesian Reconstruction Guarantees for Time Series Variational Autoencoders

2026-09-04

AI Summary

本文针对时间序列预测问题，提出了一种PAC-Bayesian框架，通过重建保证来分析具有马尔可夫潜结构的变分自编码器，从而提供不随轨迹长度增加的理论保障。

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.

Problem

• PAC-Bayesian
• time series
• Variational AutoEncoders
• latent variable models
• generalisation guarantees

Innovation

• PAC-Bayesian framework
• latent variable models
• time series
• Markovian latent structures
• reconstruction-based bounds