发表机构
LPSM, Sorbonne Université; EDF R&D; University College London; Inria（索邦大学 LPSM; 法国电力集团研发部; 伦敦大学学院; 法国国家信息与自动化研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对时间序列变分自编码器泛化保证有限的问题，开发了适用于马尔可夫隐变量结构的PAC-贝叶斯框架，该框架的保证不随轨迹长度增长，且所需假设限制较小。
AI 中文摘要
准确预测时间序列对能源系统、医疗保健和金融等复杂数据应用至关重要。在当前最先进的模型中，生成式隐变量模型的应用日益广泛，但针对现代隐变量模型的原则性泛化保证仍然有限。特别是，尽管变分自编码器（Variational AutoEncoders）被广泛用于序列数据，但其理论分析大多局限于独立同分布（i.i.d.）场景。本研究为应用于时间序列的隐变量模型开发了一种PAC-贝叶斯框架，基于重构边界，将PAC-贝叶斯保证扩展到马尔可夫隐变量结构，通过序列生成过程捕捉时间依赖关系，且这些保证不随轨迹长度增长。我们的边界依赖于文献中常见的假设，并提供了一个示例框架以验证这些假设，表明其并不像看起来那样具有限制性。
英文摘要
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.
Comments20 pages
