Being the most classical generative model for serial data, state-space models (SSM) are fundamental in AI and statistical machine learning. In SSM, any form of parameter learning or latent state inference typically involves the computation of complex latent-state posteriors. In this work, we build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference by combining particle methods and variational inference. While standard VSMC operates in the offline mode, by re-processing repeatedly a given batch of data, we distribute the approximation of the gradient of the VSMC surrogate ELBO in time using stochastic approximation, allowing for online learning in the presence of streams of data. This results in an algorithm, online VSMC, that is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation. In addition, we provide rigorous theoretical results describing the algorithm's convergence properties as the number of data tends to infinity as well as numerical illustrations of its excellent convergence properties and usefulness also in batch-processing settings.

翻译：作为序列数据最经典的生成模型，状态空间模型（SSM）是人工智能与统计机器学习的基础。在SSM中，任何形式的参数学习或隐状态推断通常涉及复杂隐状态后验分布的计算。本研究基于变分序贯蒙特卡洛（VSMC）方法，该方法通过融合粒子方法与变分推断，实现了计算高效且精确的模型参数估计与贝叶斯隐状态推断。传统VSMC以离线模式运行，需反复重处理给定的批量数据；我们通过随机逼近方法在时间维度上分布VSMC代理证据下界梯度的近似计算，从而实现对数据流的在线学习。由此产生的在线VSMC算法能够完全实时高效地执行参数估计与粒子提议自适应。此外，我们提供了严谨的理论结果，描述当数据量趋于无穷时算法的收敛特性，并通过数值实验展示了其在批处理场景中同样具备优异的收敛性能与应用价值。