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）是人工智能和统计机器学习的基础。在SSM中，任何形式的参数学习或潜在状态推断通常涉及复杂潜在状态后验的计算。本文基于变分序列蒙特卡洛（VSMC）方法，该方法通过结合粒子方法和变分推断，提供计算高效且准确的模型参数估计与贝叶斯潜在状态推断。虽然标准VSMC以离线模式运行，通过反复重新处理给定批次数据，但我们利用随机逼近将VSMC代理ELBO梯度的近似随时间分布，从而支持流式数据环境中的在线学习。由此产生的在线VSMC算法能够完全实时地高效执行参数估计和粒子建议自适应。此外，我们提供了严格的收敛理论结果（当数据量趋于无穷大时），并通过数值实验展示了其在批量处理设置中的优异收敛性能与实用价值。