Efficient Online Variational Estimation via Monte Carlo Sampling

This article addresses online variational estimation in parametric state-space models. We propose a new procedure for efficiently computing the evidence lower bound and its gradient in a streaming-data setting, where observations arrive sequentially. The algorithm allows for the simultaneous training of the model parameters and the distribution of the latent states given the observations. It is based on i.i.d. Monte Carlo sampling, coupled with a well-chosen deep architecture, enabling both computational efficiency and flexibility. The performance of the method is illustrated on both synthetic data and real-world air-quality data. The proposed approach is theoretically motivated by the existence of an asymptotic contrast function and the ergodicity of the underlying Markov chain, and applies more generally to the computation of additive expectations under posterior distributions in state-space models.

Many real-world systems, such as weather forecasting, air-quality monitoring, and financial markets, generate data continuously over time. To model these systems effectively, machine learning methods must be able to update efficiently as new data arrives. In this work, we propose a new method for training probabilistic time-series models in an online setting, where observations are processed sequentially. The approach can simultaneously learn the model parameters and infer hidden states underlying the observed data. Our method combines efficient sampling techniques with deep learning architectures, making it both scalable and flexible. We demonstrate its performance on simulated datasets and real-world air-quality data, and provide theoretical results supporting its reliability over long sequences of observations.