Efficient Online Variational Estimation via Monte Carlo Sampling

2026-02-06

AI Summary

This work addresses the problem of online variational estimation for parametric state-space models in streaming data settings. The authors propose an efficient algorithm that jointly learns model parameters and the posterior distribution of latent states by integrating independent and identically distributed Monte Carlo sampling with a deep neural network architecture. The method enables flexible online variational inference while maintaining computational efficiency and is supported by theoretical guarantees concerning the asymptotic contrast function and ergodicity of the underlying Markov chain. Experimental results demonstrate that the approach achieves accurate and efficient joint estimation of both parameters and latent states on both synthetic and real-world air quality datasets.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• online variational estimation
• state-space models
• streaming data
• evidence lower bound
• latent states

Innovation

• online variational estimation
• Monte Carlo sampling
• state-space models
• evidence lower bound
• streaming data