Efficient Online Variational Estimation via Monte Carlo Sampling

Mathis Chagneux, Mathias Müller, Pierre Gloaguen, Sylvain Le Corff, Jimmy Olsson
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:12332-12362, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chagneux26a, title = {Efficient Online Variational Estimation via {M}onte {C}arlo Sampling}, author = {Chagneux, Mathis and M\"{u}ller, Mathias and Gloaguen, Pierre and Le Corff, Sylvain and Olsson, Jimmy}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {12332--12362}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/chagneux26a/chagneux26a.pdf}, url = {https://proceedings.mlr.press/v306/chagneux26a.html}, 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.} }
Endnote
%0 Conference Paper %T Efficient Online Variational Estimation via Monte Carlo Sampling %A Mathis Chagneux %A Mathias Müller %A Pierre Gloaguen %A Sylvain Le Corff %A Jimmy Olsson %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-chagneux26a %I PMLR %P 12332--12362 %U https://proceedings.mlr.press/v306/chagneux26a.html %V 306 %X 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.
APA
Chagneux, M., Müller, M., Gloaguen, P., Le Corff, S. & Olsson, J.. (2026). Efficient Online Variational Estimation via Monte Carlo Sampling. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:12332-12362 Available from https://proceedings.mlr.press/v306/chagneux26a.html.

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