State and parameter learning with PARIS particle Gibbs

Gabriel Cardoso, Yazid Janati El Idrissi, Sylvain Le Corff, Eric Moulines, Jimmy Olsson
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:3625-3675, 2023.

Abstract

Non-linear state-space models, also known as general hidden Markov models (HMM), are ubiquitous in statistical machine learning, being the most classical generative models for serial data and sequences. Learning in HMM, either via Maximum Likelihood Estimation (MLE) or Markov Score Climbing (MSC) requires the estimation of the- smoothing expectation of some additive functionals. Controlling the bias and the variance of this estimation is crucial to establish the convergence of learning algorithms. Our first contribution is to design a novel additive smoothing algorithm, the Parisian particle Gibbs (PPG) sampler, which can be viewed as a PaRIS (Olsson, Westerborn 2017) algorithm driven by conditional SMC moves, resulting in bias-reduced estimates of the targeted quantities. We substantiate the PPG algorithm with theoretical results, including new bounds on bias and variance as well as deviation inequalities. We then establish, in the learning context, and under standard assumptions, non-asymptotic bounds highlighting the value of bias reduction and the implicit Rao–Blackwellization of PPG. These are the first non-asymptotic results of this kind in this setting. We illustrate our theoretical results with numerical experiments supporting our claims.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-cardoso23a, title = {State and parameter learning with {PARIS} particle {G}ibbs}, author = {Cardoso, Gabriel and Janati El Idrissi, Yazid and Le Corff, Sylvain and Moulines, Eric and Olsson, Jimmy}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {3625--3675}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/cardoso23a/cardoso23a.pdf}, url = {https://proceedings.mlr.press/v202/cardoso23a.html}, abstract = {Non-linear state-space models, also known as general hidden Markov models (HMM), are ubiquitous in statistical machine learning, being the most classical generative models for serial data and sequences. Learning in HMM, either via Maximum Likelihood Estimation (MLE) or Markov Score Climbing (MSC) requires the estimation of the- smoothing expectation of some additive functionals. Controlling the bias and the variance of this estimation is crucial to establish the convergence of learning algorithms. Our first contribution is to design a novel additive smoothing algorithm, the Parisian particle Gibbs (PPG) sampler, which can be viewed as a PaRIS (Olsson, Westerborn 2017) algorithm driven by conditional SMC moves, resulting in bias-reduced estimates of the targeted quantities. We substantiate the PPG algorithm with theoretical results, including new bounds on bias and variance as well as deviation inequalities. We then establish, in the learning context, and under standard assumptions, non-asymptotic bounds highlighting the value of bias reduction and the implicit Rao–Blackwellization of PPG. These are the first non-asymptotic results of this kind in this setting. We illustrate our theoretical results with numerical experiments supporting our claims.} }
Endnote
%0 Conference Paper %T State and parameter learning with PARIS particle Gibbs %A Gabriel Cardoso %A Yazid Janati El Idrissi %A Sylvain Le Corff %A Eric Moulines %A Jimmy Olsson %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-cardoso23a %I PMLR %P 3625--3675 %U https://proceedings.mlr.press/v202/cardoso23a.html %V 202 %X Non-linear state-space models, also known as general hidden Markov models (HMM), are ubiquitous in statistical machine learning, being the most classical generative models for serial data and sequences. Learning in HMM, either via Maximum Likelihood Estimation (MLE) or Markov Score Climbing (MSC) requires the estimation of the- smoothing expectation of some additive functionals. Controlling the bias and the variance of this estimation is crucial to establish the convergence of learning algorithms. Our first contribution is to design a novel additive smoothing algorithm, the Parisian particle Gibbs (PPG) sampler, which can be viewed as a PaRIS (Olsson, Westerborn 2017) algorithm driven by conditional SMC moves, resulting in bias-reduced estimates of the targeted quantities. We substantiate the PPG algorithm with theoretical results, including new bounds on bias and variance as well as deviation inequalities. We then establish, in the learning context, and under standard assumptions, non-asymptotic bounds highlighting the value of bias reduction and the implicit Rao–Blackwellization of PPG. These are the first non-asymptotic results of this kind in this setting. We illustrate our theoretical results with numerical experiments supporting our claims.
APA
Cardoso, G., Janati El Idrissi, Y., Le Corff, S., Moulines, E. & Olsson, J.. (2023). State and parameter learning with PARIS particle Gibbs. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:3625-3675 Available from https://proceedings.mlr.press/v202/cardoso23a.html.

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