Deep Latent State Space Models for Time-Series Generation

Linqi Zhou, Michael Poli, Winnie Xu, Stefano Massaroli, Stefano Ermon
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:42625-42643, 2023.

Abstract

Methods based on ordinary differential equations (ODEs) are widely used to build generative models of time-series. In addition to high computational overhead due to explicitly computing hidden states recurrence, existing ODE-based models fall short in learning sequence data with sharp transitions - common in many real-world systems - due to numerical challenges during optimization. In this work, we propose LS4, a generative model for sequences with latent variables evolving according to a state space ODE to increase modeling capacity. Inspired by recent deep state space models (S4), we achieve speedups by leveraging a convolutional representation of LS4 which bypasses the explicit evaluation of hidden states. We show that LS4 significantly outperforms previous continuous-time generative models in terms of marginal distribution, classification, and prediction scores on real-world datasets in the Monash Forecasting Repository, and is capable of modeling highly stochastic data with sharp temporal transitions. LS4 sets state-of-the-art for continuous-time latent generative models, with significant improvement of mean squared error and tighter variational lower bounds on irregularly-sampled datasets, while also being x100 faster than other baselines on long sequences.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-zhou23i, title = {Deep Latent State Space Models for Time-Series Generation}, author = {Zhou, Linqi and Poli, Michael and Xu, Winnie and Massaroli, Stefano and Ermon, Stefano}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {42625--42643}, 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/zhou23i/zhou23i.pdf}, url = {https://proceedings.mlr.press/v202/zhou23i.html}, abstract = {Methods based on ordinary differential equations (ODEs) are widely used to build generative models of time-series. In addition to high computational overhead due to explicitly computing hidden states recurrence, existing ODE-based models fall short in learning sequence data with sharp transitions - common in many real-world systems - due to numerical challenges during optimization. In this work, we propose LS4, a generative model for sequences with latent variables evolving according to a state space ODE to increase modeling capacity. Inspired by recent deep state space models (S4), we achieve speedups by leveraging a convolutional representation of LS4 which bypasses the explicit evaluation of hidden states. We show that LS4 significantly outperforms previous continuous-time generative models in terms of marginal distribution, classification, and prediction scores on real-world datasets in the Monash Forecasting Repository, and is capable of modeling highly stochastic data with sharp temporal transitions. LS4 sets state-of-the-art for continuous-time latent generative models, with significant improvement of mean squared error and tighter variational lower bounds on irregularly-sampled datasets, while also being x100 faster than other baselines on long sequences.} }
Endnote
%0 Conference Paper %T Deep Latent State Space Models for Time-Series Generation %A Linqi Zhou %A Michael Poli %A Winnie Xu %A Stefano Massaroli %A Stefano Ermon %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-zhou23i %I PMLR %P 42625--42643 %U https://proceedings.mlr.press/v202/zhou23i.html %V 202 %X Methods based on ordinary differential equations (ODEs) are widely used to build generative models of time-series. In addition to high computational overhead due to explicitly computing hidden states recurrence, existing ODE-based models fall short in learning sequence data with sharp transitions - common in many real-world systems - due to numerical challenges during optimization. In this work, we propose LS4, a generative model for sequences with latent variables evolving according to a state space ODE to increase modeling capacity. Inspired by recent deep state space models (S4), we achieve speedups by leveraging a convolutional representation of LS4 which bypasses the explicit evaluation of hidden states. We show that LS4 significantly outperforms previous continuous-time generative models in terms of marginal distribution, classification, and prediction scores on real-world datasets in the Monash Forecasting Repository, and is capable of modeling highly stochastic data with sharp temporal transitions. LS4 sets state-of-the-art for continuous-time latent generative models, with significant improvement of mean squared error and tighter variational lower bounds on irregularly-sampled datasets, while also being x100 faster than other baselines on long sequences.
APA
Zhou, L., Poli, M., Xu, W., Massaroli, S. & Ermon, S.. (2023). Deep Latent State Space Models for Time-Series Generation. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:42625-42643 Available from https://proceedings.mlr.press/v202/zhou23i.html.

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