Deep Latent State Space Models for Time-Series Generation

• URL: http://arxiv.org/abs/2212.12749v1
• Date: Sat, 24 Dec 2022 15:17:42 GMT
• Title: Deep Latent State Space Models for Time-Series Generation
• Authors: Linqi Zhou, Michael Poli, Winnie Xu, Stefano Massaroli, Stefano Ermon
• Abstract summary: We propose LS4, a generative model for sequences with latent variables evolving according to a state space ODE. Inspired by recent deep state space models (S4), we achieve speedups by leveraging a convolutional representation of LS4. We show that LS4 significantly outperforms previous continuous-time generative models in terms of marginal distribution, classification, and prediction scores on real-world datasets.
• Score: 68.45746489575032
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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