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A projected nonlinear state-space model for forecasting time series signals

arXiv 2311.13247 ↗First posted 22 Nov 2023stat.ME stat.MLcited by 0

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Abstract (arXiv)

Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy samples and predict future trajectories with uncertainty estimates while maintaining computational efficiency. Here, we propose a fast algorithm to learn and forecast nonlinear dynamics from noisy time series data. A key feature of the proposed model is kernel functions applied to projected lines, enabling fast and efficient capture of nonlinearities in the latent dynamics. Through empirical case studies and benchmarking, the model demonstrates its effectiveness in learning and forecasting complex nonlinear dynamics, offering a valuable tool for researchers and practitioners in time series analysis.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 16 of its 42 references that are in the map. First posted on arXiv 22 Nov 2023.

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References · 16

  1. 2017Attention Is All You Needcited by 60,361
  2. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  3. 2014Neural Machine Translation by Jointly Learning to Align and Translatecited by 4,548
  4. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,013
  5. 2023iTransformer: Inverted Transformers Are Effective for Time Series Forecastingcited by 931
  6. 2019N-BEATS: Neural basis expansion analysis for interpretable time series forecastingcited by 753
  7. 2016Structured Inference Networks for Nonlinear State Space Modelscited by 182
  8. 2015Deep Kalman Filterscited by 166
  9. 2021Darts: User-Friendly Modern Machine Learning for Time Seriescited by 91
  10. 2021Chaos as an interpretable benchmark for forecasting and data-driven modellingcited by 88
  11. 2023ODEFormer: Symbolic Regression of Dynamical Systems with Transformerscited by 62
  12. 2014Variational Gaussian Process State-Space Modelscited by 43
4 more
  1. 2019Learning interpretable continuous-time models of latent stochastic dynamical systemscited by 30
  2. 2013Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMCcited by 24
  3. 2022Neural Laplace: Learning diverse classes of differential equations in the Laplace domaincited by 24
  4. 2018Dimension Reduction via Gaussian Ridge Functionscited by 4

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  1. 2021Stochastic Recurrent Neural Network for Multistep Time Series Forecasting
  2. 2023Effectively Modeling Time Series with Simple Discrete State Spaces
  3. 2021Deep Switching State Space Model (DS3M) for Nonlinear Time Series Forecasting with Regime Switching
  4. 2025StoxLSTM: A Stochastic Extended Long Short-Term Memory Network for Time Series Forecasting
  5. 2022Deep Latent State Space Models for Time-Series Generation
  6. 2021Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecasting
  7. 2024Time-SSM: Simplifying and Unifying State Space Models for Time Series Forecasting
  8. 2024Deep Learning-based Approaches for State Space Models: A Selective Review