# Decoupling Local and Global Representations of Time Series

arXiv: https://arxiv.org/abs/2202.02262 · HTML: https://mlsanity.com/paper/2202.02262/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 49 references that are in the map.
- First posted on arXiv 4 Feb 2022.

## Builds on (most cited first, 25 of 25)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Unsupervised Scalable Representation Learning for Multivariate Time Series](https://mlsanity.com/paper/1901.10738/) (2019)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [CLUB: A Contrastive Log-ratio Upper Bound of Mutual Information](https://mlsanity.com/paper/2006.12013/) (2020)
- [Unsupervised Representation Learning for Time Series with Temporal Neighborhood Coding](https://mlsanity.com/paper/2106.00750/) (2021)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/1905.03806/) (2019)
- [Disentangled Sequential Autoencoder](https://mlsanity.com/paper/1803.02991/) (2018)
- [Invariant Representations without Adversarial Training](https://mlsanity.com/paper/1805.09458/) (2018)
- [Unsupervised Learning of Disentangled and Interpretable Representations from Sequential Data](https://mlsanity.com/paper/1709.07902/) (2017)
- [Unsupervised speech representation learning using WaveNet autoencoders](https://mlsanity.com/paper/1901.08810/) (2019)
- [Disentangling factors of variation in deep representations using adversarial training](https://mlsanity.com/paper/1611.03383/) (2016)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [S3VAE: Self-Supervised Sequential VAE for Representation Disentanglement and Data Generation](https://mlsanity.com/paper/2005.11437/) (2020)
- [SOM-VAE: Interpretable Discrete Representation Learning on Time Series](https://mlsanity.com/paper/1806.02199/) (2018)
- [Learning Latent Subspaces in Variational Autoencoders](https://mlsanity.com/paper/1812.06190/) (2018)
- [Contrastively Disentangled Sequential Variational Autoencoder](https://mlsanity.com/paper/2110.12091/) (2021)
- [Temporal Latent Auto-Encoder: A Method for Probabilistic Multivariate Time Series Forecasting](https://mlsanity.com/paper/2101.10460/) (2021)
- [Weakly-supervised Disentangling with Recurrent Transformations for 3D View Synthesis](https://mlsanity.com/paper/1601.00706/) (2016)
- [A Framework for Individualizing Predictions of Disease Trajectories by Exploiting Multi-Resolution Structure](https://mlsanity.com/paper/1601.04674/) (2016)

## Built on by (most cited first, 17 of 17)

- [Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts](https://mlsanity.com/paper/2210.03675/) (2022)
- [Universal Time-Series Representation Learning: A Survey](https://mlsanity.com/paper/2401.03717/) (2024)
- [Sequential Multi-Dimensional Self-Supervised Learning for Clinical Time Series](https://mlsanity.com/paper/2307.10923/) (2023)
- [Sample and Predict Your Latent: Modality-free Sequential Disentanglement via Contrastive Estimation](https://mlsanity.com/paper/2305.15924/) (2023)
- [Sequential Disentanglement by Extracting Static Information From A Single Sequence Element](https://mlsanity.com/paper/2406.18131/) (2024)
- [Half-VAE: An Encoder-Free VAE to Bypass Explicit Inverse Mapping](https://mlsanity.com/paper/2409.04140/) (2024)
- [Learning from Polar Representation: An Extreme-Adaptive Model for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2312.08763/) (2023)
- [Sequential Representation Learning via Static-Dynamic Conditional Disentanglement](https://mlsanity.com/paper/2408.05599/) (2024)
- [Weakly Augmented Variational Autoencoder in Time Series Anomaly Detection](https://mlsanity.com/paper/2401.03341/) (2024)
- [ParamReL: Learning Parameter Space Representation via Progressively Encoding Bayesian Flow Networks](https://mlsanity.com/paper/2405.15268/) (2024)
- [Unsupervised Representation Learning from Sparse Transformation Analysis](https://mlsanity.com/paper/2410.05564/) (2024)
- [Structured Kernel Regression VAE: A Computationally Efficient Surrogate for GP-VAEs in ICA](https://mlsanity.com/paper/2508.09721/) (2025)
- [MultiLoReFT: Decoupling Shared and Modality-Specific Subspaces in Multimodal Learning via Low-Rank Representation Fine-Tuning](https://mlsanity.com/paper/2607.16789/) (2026)
- [PAC-Bayesian Reconstruction Guarantees for Time Series Variational Autoencoders](https://mlsanity.com/paper/2609.05212/) (2026)
- [Interpretable Spectral Variational AutoEncoder (ISVAE) for time series clustering](https://mlsanity.com/paper/2310.11940/) (2023)
- [Unsupervised Representation Learning of Complex Time Series for Maneuverability State Identification in Smart Mobility](https://mlsanity.com/paper/2409.06718/) (2024)
- [MTS-DMAE: Dual-Masked Autoencoder for Unsupervised Multivariate Time Series Representation Learning](https://mlsanity.com/paper/2509.16078/) (2025)

## Abstract (arXiv)

Real-world time series data are often generated from several sources of variation. Learning representations that capture the factors contributing to this variability enables a better understanding of the data via its underlying generative process and improves performance on downstream machine learning tasks. This paper proposes a novel generative approach for learning representations for the global and local factors of variation in time series. The local representation of each sample models non-stationarity over time with a stochastic process prior, and the global representation of the sample encodes the time-independent characteristics. To encourage decoupling between the representations, we introduce counterfactual regularization that minimizes the mutual information between the two variables. In experiments, we demonstrate successful recovery of the true local and global variability factors on simulated data, and show that representations learned using our method yield superior performance on downstream tasks on real-world datasets. We believe that the proposed way of defining representations is beneficial for data modelling and yields better insights into the complexity of real-world data.