# Learning Gaussian Mixture Representations for Tensor Time Series Forecasting

arXiv: https://arxiv.org/abs/2306.00390 · HTML: https://mlsanity.com/paper/2306.00390/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 44 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [Decoupled Dynamic Spatial-Temporal Graph Neural Network for Traffic Forecasting](https://mlsanity.com/paper/2206.09112/) (2022)
- [Spatio-Temporal Meta-Graph Learning for Traffic Forecasting](https://mlsanity.com/paper/2211.14701/) (2022)
- [DL-Traff: Survey and Benchmark of Deep Learning Models for Urban Traffic Prediction](https://mlsanity.com/paper/2108.09091/) (2021)
- [Multi-Range Attentive Bicomponent Graph Convolutional Network for Traffic Forecasting](https://mlsanity.com/paper/1911.12093/) (2019)
- [Unsupervised Discrete Sentence Representation Learning for Interpretable Neural Dialog Generation](https://mlsanity.com/paper/1804.08069/) (2018)
- [Network of Tensor Time Series](https://mlsanity.com/paper/2102.07736/) (2021)
- [FC-GAGA: Fully Connected Gated Graph Architecture for Spatio-Temporal Traffic Forecasting](https://mlsanity.com/paper/2007.15531/) (2020)
- [Disentangled Variational Autoencoder based Multi-Label Classification with Covariance-Aware Multivariate Probit Model](https://mlsanity.com/paper/2007.06126/) (2020)
- [A Multi-view Multi-task Learning Framework for Multi-variate Time Series Forecasting](https://mlsanity.com/paper/2109.01657/) (2021)
- [Event-Aware Multimodal Mobility Nowcasting](https://mlsanity.com/paper/2112.08443/) (2021)
- [MixSeq: Connecting Macroscopic Time Series Forecasting with Microscopic Time Series Data](https://mlsanity.com/paper/2110.14354/) (2021)
- [Space Meets Time: Local Spacetime Neural Network For Traffic Flow Forecasting](https://mlsanity.com/paper/2109.05225/) (2021)

## Built on by (most cited first, 6 of 6)

- [Heterogeneity-Informed Meta-Parameter Learning for Spatiotemporal Time Series Forecasting](https://mlsanity.com/paper/2405.10800/) (2024)
- [Multi-Modality Spatio-Temporal Forecasting via Self-Supervised Learning](https://mlsanity.com/paper/2405.03255/) (2024)
- [How Different from the Past? Spatio-Temporal Time Series Forecasting with Self-Supervised Deviation Learning](https://mlsanity.com/paper/2510.04908/) (2025)
- [Unveiling the Inflexibility of Adaptive Embedding in Traffic Forecasting](https://mlsanity.com/paper/2411.11448/) (2024)
- [Disentangled Mode-Specific Representations for Tensor Time Series via Contrastive Learning](https://mlsanity.com/paper/2602.23663/) (2026)
- [Frequency-Domain Multi-Modality Transportation Modeling](https://mlsanity.com/paper/2607.08475/) (2026)

## Abstract (arXiv)

Tensor time series (TTS) data, a generalization of one-dimensional time series on a high-dimensional space, is ubiquitous in real-world scenarios, especially in monitoring systems involving multi-source spatio-temporal data (e.g., transportation demands and air pollutants). Compared to modeling time series or multivariate time series, which has received much attention and achieved tremendous progress in recent years, tensor time series has been paid less effort. Properly coping with the tensor time series is a much more challenging task, due to its high-dimensional and complex inner structure. In this paper, we develop a novel TTS forecasting framework, which seeks to individually model each heterogeneity component implied in the time, the location, and the source variables. We name this framework as GMRL, short for Gaussian Mixture Representation Learning. Experiment results on two real-world TTS datasets verify the superiority of our approach compared with the state-of-the-art baselines. Code and data are published on https://github.com/beginner-sketch/GMRL.