# Discrete Graph Structure Learning for Forecasting Multiple Time Series

arXiv: https://arxiv.org/abs/2101.06861 · HTML: https://mlsanity.com/paper/2101.06861/

## Key facts

- Cited by 171 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 35 references that are in the map.
- First posted on arXiv 18 Jan 2021.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [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)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Forward and Reverse Gradient-Based Hyperparameter Optimization](https://mlsanity.com/paper/1703.01785/) (2017)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Temporal Pattern Attention for Multivariate Time Series Forecasting](https://mlsanity.com/paper/1809.04206/) (2018)

## Built on by (most cited first, 30 of 171)

- [Spatial-Temporal Identity: A Simple yet Effective Baseline for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2208.05233/) (2022)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [Pre-training Enhanced Spatial-temporal Graph Neural Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2206.09113/) (2022)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2306.10125/) (2023)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [Spatio-Temporal Meta-Graph Learning for Traffic Forecasting](https://mlsanity.com/paper/2211.14701/) (2022)
- [Multivariate Time Series Forecasting with Dynamic Graph Neural ODEs](https://mlsanity.com/paper/2202.08408/) (2022)
- [FBNETGEN: Task-aware GNN-based fMRI Analysis via Functional Brain Network Generation](https://mlsanity.com/paper/2205.12465/) (2022)
- [Graph Data Augmentation for Graph Machine Learning: A Survey](https://mlsanity.com/paper/2202.08871/) (2022)
- [A Comprehensive Survey of Deep Learning for Multivariate Time Series Forecasting: A Channel Strategy Perspective](https://mlsanity.com/paper/2502.10721/) (2025)
- [Does Graph Distillation See Like Vision Dataset Counterpart?](https://mlsanity.com/paper/2310.09192/) (2023)
- [Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Series](https://mlsanity.com/paper/2202.07857/) (2022)
- [TS-RAG: Retrieval-Augmented Generation based Time Series Foundation Models are Stronger Zero-Shot Forecaster](https://mlsanity.com/paper/2503.07649/) (2025)
- [Accelerating Training and Inference of Graph Neural Networks with Fast Sampling and Pipelining](https://mlsanity.com/paper/2110.08450/) (2021)
- [Taming Local Effects in Graph-based Spatiotemporal Forecasting](https://mlsanity.com/paper/2302.04071/) (2023)
- [Learning the Evolutionary and Multi-scale Graph Structure for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2206.13816/) (2022)
- [Modeling Multivariate Biosignals With Graph Neural Networks and Structured State Space Models](https://mlsanity.com/paper/2211.11176/) (2022)
- [MBrain: A Multi-channel Self-Supervised Learning Framework for Brain Signals](https://mlsanity.com/paper/2306.13102/) (2023)
- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [AirPhyNet: Harnessing Physics-Guided Neural Networks for Air Quality Prediction](https://mlsanity.com/paper/2402.03784/) (2024)
- [Air Quality Prediction with Physics-Guided Dual Neural ODEs in Open Systems](https://mlsanity.com/paper/2410.19892/) (2024)
- [Regularized Graph Structure Learning with Semantic Knowledge for Multi-variates Time-Series Forecasting](https://mlsanity.com/paper/2210.06126/) (2022)
- [Sparse Graph Learning from Spatiotemporal Time Series](https://mlsanity.com/paper/2205.13492/) (2022)
- [ST-MLP: A Cascaded Spatio-Temporal Linear Framework with Channel-Independence Strategy for Traffic Forecasting](https://mlsanity.com/paper/2308.07496/) (2023)
- [MLPST: MLP is All You Need for Spatio-Temporal Prediction](https://mlsanity.com/paper/2309.13363/) (2023)
- [Multivariate Time Series Forecasting with Latent Graph Inference](https://mlsanity.com/paper/2203.03423/) (2022)
- [LibCity: A Unified Library Towards Efficient and Comprehensive Urban Spatial-Temporal Prediction](https://mlsanity.com/paper/2304.14343/) (2023)
- [PromptST: Prompt-Enhanced Spatio-Temporal Multi-Attribute Prediction](https://mlsanity.com/paper/2309.09500/) (2023)

## Abstract (arXiv)

Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the performance of a time series model. When using deep neural networks as forecasting models, we hypothesize that exploiting the pairwise information among multiple (multivariate) time series also improves their forecast. If an explicit graph structure is known, graph neural networks (GNNs) have been demonstrated as powerful tools to exploit the structure. In this work, we propose learning the structure simultaneously with the GNN if the graph is unknown. We cast the problem as learning a probabilistic graph model through optimizing the mean performance over the graph distribution. The distribution is parameterized by a neural network so that discrete graphs can be sampled differentiably through reparameterization. Empirical evaluations show that our method is simpler, more efficient, and better performing than a recently proposed bilevel learning approach for graph structure learning, as well as a broad array of forecasting models, either deep or non-deep learning based, and graph or non-graph based.