# Multivariate Time Series Forecasting with Latent Graph Inference

arXiv: https://arxiv.org/abs/2203.03423 · HTML: https://mlsanity.com/paper/2203.03423/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 58 references that are in the map.
- First posted on arXiv 7 Mar 2022.

## Builds on (most cited first, 30 of 41)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [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)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Few-Shot Learning with Graph Neural Networks](https://mlsanity.com/paper/1711.04043/) (2017)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)

## Built on by (most cited first, 20 of 20)

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Scalable Spatiotemporal Graph Neural Networks](https://mlsanity.com/paper/2209.06520/) (2022)
- [Taming Local Effects in Graph-based Spatiotemporal Forecasting](https://mlsanity.com/paper/2302.04071/) (2023)
- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [Sparse Graph Learning from Spatiotemporal Time Series](https://mlsanity.com/paper/2205.13492/) (2022)
- [Graph-based Time Series Clustering for End-to-End Hierarchical Forecasting](https://mlsanity.com/paper/2305.19183/) (2023)
- [Relational Conformal Prediction for Correlated Time Series](https://mlsanity.com/paper/2502.09443/) (2025)
- [Inferring Latent Temporal Sparse Coordination Graph for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2403.19253/) (2024)
- [Joint Estimation and Prediction of City-wide Delivery Demand: A Large Language Model Empowered Graph-based Learning Approach](https://mlsanity.com/paper/2408.17258/) (2024)
- [Over-squashing in Spatiotemporal Graph Neural Networks](https://mlsanity.com/paper/2506.15507/) (2025)
- [AZ-whiteness test: a test for uncorrelated noise on spatio-temporal graphs](https://mlsanity.com/paper/2204.11135/) (2022)
- [Contextually Enhanced ES-dRNN with Dynamic Attention for Short-Term Load Forecasting](https://mlsanity.com/paper/2212.09030/) (2022)
- [Contextualizing MLP-Mixers Spatiotemporally for Urban Data Forecast at Scale](https://mlsanity.com/paper/2307.01482/) (2023)
- [Forecasting Irregularly Sampled Time Series using Graphs](https://mlsanity.com/paper/2305.12932/) (2023)
- [GEANN: Scalable Graph Augmentations for Multi-Horizon Time Series Forecasting](https://mlsanity.com/paper/2307.03595/) (2023)
- [On the Regularization of Learnable Embeddings for Time Series Forecasting](https://mlsanity.com/paper/2410.14630/) (2024)
- [Modeling Oceanic Variables with Dynamic Graph Neural Networks](https://mlsanity.com/paper/2206.12746/) (2022)
- [Spatiotemporal Graph Neural Networks in short term load forecasting: Does adding Graph Structure in Consumption Data Improve Predictions?](https://mlsanity.com/paper/2502.12175/) (2025)
- [Select, then Balance: Exploring Exogenous Variable Modeling of Spatio-Temporal Forecasting](https://mlsanity.com/paper/2509.05779/) (2025)
- [AdaKernel: Learning Adaptive Kernel Parameters for Spatiotemporal Graph Neural Networks](https://mlsanity.com/paper/2606.01283/) (2026)

## Abstract (arXiv)

This paper introduces a new approach for Multivariate Time Series forecasting that jointly infers and leverages relations among time series. Its modularity allows it to be integrated with current univariate methods. Our approach allows to trade-off accuracy and computational efficiency gradually via offering on one extreme inference of a potentially fully-connected graph or on another extreme a bipartite graph. In the potentially fully-connected case we consider all pair-wise interactions among time-series which yields the best forecasting accuracy. Conversely, the bipartite case leverages the dependency structure by inter-communicating the N time series through a small set of K auxiliary nodes that we introduce. This reduces the time and memory complexity w.r.t. previous graph inference methods from O(N^2) to O(NK) with a small trade-off in accuracy. We demonstrate the effectiveness of our model in a variety of datasets where both of its variants perform better or very competitively to previous graph inference methods in terms of forecasting accuracy and time efficiency.