# Graph-based Forecasting with Missing Data through Spatiotemporal Downsampling

arXiv: https://arxiv.org/abs/2402.10634 · HTML: https://mlsanity.com/paper/2402.10634/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 67 references that are in the map.
- First posted on arXiv 16 Feb 2024.

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [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)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [GaAN: Gated Attention Networks for Learning on Large and Spatiotemporal Graphs](https://mlsanity.com/paper/1803.07294/) (2018)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Conditional Time Series Forecasting with Convolutional Neural Networks](https://mlsanity.com/paper/1703.04691/) (2017)
- [Multi-Scale Convolutional Neural Networks for Time Series Classification](https://mlsanity.com/paper/1603.06995/) (2016)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [Inductive Graph Neural Networks for Spatiotemporal Kriging](https://mlsanity.com/paper/2006.07527/) (2020)
- [Dilated Recurrent Neural Networks](https://mlsanity.com/paper/1710.02224/) (2017)
- [Understanding Pooling in Graph Neural Networks](https://mlsanity.com/paper/2110.05292/) (2021)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [Scalable Spatiotemporal Graph Neural Networks](https://mlsanity.com/paper/2209.06520/) (2022)
- [Multi-Scale Adaptive Graph Neural Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2201.04828/) (2022)

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

- [Agentic Retrieval-Augmented Generation for Time Series Analysis](https://mlsanity.com/paper/2408.14484/) (2024)
- [A Systematic Literature Review of Spatio-Temporal Graph Neural Network Models for Time Series Forecasting and Classification](https://mlsanity.com/paper/2410.22377/) (2024)
- [Over-squashing in Spatiotemporal Graph Neural Networks](https://mlsanity.com/paper/2506.15507/) (2025)
- [MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networks](https://mlsanity.com/paper/2409.05100/) (2024)
- [Spatiotemporal Imputation with Graph-Informed Flow Matching](https://mlsanity.com/paper/2606.06682/) (2026)
- [Interpreting Temporal Graph Neural Networks with Koopman Theory](https://mlsanity.com/paper/2410.13469/) (2024)
- [BN-Pool: Bayesian Nonparametric Pooling for Graphs](https://mlsanity.com/paper/2501.09821/) (2025)
- [On the Regularization of Learnable Embeddings for Time Series Forecasting](https://mlsanity.com/paper/2410.14630/) (2024)
- [UrbanFM: Scaling Urban Spatio-Temporal Foundation Models](https://mlsanity.com/paper/2602.20677/) (2026)
- [Nested Spatio-Temporal Time Series Forecasting](https://mlsanity.com/paper/2605.16447/) (2026)
- [Graph Structure Learning with Temporal Graph Information Bottleneck for Inductive Representation Learning](https://mlsanity.com/paper/2508.14859/) (2025)
- [Tackling Incomplete Data in Air Quality Prediction: A Bayesian Deep Learning Framework for Uncertainty Quantification](https://mlsanity.com/paper/2511.02175/) (2025)
- [Learning Recursive Multi-Scale Representations for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2602.21498/) (2026)
- [STEPS: A Temporal Smooth Error Propagation Solver on the Manifolds for Test-Time Adaptation in Time Series Forecasting](https://mlsanity.com/paper/2605.08005/) (2026)
- [Pattern-Aware Graph Neural Networks for Handling Missing Data](https://mlsanity.com/paper/2607.08915/) (2026)
- [Just for FUNS: LLM-Guided Spatio-Temporal Graph Node Generation for Forecasting Unobserved Node States](https://mlsanity.com/paper/2610.08818/) (2026)
- [When Missingness Follows the Graph: Beyond Feature Propagation for Missing Features](https://mlsanity.com/paper/2610.18113/) (2026)

## Abstract (arXiv)

Given a set of synchronous time series, each associated with a sensor-point in space and characterized by inter-series relationships, the problem of spatiotemporal forecasting consists of predicting future observations for each point. Spatiotemporal graph neural networks achieve striking results by representing the relationships across time series as a graph. Nonetheless, most existing methods rely on the often unrealistic assumption that inputs are always available and fail to capture hidden spatiotemporal dynamics when part of the data is missing. In this work, we tackle this problem through hierarchical spatiotemporal downsampling. The input time series are progressively coarsened over time and space, obtaining a pool of representations that capture heterogeneous temporal and spatial dynamics. Conditioned on observations and missing data patterns, such representations are combined by an interpretable attention mechanism to generate the forecasts. Our approach outperforms state-of-the-art methods on synthetic and real-world benchmarks under different missing data distributions, particularly in the presence of contiguous blocks of missing values.