# Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations

arXiv: https://arxiv.org/abs/2205.13479 · HTML: https://mlsanity.com/paper/2205.13479/

## Key facts

- Cited by 64 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 78 references that are in the map.
- First posted on arXiv 26 May 2022.

## Builds on (most cited first, 30 of 40)

- [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)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [Time2Vec: Learning a Vector Representation of Time](https://mlsanity.com/paper/1907.05321/) (2019)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [GaAN: Gated Attention Networks for Learning on Large and Spatiotemporal Graphs](https://mlsanity.com/paper/1803.07294/) (2018)
- [Handling Missing Data with Graph Representation Learning](https://mlsanity.com/paper/2010.16418/) (2020)
- [Attention-based Graph Neural Network for Semi-supervised Learning](https://mlsanity.com/paper/1803.03735/) (2018)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networks](https://mlsanity.com/paper/1711.08742/) (2017)

## Built on by (most cited first, 30 of 64)

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Graph Neural Networks for temporal graphs: State of the art, open challenges, and opportunities](https://mlsanity.com/paper/2302.01018/) (2023)
- [Deep Learning for Multivariate Time Series Imputation: A Survey](https://mlsanity.com/paper/2402.04059/) (2024)
- [Scalable Spatiotemporal Graph Neural Networks](https://mlsanity.com/paper/2209.06520/) (2022)
- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Taming Local Effects in Graph-based Spatiotemporal Forecasting](https://mlsanity.com/paper/2302.04071/) (2023)
- [TSI-Bench: Benchmarking Time Series Imputation](https://mlsanity.com/paper/2406.12747/) (2024)
- [Networked Time Series Imputation via Position-aware Graph Enhanced Variational Autoencoders](https://mlsanity.com/paper/2305.18612/) (2023)
- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [Irregular Traffic Time Series Forecasting Based on Asynchronous Spatio-Temporal Graph Convolutional Network](https://mlsanity.com/paper/2308.16818/) (2023)
- [GinAR: An End-To-End Multivariate Time Series Forecasting Model Suitable for Variable Missing](https://mlsanity.com/paper/2405.11333/) (2024)
- [Merlin: Multi-View Representation Learning for Robust Multivariate Time Series Forecasting with Unfixed Missing Rates](https://mlsanity.com/paper/2506.12459/) (2025)
- [SSD-TS: Exploring the Potential of Linear State Space Models for Diffusion Models in Time Series Imputation](https://mlsanity.com/paper/2410.13338/) (2024)
- [Graph-based Forecasting with Missing Data through Spatiotemporal Downsampling](https://mlsanity.com/paper/2402.10634/) (2024)
- [Agentic Retrieval-Augmented Generation for Time Series Analysis](https://mlsanity.com/paper/2408.14484/) (2024)
- [Reconstructing Graph Diffusion History from a Single Snapshot](https://mlsanity.com/paper/2306.00488/) (2023)
- [Causality-Aware Spatiotemporal Graph Neural Networks for Spatiotemporal Time Series Imputation](https://mlsanity.com/paper/2403.11960/) (2024)
- [Temporal Graph ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/2404.19508/) (2024)
- [Glocal Information Bottleneck for Time Series Imputation](https://mlsanity.com/paper/2510.04910/) (2025)
- [Machine Learning for Urban Air Quality Analytics: A Survey](https://mlsanity.com/paper/2310.09620/) (2023)
- [Graph-based Virtual Sensing from Sparse and Partial Multivariate Observations](https://mlsanity.com/paper/2402.12598/) (2024)
- [sasdim: self-adaptive noise scaling diffusion model for spatial time series imputation](https://mlsanity.com/paper/2309.01988/) (2023)
- [Review for Handling Missing Data with special missing mechanism](https://mlsanity.com/paper/2404.04905/) (2024)
- [Revisiting Multivariate Time Series Forecasting with Missing Values](https://mlsanity.com/paper/2509.23494/) (2025)
- [Score-CDM: Score-Weighted Convolutional Diffusion Model for Multivariate Time Series Imputation](https://mlsanity.com/paper/2405.13075/) (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)
- [Task-oriented Time Series Imputation Evaluation via Generalized Representers](https://mlsanity.com/paper/2410.06652/) (2024)
- [S4M: S4 for multivariate time series forecasting with Missing values](https://mlsanity.com/paper/2503.00900/) (2025)
- [How Deep is your Guess? A Fresh Perspective on Deep Learning for Medical Time-Series Imputation](https://mlsanity.com/paper/2407.08442/) (2024)
- [Graph State-Space Models and Latent Relational Inference](https://mlsanity.com/paper/2301.01741/) (2023)

## Abstract (arXiv)

Modeling multivariate time series as temporal signals over a (possibly dynamic) graph is an effective representational framework that allows for developing models for time series analysis. In fact, discrete sequences of graphs can be processed by autoregressive graph neural networks to recursively learn representations at each discrete point in time and space. Spatiotemporal graphs are often highly sparse, with time series characterized by multiple, concurrent, and long sequences of missing data, e.g., due to the unreliable underlying sensor network. In this context, autoregressive models can be brittle and exhibit unstable learning dynamics. The objective of this paper is, then, to tackle the problem of learning effective models to reconstruct, i.e., impute, missing data points by conditioning the reconstruction only on the available observations. In particular, we propose a novel class of attention-based architectures that, given a set of highly sparse discrete observations, learn a representation for points in time and space by exploiting a spatiotemporal propagation architecture aligned with the imputation task. Representations are trained end-to-end to reconstruct observations w.r.t. the corresponding sensor and its neighboring nodes. Compared to the state of the art, our model handles sparse data without propagating prediction errors or requiring a bidirectional model to encode forward and backward time dependencies. Empirical results on representative benchmarks show the effectiveness of the proposed method.