# Towards Learning in Grey Spatiotemporal Systems: A Prophet to Non-consecutive Spatiotemporal Dynamics

arXiv: https://arxiv.org/abs/2208.08878 · HTML: https://mlsanity.com/paper/2208.08878/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 56 references that are in the map.
- First posted on arXiv 17 Aug 2022.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [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)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [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)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2012.09641/) (2020)
- [SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates](https://mlsanity.com/paper/2008.10546/) (2020)
- [Learning Graph Convolutional Network for Skeleton-based Human Action Recognition by Neural Searching](https://mlsanity.com/paper/1911.04131/) (2019)
- [STG2Seq: Spatial-temporal Graph to Sequence Model for Multi-step Passenger Demand Forecasting](https://mlsanity.com/paper/1905.10069/) (2019)
- [Quantifying Uncertainty in Deep Spatiotemporal Forecasting](https://mlsanity.com/paper/2105.11982/) (2021)
- [RiskOracle: A Minute-level Citywide Traffic Accident Forecasting Framework](https://mlsanity.com/paper/2003.00819/) (2020)
- [Weakly-Supervised Spatio-Temporal Anomaly Detection in Surveillance Video](https://mlsanity.com/paper/2108.03825/) (2021)
- [Dynamic Gaussian Mixture based Deep Generative Model For Robust Forecasting on Sparse Multivariate Time Series](https://mlsanity.com/paper/2103.02164/) (2021)
- [Quantifying Uncertainty in Discrete-Continuous and Skewed Data with Bayesian Deep Learning](https://mlsanity.com/paper/1802.04742/) (2018)
- [STUaNet: Understanding uncertainty in spatiotemporal collective human mobility](https://mlsanity.com/paper/2102.06027/) (2021)
- [Probabilistic Time Series Forecasting with Structured Shape and Temporal Diversity](https://mlsanity.com/paper/2010.07349/) (2020)
- [Location Prediction via Bi-direction Speculation and Dual-level Association](https://mlsanity.com/paper/2106.15070/) (2021)
- [Graph Similarity Description: How Are These Graphs Similar?](https://mlsanity.com/paper/2105.14364/) (2021)

## Built on by (most cited first, 1 of 1)

- [FRIGATE: Frugal Spatio-temporal Forecasting on Road Networks](https://mlsanity.com/paper/2306.08277/) (2023)

## Abstract (arXiv)

Spatiotemporal forecasting is an imperative topic in data science due to its diverse and critical applications in smart cities. Existing works mostly perform consecutive predictions of following steps with observations completely and continuously obtained, where nearest observations can be exploited as key knowledge for instantaneous status estimation. However, the practical issues of early activity planning and sensor failures elicit a brand-new task, i.e., non-consecutive forecasting. In this paper, we define spatiotemporal learning systems with missing observation as Grey Spatiotemporal Systems (G2S) and propose a Factor-Decoupled learning framework for G2S (FDG2S), where the core idea is to hierarchically decouple multi-level factors and enable both flexible aggregations and disentangled uncertainty estimations. Firstly, to compensate for missing observations, a generic semantic-neighboring sequence sampling is devised, which selects representative sequences to capture both periodical regularity and instantaneous variations. Secondly, we turn the predictions of non-consecutive statuses into inferring statuses under expected combined exogenous factors. In particular, a factor-decoupled aggregation scheme is proposed to decouple factor-induced predictive intensity and region-wise proximity by two energy functions of conditional random field. To infer region-wise proximity under flexible factor-wise combinations and enable dynamic neighborhood aggregations, we further disentangle compounded influences of exogenous factors on region-wise proximity and learn to aggregate them. Given the inherent incompleteness and critical applications of G2S, a DisEntangled Uncertainty Quantification is put forward, to identify two types of uncertainty for reliability guarantees and model interpretations.