# Assessment of Spatio-Temporal Predictors in the Presence of Missing and Heterogeneous Data

arXiv: https://arxiv.org/abs/2302.01701 · HTML: https://mlsanity.com/paper/2302.01701/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 54 references that are in the map.
- First posted on arXiv 3 Feb 2023.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [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)
- [Principles and Algorithms for Forecasting Groups of Time Series: Locality and Globality](https://mlsanity.com/paper/2008.00444/) (2020)
- [Gated Graph Recurrent Neural Networks](https://mlsanity.com/paper/2002.01038/) (2020)
- [Sparse Graph Learning from Spatiotemporal Time Series](https://mlsanity.com/paper/2205.13492/) (2022)
- [RNN with Particle Flow for Probabilistic Spatio-temporal Forecasting](https://mlsanity.com/paper/2106.06064/) (2021)
- [Asymptotic Distribution-Free Change-Point Detection for Multivariate and non-Euclidean Data](https://mlsanity.com/paper/1707.00167/) (2017)
- [Graph Signal Processing -- Part III: Machine Learning on Graphs, from Graph Topology to Applications](https://mlsanity.com/paper/2001.00426/) (2020)

## Built on by (most cited first, 2 of 2)

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)

## Abstract (arXiv)

Deep learning methods achieve remarkable predictive performance in modeling complex, large-scale data. However, assessing the quality of derived models has become increasingly challenging, as more classical statistical assumptions may no longer apply. These difficulties are particularly pronounced for spatio-temporal data, which exhibit dependencies across both space and time and are often characterized by nonlinear dynamics, time variance, and missing observations, hence calling for new accuracy assessment methodologies. This paper introduces a residual correlation analysis framework for assessing the optimality of spatio-temporal relational-enabled neural predictive models, notably in settings with incomplete and heterogeneous data. By leveraging the principle that residual correlation indicates information not captured by the model, enabling the identification and localization of regions in space and time where predictive performance can be improved. A strength of the proposed approach is that it operates under minimal assumptions, allowing also for robust evaluation of deep learning models applied to multivariate time series, even in the presence of missing and heterogeneous data. In detail, the methodology constructs tailored spatio-temporal graphs to encode sparse spatial and temporal dependencies and employs asymptotically distribution-free summary statistics to detect time intervals and spatial regions where the model underperforms. The effectiveness of what proposed is demonstrated through experiments on both synthetic and real-world datasets using state-of-the-art predictive models.