• Corpus ID: 244129842

Non-separable Spatio-temporal Graph Kernels via SPDEs

@inproceedings{Nikitin2022NonseparableSG,
  title={Non-separable Spatio-temporal Graph Kernels via SPDEs},
  author={Alexander P. Nikitin and S. T. John and A. Solin and Samuel Kaski},
  booktitle={AISTATS},
  year={2022}
}
Gaussian processes (GPs) provide a principled and direct approach for inference and learning on graphs. However, the lack of justified graph kernels for spatio-temporal modelling has held back their use in graph problems. We leverage an explicit link between stochastic partial di ↵ erential equations (SPDEs) and GPs on graphs, introduce a framework for deriving graph kernels via SPDEs, and derive non-separable spatio-temporal graph kernels that capture interaction across space and time. We… 

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References

SHOWING 1-10 OF 62 REFERENCES
Kernel-Based Reconstruction of Space-Time Functions on Dynamic Graphs
TLDR
The present paper broadens the kernel-based graph function estimation framework to reconstruct time-evolving functions over possibly time-varying topologies, and includes a novel kernel Kalman filter, developed to reconstruct space-time functions at affordable computational cost.
Kernel-Based Reconstruction of Graph Signals
TLDR
This paper advocates kernel regression as a framework generalizing popular SPoG modeling and reconstruction and expanding their capabilities, capitalizes on the so-called representer theorem to devise simpler versions of existing Tikhonov regularized estimators, and offers a novel probabilistic interpretation of kernel methods on graphs based on graphical models.
The SPDE Approach to Matérn Fields: Graph Representations
This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish
Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting
TLDR
This paper proposes a novel deep learning framework, Spatio-Temporal Graph Convolutional Networks (STGCN), to tackle the time series prediction problem in traffic domain, and builds the model with complete convolutional structures, which enable much faster training speed with fewer parameters.
Matern Gaussian Processes on Graphs
Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process
PyTorch Geometric Temporal: Spatiotemporal Signal Processing with Neural Machine Learning Models
TLDR
PyTorch Geometric Temporal is presented, a deep learning framework combining state-of-the-art machine learning algorithms for neural spatiotemporal signal processing and can potentially operate on web-scale datasets with rich temporal features and spatial structure.
Diffusion Convolutional Recurrent Neural Network: Data-Driven Traffic Forecasting
TLDR
Diffusion Convolutional Recurrent Neural Network (DCRNN), a deep learning framework for traffic forecasting that incorporates both spatial and temporal dependency in the traffic flow and evaluates the framework on two real-world large scale road network traffic datasets and observes consistent improvement.
Matern Gaussian processes on Riemannian manifolds
TLDR
This work proposes techniques for computing the kernels of these processes via spectral theory of the Laplace--Beltrami operator in a fully constructive manner, thereby allowing them to be trained via standard scalable techniques such as inducing point methods.
T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction
TLDR
A novel neural network-based traffic forecasting method, the temporal graph convolutional network (T-GCN) model, which is combined with the graph convolved network (GCN), and the gated recurrent unit (GRU) to capture the spatial and temporal dependences simultaneously.
An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach
TLDR
It is shown that, using an approximate stochastic weak solution to (linear) stochastically partial differential equations, some Gaussian fields in the Matérn class can provide an explicit link, for any triangulation of , between GFs and GMRFs, formulated as a basis function representation.
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