Simplicial Vector Autoregressive Model For Streaming Edge Flows

Conference paper (2023)

Authors

Joshin Krishnan Simula Metropolitan Center for Digital Engineering
Rohan Money University of Agder
Baltasar Beferull-Lozano University of Agder, Simula Metropolitan Center for Digital Engineering
Copyright: © 2023 Joshin Krishnan, Rohan Money, Baltasar Beferull-Lozano, E. Isufi
DOI: https://doi.org/10.1109/ICASSP49357.2023.10096095
Hodge Laplacians Simplicial convolution Simplicial vector autoregressive model
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Published Date

2023

Language

English

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Abstract

Vector autoregressive (VAR) model is widely used to model time-varying processes, but it suffers from prohibitive growth of the parameters when the number of time series exceeds a few hundreds. We propose a simplicial VAR model to mitigate the curse of dimensionality of the VAR models when the time series are defined over higher-order network structures such as edges, triangles, etc. The proposed model shares parameters across the simplicial signals by leveraging the simplicial convolutional filter and captures structure-aware spatio-temporal dependencies of the time-varying processes. Targetting the streaming signals from the real-world nonstationary networks, we develop a group-lasso-based online strategy to learn the proposed model. Using traffic and water distribution networks, we demonstrate that the proposed model achieves competitive signal prediction accuracy with a significantly less number of parameters than the VAR models.