@article{17720,
  author = {Joshin Krishnan and Rohan Money and Baltasar Beferull-Lozano and Elvin Isufi},
  title = {Simplicial Vector Autoregressive Models},
  abstract = {The vector autoregressive (VAR) model is extensively employed for modelling dynamic processes, yet its scalability is challenged by an overwhelming growth in parameters when dealing with several hundred time series. To overcome this issue, inductive priors (e.g., data structure) can be leveraged to restrict the parameter space while still effectively modelling the time series. We present simplicial VAR models to mitigate the curse of dimensionality in VAR models, demonstrating also their utility in capturing the dynamics of time series defined over higher-order network structures such as edges and trian- gles. The proposed models use simplicial convolutional filters to facilitate parameter sharing across simplicial signals and capture structure-aware spatio-temporal dependencies among them. We also develop a joint simplicial-temporal Fourier transform to analyze the spectral characteristics of the models, depicting them as simplicial-temporal filters. We focus on streaming signals from real-world time-varying networks and develop an online algorithm for learning simplicial VAR models with a sublinear dynamic regret bound, ensuring convergence under reasonable assumptions. Through experiments on synthetic networks, water distribution networks, and collaborating agents, we demonstrate that the proposed models attain competitive signal modelling accuracy with orders of magnitude fewer parameters than VAR models.},
  year = {2024},
  journal = {IEEE Transactions on Signal Processing},
  publisher = {IEEE Transactions on Signal Processing},
  url = {https://doi.org/10.36227/techrxiv.171560860.00003811/v1},
}