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.

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In this paper, we investigate the application of transfer learning to train a DNN model for joint channel and power allocation in underlay Device-to-Device communication. Based on the traditional optimization solutions, generating training dataset for scenarios with perfect CSI is not computationally demanding, compared to scenarios with imperfect CSI. Thus, a transfer learning-based approach can be exploited to transfer the DNN model trained for the perfect CSI scenarios to the imperfect CSI scenarios. We also consider the issue of defining the similarity between two types of resource allocation tasks. For this, we first determine the value of outage probability for which two resource allocation tasks are same, that is, for which our numerical results illustrate the minimal need of relearning from the transferred DNN model. For other values of outage probability, there is a mismatch between the two tasks and our results illustrate a more efficient relearning of the transferred DNN model. Our results show that the learning dataset required for relearning of the transferred DNN model is significantly smaller than the required training dataset for a DNN model without transfer learning.