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Sparse and low-rank multivariate Hawkes processes

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Academic year: 2021

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Figure 1: Toy example with d = 10 nodes. Based on actions’ timestamps of the nodes, represented by ver- ver-tical bars (top), we aim at recovering the vector µ 0 and the tensor A of implicit influence between nodes (bottom).
Figure 2: Ground truth vector µ and tensor A in dimension 30. Each row corresponds to a different example used in our experiments.
Figure 3: Ground truth tensor A and recovered tensors using all procedures. We observe that wL1 and wL1Nuclear leads to a much better support recovery, since we observe less false positives outside of the node communities.
Figure 4: Average metrics achieved by all procedures on the three considered examples of A (in the same order as the display from Figure 2), and 95% confidence bands, with increasing observation length T over repeated simulations
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