Information-Theoretic Lower Bounds for Recovery of Diffusion Network Structures
This work addresses the fundamental limits of network structure recovery in diffusion processes, which is crucial for applications like social network analysis and epidemiology, and is incremental in extending lower bounds to continuous-time models.
The paper tackles the problem of determining the minimum sample complexity needed to correctly recover diffusion network structures, establishing a lower bound of order Ω(k log p) for both discrete-time and continuous-time diffusion models on directed graphs with p nodes and at most k parents per node.
We study the information-theoretic lower bound of the sample complexity of the correct recovery of diffusion network structures. We introduce a discrete-time diffusion model based on the Independent Cascade model for which we obtain a lower bound of order $Ω(k \log p)$, for directed graphs of $p$ nodes, and at most $k$ parents per node. Next, we introduce a continuous-time diffusion model, for which a similar lower bound of order $Ω(k \log p)$ is obtained. Our results show that the algorithm of Pouget-Abadie et al. is statistically optimal for the discrete-time regime. Our work also opens the question of whether it is possible to devise an optimal algorithm for the continuous-time regime.