Information-Theoretic Lower Bounds for Recovery of Diffusion Network Structures
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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 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 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.
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