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arXiv · 1601.07932

Information-Theoretic Lower Bounds for Recovery of Diffusion Network Structures

Keehwan Park·Jean Honorio
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Abstract

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 $\Omega(k \log p)$, 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 $\Omega(k \log p)$ 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.

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Keehwan Park, Jean Honorio. 2016-01-28. Information-Theoretic Lower Bounds for Recovery of Diffusion Network Structures. https://arxiv.org/abs/1601.07932

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