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Estimating diffusion network structures: Recovery conditions, sample complexity & soft-thresholding algorithm (2014)
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| Venue: | In Proc. of the 31st International Conference on Machine Learning (ICML |
| Citations: | 6 - 3 self |
BibTeX
@INPROCEEDINGS{Daneshmand14estimatingdiffusion,
author = {Hadi Daneshmand and Manuel Gomez-rodriguez and Le Song},
title = {Estimating diffusion network structures: Recovery conditions, sample complexity & soft-thresholding algorithm},
booktitle = {In Proc. of the 31st International Conference on Machine Learning (ICML},
year = {2014}
}
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Abstract
Information spreads across social and techno-logical networks, but often the network struc-tures are hidden from us and we only observe the traces left by the diffusion processes, called cascades. Can we recover the hidden network structures from these observed cascades? What kind of cascades and how many cascades do we need? Are there some network structures which are more difficult than others to recover? Can we design efficient inference algorithms with prova-ble guarantees? Despite the increasing availability of cascade-data and methods for inferring networks from these data, a thorough theoretical understanding of the above questions remains largely unex-plored in the literature. In this paper, we inves-tigate the network structure inference problem for a general family of continuous-time diffusion models using an `1-regularized likelihood ma-ximization framework. We show that, as long as the cascade sampling process satisfies a na-tural incoherence condition, our framework can recover the correct network structure with high probability if we observe O(d3 logN) cascades, where d is the maximum number of parents of a node and N is the total number of nodes. More-over, we develop a simple and efficient soft-thresholding inference algorithm, which we use to illustrate the consequences of our theoreti-cal results, and show that our framework outper-forms other alternatives in practice.
Keyphrases
diffusion network structure sample complexity soft-thresholding algorithm recovery condition maximum number network structure inference problem techno-logical network correct network structure high probability efficient inference algorithm continuous-time diffusion model information spread many cascade theoreti-cal result na-tural incoherence condition prova-ble guarantee network struc-tures total number general family thorough theoretical understanding efficient soft-thresholding inference algorithm process satisfies 1-regularized likelihood ma-ximization framework network structure hidden network structure d3 logn
