Influential node detection is a central research topic in social network analysis. Many existing methods rely on the assumption that the network structure is completely known a priori. However, in many applications, network structure is unavailable to explain the underlying information diffusion phenomenon. To address the challenge of information diffusion analysis with incomplete knowledge of network structure, we develop a multi-task low rank linear influence model. By exploiting the relationships between contagions, our approach can simultaneously predict the volume (i.e. time series prediction) for each contagion (or topic) and automatically identify the most influential nodes for each contagion. The proposed model is validated using synthetic data and an ISIS twitter dataset. In addition to improving the volume prediction performance significantly, we show that the proposed approach can reliably infer the most influential users for specific contagions.