How to identify influential nodes is a central research topic in information diffusion analysis. Many existing methods rely on the assumption that the network structure is completely known by the model. However, in many applications, such a network is either unavailable or insufficient to explain the underlying information diffusion phenomena. To address this challenge, we develop a multi-task sparse linear influence model (MSLIM), which can simultaneously predict the volume for each contagion and automatically identify sets of the most influential nodes for different contagions. Our method is based on the linear influence model with two main advantages: 1) it does not require the network structure; 2) it can detect different sets of the most influential nodes for different contagions. To solve the corresponding convex optimization problem for learning the model, we adopt the accelerated gradient method (AGM) framework and show that there is an exact closed-form solution for the proximal mapping. Therefore, the optimization procedure achieves the optimal first-order convergence rate and can be scaled to very large datasets. The proposed model is validated on a set of 2.6 millions tweets from 1000 users of Twitter. We show that MSLIM can efficiently select the most influential users for specific contagions. We also present several interesting patterns of the selected influential users.