Users' locations are important to many applications such as targeted advertisement and news recommendation. In this paper, we focus on the problem of profiling users' home locations in the context of social network (Twitter). The problem is nontrivial, because signals, which may help to identify a user's location, are scarce and noisy. We propose a unified discriminative influence model, named as UDI, to solve the problem. To overcome the challenge of scarce signals, UDI integrates signals observed from both social network (friends) and user-centric data (tweets) in a unified probabilistic framework. To overcome the challenge of noisy signals, UDI captures how likely a user connects to a signal with respect to 1) the distance between the user and the signal, and 2) the influence scope of the signal. Based on the model, we develop local and global location prediction methods. The experiments on a large scale data set show that our methods improve the state-of-the-art methods by 13%, and achieve the best performance.