Collaborative networks are common in real life, where domain experts work together to solve tasks issued by customers. How to model the proficiency of experts is critical for us to understand and optimize collaborative networks. Traditional expertise models, such as topic model based methods, cannot capture two aspects of human expertise simultaneously: Specialization (what area an expert is good at?) and Proficiency Level (to what degree?). In this paper, we propose new models to overcome this problem. We embed all historical task data in a lower dimension space and learn vector representations of expertise based on both solved and unsolved tasks. Specifically, in our first model, we assume that each expert will only handle tasks whose difficulty level just matches his/her proficiency level, while experts in the second model accept tasks whose levels are equal to or lower than his/her proficiency level. Experiments on real world datasets show that both models outperform topic model based approaches and standard classifiers such as logistic regression and support vector machine in terms of prediction accuracy. The learnt vector representations can be used to compare expertise in a large organization and optimize expert allocation.