Link prediction is a key technique in many applications such as recommender systems, where potential links between users and items need to be predicted. A challenge in link prediction is the data sparsity problem. In this paper, we address this problem by jointly considering multiple heterogeneous link prediction tasks such as predicting links between users and different types of items including books, movies and songs, which we refer to as the collective link prediction (CLP) problem. We propose a nonparametric Bayesian framework for solving the CLP problem, which allows knowledge to be adaptively transferred across heterogeneous tasks while taking into account the similarities between tasks. We learn the inter-task similarity automatically. We also introduce link functions for different tasks to correct their biases and skewness of distributions in their link data. We conduct experiments on several real world datasets and demonstrate significant improvements over several existing st...