Learning to rank has received great attention in recent years as it plays a crucial role in many applications such as information retrieval and data mining. The existing concept of learning to rank assumes that each training instance is associated with a reliable label. However, in practice, this assumption does not necessarily hold true as it may be infeasible or remarkably expensive to obtain reliable labels for many learning to rank applications. Therefore, a feasible approach is to collect labels from crowds and then learn a ranking function from crowdsourcing labels. This study explores the listwise learning to rank with crowdsourcing labels obtained from multiple annotators, who may be unreliable. A new probabilistic ranking model is first proposed by combining two existing models. Subsequently, a ranking function is trained by proposing a maximum likelihood learning approach, which estimates ground-truth labels and annotator expertise, and trains the ranking function iteratively. In practical crowdsourcing machine learning, valuable side information (e.g., professional grades) about involved annotators is normally attainable. Therefore, this study also investigates learning to rank from crowd labels when side information on the expertise of involved annotators is available. In particular, three basic types of side information are investigated, and corresponding learning algorithms are consequently introduced. Further, the top-k learning to rank from crowdsourcing labels are explored to deal with long training ranking lists. The proposed algorithms are tested on both synthetic and real-world data. Results reveal that the maximum likelihood estimation approach significantly outperforms the average approach and existing crowdsourcing regression methods. The performances of the proposed algorithms are comparable to those of the learning model in consideration reliable labels. The results of the investigation further indicate that side information is helpful in inferring both ranking functions and expertise degrees of annotators.

Listwise learning to rank (LTR) is aimed at constructing a ranking model from listwise training data to order objects. In most existing studies, each training instance consists of a set of objects described by preference features. In a preference feature space for the objects in training, the structure of the objects is associated with the absolute preference degrees for the objects. The degrees significantly influence the ordering of the objects. Nevertheless, the structure of the training objects in their preference feature space has rarely been studied. In addition, most listwise LTR algorithms yield a single linear ranking model for all objects, but this ranking model may be insufficient to capture the underlying nonlinear ranking mechanism among all objects. This study proposes a divide-and-train method to learn a nonlinear ranking model from listwise training data. First, a rank-preserving clustering approach is used to infer the structure of objects in their preference feature space and all the objects in training data are divided into several clusters. Each cluster is assumed to correspond to a preference degree and an ordinal regression function is then learned. Second, considering that relations exist among the clusters, a multi-task listwise ranking approach is then employed to train linear ranking functions for all the clusters (or preference degrees) simultaneously. Our proposed method utilizes both the (relative) preferences among objects and the intrinsic structure of objects. Experimental results on benchmark data sets suggest that the proposed method outperforms state-oft-the-art listwise LTR algorithms.