Listwise learning to rank models, which optimize the ranking of a document list, are among the most widely adopted algorithms for finding and ranking relevant documents to user information needs. In this paper, we propose ListMAP, a new listwise learning to rank model with prior distribution that encodes the informativeness of training data and assigns different weights to training instances. The main intuition behind ListMAP is that documents in the training dataset do not have the same impact on training a ranking function. ListMAP formalizes the listwise loss function as a maximum a posteriori estimation problem in which the scoring function must be estimated such that the log probability of the predicted ranked list is maximized given a prior distribution on the labeled data. We provide a model for approximating the prior distribution parameters from a set of observation data. We implement the proposed learning to rank model using neural networks. We theoretically discuss and analyze the characteristics of the introduced model and empirically illustrate its performance on a number of benchmark datasets; namely MQ2007 and MQ2008 of the Letor 4.0 benchmark, Set 1 and Set 2 of the Yahoo! learning to rank challenge data set, and Microsoft 30k and Microsoft 10K datasets. We show that the proposed models are effective across different datasets in terms of information retrieval evaluation metrics NDCG and MRR at positions 1, 3, 5, 10, and 20.

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