In the area of Learning to Rank, the models whose output is ranking are trained from data. The exponential model proposed by Petterson showed good performance for predicting rankings. The model is closely related to permanent in the sense that the partition function is equivalent to permanent. The learning of the model requires intensive computation which is derived from the difficulty of calculating permanent. For approximating permanent, utilizing BP is proposed, which is computationally very efficient. In this paper we propose the application of BP to reduce the computational cost to learn the model proposed by Petterson et al. In addition to that, we apply the idea of initializing BP with the messages from the previous step to reduce the number of the iterations for BP to converge.
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