This paper is concerned with examining the relationship between users' page view (PV) history and their item-choice behavior on an e-commerce website. We focus particularly on the PV sequence, which represents a time series of the number of PVs for each user--item pair. We propose a shape-restricted optimization model to accurately estimate item-choice probabilities for all possible PV sequences. In this model, we impose monotonicity constraints on item-choice probabilities by exploiting partial orders specialized for the PV sequences based on the recency and frequency of each user's previous PVs. To improve the computational efficiency of our optimization model, we devise efficient algorithms for eliminating all redundant constraints according to the transitivity of the partial orders. Experimental results using real-world clickstream data demonstrate that higher prediction performance is achieved with our method than with the state-of-the-art optimization model and common machine learning methods.
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