  This paper examines the relationship between user pageview (PV) histories and
their item-choice behavior on an e-commerce website. We focus on PV sequences,
which represent time series of the number of PVs for each user--item pair. We
propose a shape-restricted optimization model that accurately estimates
item-choice probabilities for all possible PV sequences. This model imposes
monotonicity constraints on item-choice probabilities by exploiting partial
orders for PV sequences, according to the recency and frequency of a 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 our method achieves higher
prediction performance than that of a state-of-the-art optimization model and
common machine learning methods.
