# Predicting Online Item-Choice Behavior: A Shape-Restricted Regression Approach
## 2 Related Work
### Prediction of Online User Behavior  
A number of prior studies have aimed at predicting users' purchase behavior on e-commerce websites [14]. Mainstream research has applied stochastic or statistical models for predicting purchase sessions [9; 15; 16; 17; 18; 19; 20], but these approaches do not consider which items users choose.  
Various machine learning methods have been used to predict online item-choice behavior, including logistic regression [21; 22], association rule mining [23], support vector machines [22; 24], ensemble learning methods [25; 26; 27; 28; 29], and artificial neural networks [30; 31; 32]. Tailored statistical models have also been proposed. For instance, [PERSON] [33] devised a two-stage multinomial logit model that separates the decision-making process into item views and purchase decisions. [PERSON] et al. [34] proposed a joint framework consisting of user-level factor estimation and item-level factor aggregation based on the buyer decision process.  
[PERSON] and [PERSON] [35] used Markov chain models to estimate the probability of the next link choice of a user.  
These prior studies effectively utilized clickstream data in various prediction methods and showed that the consideration of time-evolving user behavior is crucial for the precise prediction of online item-choice behavior. We therefore focused on user PV sequences to estimate item-choice probabilities on e-commerce websites.  
On the other hand, various predictive features have been used for analyzing online user behavior; these include user demographics, item characteristics, transaction timestamps, accessing devices, touchpoints, and user locations [14]. Indeed, [PERSON] et al. [12] demonstrated that the prediction performance can be improved by combining PV histories with item categories. To further upgrade the prediction performance, we aim at exploiting the detailed information contained in the PV history rather than developing a comprehensive model that integrates various predictive features. If successful, we can improve the prediction performance of comprehensive models through ensemble learning. Additionally, user PV histories are often easily accessible in practical situations, whereas detailed personal information can be unavailable due to a privacy issue.  
Recently, deep learning methods have been actively studied to predict online user behavior especially in recommender systems; these include the multilayer perceptron, the autoencoder, convolutional/recurrent neural networks, and neural attention models [36]. In particular, graph neural networks [37; 38] that operate on graph data have been used effectively because most of the information about users' item-choice behavior has a graph structure. Sophisticated methods based on graph neural networks have been proposed for purchase prediction [39; 40; 41; 42], and these can be considered as a top line on the prediction performance. In contrast, our method has a different advantage from such deep learning methods; it is a simple interpretable nonparametric model specialized in handling PV sequences based on properties indicated by the recency and frequency. Moreover, we evaluated the validity of our method by comparison with machine learning methods that have commonly been used in prior studies.