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2021 Two-level monotonic multistage recommender systems
Ben Dai, Xiaotong Shen, Wei Pan
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Electron. J. Statist. 15(2): 5545-5569 (2021). DOI: 10.1214/21-EJS1924


A recommender system learns to predict the user-specific preference or intention over many items simultaneously for all users, making personalized recommendations based on a relatively small number of observations. One central issue is how to leverage three-way interactions, referred to as user-item-stage dependencies on a monotonic chain of events, to enhance the prediction accuracy. A monotonic chain of events occurs, for instance, in an article sharing dataset, where a “follow” action implies a “like” action, which in turn implies a “view” action. In this article, we develop a multistage recommender system utilizing a two-level monotonic property characterizing a monotonic chain of events for personalized prediction. Particularly, we derive a large-margin classifier based on a nonnegative additive latent factor model in the presence of a high percentage of missing observations, particularly between stages, reducing the number of model parameters for personalized prediction while guaranteeing prediction consistency. On this ground, we derive a regularized cost function to learn user-specific behaviors at different stages, linking decision functions to numerical and categorical covariates to model user-item-stage interactions. Computationally, we derive an algorithm based on blockwise coordinate descent. Theoretically, we show that the two-level monotonic property enhances the accuracy of learning as compared to a standard method treating each stage individually and an ordinal method utilizing only one-level monotonicity. Finally, the proposed method compares favorably with existing methods in simulations and an article sharing dataset.

Funding Statement

Research supported in part by NSF grants DMS-1712564, DMS-1721216, DMS-1952539, and NIH grants 1R01GM126002, R01HL105397, R01AG069895.


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Ben Dai. Xiaotong Shen. Wei Pan. "Two-level monotonic multistage recommender systems." Electron. J. Statist. 15 (2) 5545 - 5569, 2021.


Received: 1 May 2021; Published: 2021
First available in Project Euclid: 27 December 2021

Digital Object Identifier: 10.1214/21-EJS1924

Primary: 62H30
Secondary: 68T05

Keywords: implicit feedback , Monotonicity , nonconvex minimization , nonnegative latent factor model


Vol.15 • No. 2 • 2021
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