# Two-level monotonic multistage recommender systems

arXiv: https://arxiv.org/abs/2110.06116 · HTML: https://mlsanity.com/paper/2110.06116/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 35 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 9 of 9)

- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Distributed Representations of Sentences and Documents](https://mlsanity.com/paper/1405.4053/) (2014)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Global Optimality in Tensor Factorization, Deep Learning, and Beyond](https://mlsanity.com/paper/1506.07540/) (2015)
- [Provable Sparse Tensor Decomposition](https://mlsanity.com/paper/1502.01425/) (2015)
- [Multilayer tensor factorization with applications to recommender systems](https://mlsanity.com/paper/1711.01598/) (2017)
- [Matrix Completion with Model-free Weighting](https://mlsanity.com/paper/2106.05850/) (2021)
- [Individualized Multilayer Tensor Learning with An Application in Imaging Analysis](https://mlsanity.com/paper/1903.08871/) (2019)

## Abstract (arXiv)

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.