# MFAI: A Scalable Bayesian Matrix Factorization Approach to Leveraging Auxiliary Information

arXiv: https://arxiv.org/abs/2303.02566 · HTML: https://mlsanity.com/paper/2303.02566/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 70 references that are in the map.
- First posted on arXiv 5 Mar 2023.

## Builds on (most cited first, 13 of 13)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares](https://mlsanity.com/paper/1410.2596/) (2014)
- [Metadata Embeddings for User and Item Cold-start Recommendations](https://mlsanity.com/paper/1507.08439/) (2015)
- [Gaussian Process Boosting](https://mlsanity.com/paper/2004.02653/) (2020)
- [Low-Rank Modeling and Its Applications in Image Analysis](https://mlsanity.com/paper/1401.3409/) (2014)
- [Gradient and Newton Boosting for Classification and Regression](https://mlsanity.com/paper/1808.03064/) (2018)
- [Empirical Bayes Matrix Factorization](https://mlsanity.com/paper/1802.06931/) (2018)
- [Latent Gaussian Model Boosting](https://mlsanity.com/paper/2105.08966/) (2021)
- [Characterizing Spatiotemporal Transcriptome of Human Brain via Low Rank Tensor Decomposition](https://mlsanity.com/paper/1702.07449/) (2017)
- [Cold-start recommendations in Collective Matrix Factorization](https://mlsanity.com/paper/1809.00366/) (2018)
- [Inductive Matrix Completion: No Bad Local Minima and a Fast Algorithm](https://mlsanity.com/paper/2201.13052/) (2022)
- [On Joint Estimation of Gaussian Graphical Models for Spatial and Temporal Data](https://mlsanity.com/paper/1507.01933/) (2015)
- [Multimodal Data Fusion in High-Dimensional Heterogeneous Datasets via Generative Models](https://mlsanity.com/paper/2108.12445/) (2021)

## Abstract (arXiv)

In various practical situations, matrix factorization methods suffer from poor data quality, such as high data sparsity and low signal-to-noise ratio (SNR). Here, we consider a matrix factorization problem by utilizing auxiliary information, which is massively available in real-world applications, to overcome the challenges caused by poor data quality. Unlike existing methods that mainly rely on simple linear models to combine auxiliary information with the main data matrix, we propose to integrate gradient boosted trees in the probabilistic matrix factorization framework to effectively leverage auxiliary information (MFAI). Thus, MFAI naturally inherits several salient features of gradient boosted trees, such as the capability of flexibly modeling nonlinear relationships and robustness to irrelevant features and missing values in auxiliary information. The parameters in MFAI can be automatically determined under the empirical Bayes framework, making it adaptive to the utilization of auxiliary information and immune to overfitting. Moreover, MFAI is computationally efficient and scalable to large datasets by exploiting variational inference. We demonstrate the advantages of MFAI through comprehensive numerical results from simulation studies and real data analyses. Our approach is implemented in the R package mfair available at https://github.com/YangLabHKUST/mfair.