MFAI: A Scalable Bayesian Matrix Factorization Approach to Leveraging Auxiliary Information
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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 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 MAFI 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-scale datasets by exploiting variational inference. We demonstrate the advantages of MFAI through comprehensive numerical results from simulation studies and real data analysis. Our approach is implemented in the R package mfair available at https://github.com/YangLabHKUST/mfair.
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