Boolean Matrix Factorization and Noisy Completion via Message Passing

@InProceedings{pmlr-v48-ravanbakhsha16,
  title = 	 {Boolean Matrix Factorization and Noisy Completion via Message Passing},
  author = 	 {Ravanbakhsh, Siamak and Poczos, Barnabas and Greiner, Russell},
  booktitle = 	 {Proceedings of The 33rd International Conference on Machine Learning},
  pages = 	 {945--954},
  year = 	 {2016},
  editor = 	 {Balcan, Maria Florina and Weinberger, Kilian Q.},
  volume = 	 {48},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {New York, New York, USA},
  month = 	 {20--22 Jun},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v48/ravanbakhsha16.pdf},
  url = 	 {https://proceedings.mlr.press/v48/ravanbakhsha16.html},
  abstract = 	 {Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as maximum a posteriori inference problems in a graphical model and present a message passing approach that scales linearly with the number of observations and factors. Our empirical study demonstrates that message passing is able to recover low-rank Boolean matrices, in the boundaries of theoretically possible recovery and compares favorably with state-of-the-art in real-world applications, such collaborative filtering with large-scale Boolean data.}
}