Science of Machine Learning

Exhibition Program 2

Learning feature combinations from multiple tasks

MOFM: low-rank regression for learning common factors


Multi-output Factorization Machines (MOFM) are an extension of Convex Factorization Machines that can learn the model of several tasks simultaneously. MOFM can find combinations of factors that are predictive across tasks.
MOFM decompose the potentially very large weight matrix associated with each task using a small number of common basis vectors. Hence, MOFM are able to scale to very high-dimensional data. In addition, we propose a convex formulation for learning this decomposition with optimality guarantee.
MOFM find applications to numerous real-world problems, including medical diagnosis, recommendation systems and genomic selection of plants. In future work, we plan to further study the theoretical properties of MOFM.


  • [1] M. Blondel, A. Fujino, N. Ueda, “Convex Factorization Machines,” in Proc. European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2015.
    [2] M. Blondel, V. Niculae, T. Otsuka, N. Ueda, “Multi-output Polynomial Networks and Factorization Machines,” in Proc. Neural Information Processing Systems, 2017.




Mathieu Blondel
Mathieu Blondel
Ueda Research Laboratory