Convex Factorization Machine for Regression [article]

Makoto Yamada, Wenzhao Lian, Amit Goyal, Jianhui Chen, Kishan Wimalawarne, Suleiman A Khan, Samuel Kaski, Hiroshi Mamitsuka, Yi Chang
2016 arXiv   pre-print
We propose the convex factorization machine (CFM), which is a convex variant of the widely used Factorization Machines (FMs). Specifically, we employ a linear+quadratic model and regularize the linear term with the ℓ_2-regularizer and the quadratic term with the trace norm regularizer. Then, we formulate the CFM optimization as a semidefinite programming problem and propose an efficient optimization procedure with Hazan's algorithm. A key advantage of CFM over existing FMs is that it can find a
more » ... globally optimal solution, while FMs may get a poor locally optimal solution since the objective function of FMs is non-convex. In addition, the proposed algorithm is simple yet effective and can be implemented easily. Finally, CFM is a general factorization method and can also be used for other factorization problems including including multi-view matrix factorization and tensor completion problems. Through synthetic and movielens datasets, we first show that the proposed CFM achieves results competitive to FMs. Furthermore, in a toxicogenomics prediction task, we show that CFM outperforms a state-of-the-art tensor factorization method.
arXiv:1507.01073v5 fatcat:awqbv6lvejbytmvcs2p25lb4iy