Polynomial Networks and Factorization Machines: New Insights and   Efficient Training Algorithms
  Polynomial networks and factorization machines are two recently-proposed models that can efficiently use feature interactions in classification and regression tasks. In this paper, we revisit both models from a unified perspective. Based on this new view, we study the properties of both models and propose new efficient training algorithms. Key to our approach is to cast parameter learning as a low-rank symmetric tensor estimation problem, which we solve by multi-convex optimization. We demonstrate our approach on regression and recommender system tasks. 
Mathieu Blondel, Masakazu Ishihata, Akinori Fujino, Naonori Ueda
stat.ML cs.LG