  Factorization machines (FMs) are a supervised learning approach that can use
second-order feature combinations even when the data is very high-dimensional.
Unfortunately, despite increasing interest in FMs, there exists to date no
efficient training algorithm for higher-order FMs (HOFMs). In this paper, we
present the first generic yet efficient algorithms for training arbitrary-order
HOFMs. We also present new variants of HOFMs with shared parameters, which
greatly reduce model size and prediction times while maintaining similar
accuracy. We demonstrate the proposed approaches on four different link
prediction tasks.
