Factorization machines are a great way to model interactions between different features, in a way that is more efficient than full-blown quadratic interactions. There exist efficient implementations like libFM and Vowpal Wabbit's --lrq option. My question is about higher order interactions: the FM paper mentions that it is easy to extend it to higher orders (Tensor FM?), see. Eq. (5) in the paper. Are there any good implementations of 3-way factorization machines?[moved from cross-validated]
3-way factorization machines
machine learning