Reviews: Multi-way Interacting Regression via Factorization Machines

The paper presents a Bayesian method for regression problems where the response variables can depend on multi-way combinations of the predictors. Via a hyper graph representation of the covariates interactions, the model is obtained from a refinement of the Finite Feature Model. The idea of modelling the interactions as the hyper edges of a hyper graph is interesting but the proposed model seems to be technically equivalent to the original Finite Mixture Model. Moreover, from the experimental results, it is hard to assess if the new parametrised extension is an improvement respect to the baseline. Here are few questions and comments: - is the idea of modelling interactions via an unbounded membership model new?