Ordinal factorization machine with hierarchical sparsity

Ordinal regression (OR) or classification is a machine learning paradigm for ordinal labels. To date, there have been a variety of methods proposed including kernel based and neural network based methods with significant performance. However, existing OR methods rarely consider latent structures of given data, particularly the interaction among covariates, thus losing interpretability to some extent. To compensate this, in this paper, we present a new OR method: ordinal factorization machine with hierarchical sparsity (OFMHS), which combines factorization machine and hierarchical sparsity together to explore the hierarchical structure behind the input variables. For the sake of optimization, we formulate OFMHS as a convex optimization problem and solve it by adopting the efficient alternating directions method of multipliers (ADMM) algorithm. Experimental results on synthetic and real datasets demonstrate the superiority of our method in both performance and significant variable selection.