Mixture-Based Probabilistic Graphical Models for the Label Ranking Problem.

The goal of the is to learn that predict the preferred ranking of class labels for a given unlabeled instance. Different well-known machine learning algorithms have been adapted to deal with the LR problem. In particular, fine-tuned instance-based algorithms (e.g., k-nearest neighbors) and model-based algorithms (e.g., decision trees) have performed remarkably well in tackling the LR problem. (, e.g., ) have not been considered to deal with this problem because of the difficulty of modeling permutations in that framework. In this paper, we propose a () to cope with the LR problem. By introducing a hidden variable, we can design a hybrid Bayesian network in which several types of distributions can be combined: multinomial for discrete variables, Gaussian for numerical variables, and for permutations. We consider two kinds of probabilistic models: one based on a graphical structure (where only univariate probability distributions are estimated for each state of the hidden variable) and another where we allow interactions among the predictive attributes (using a multivariate Gaussian distribution for the parameter estimation). The experimental evaluation shows that our proposals are competitive with the start-of-the-art algorithms in both accuracy and in CPU time requirements.