The Label Ranking problem consists in learning preference models from training datasets labeled with a ranking of class labels, and the goal is to predict a ranking for a given unlabeled instance. In this work, we focus on the particular case where both, the training dataset and the prediction given as output allow tied labels (i.e., there is no particular preference among them), known as the Partial Label Ranking problem. In particular, we propose probabilistic graphical models to solve this problem. As far as we know, there is no probability distribution to model rankings with ties, so we transform the rankings into discrete variables to represent the precedence relations (precedes, ties and succeeds) among pair of class labels (multinomial distribution). In this proposal, we use a Bayesian network with Naive Bayes structure and a hidden variable as root to collect the interactions among the different variables (predictive and target). The inference works as follows. First, we obtain the posterior-probability for each pair of class labels, and then we input these probabilities to the pair order matrix used to solve the corresponding rank aggregation problem. The experimental evaluation shows that our proposals are competitive (in accuracy) with the state-of-the-art Instance Based Partial Label Ranking (nearest neighbors paradigm) and Partial Label Ranking Trees (decision tree induction) algorithms
