Mixture-Based Probabilistic Graphical Models for the Label Ranking Problem

Abstract

The goal of the Label Ranking (LR) problem is to learn preference models 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. Probabilistic Graphical Models (PGMs, e.g., Bayesian networks) 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 Hidden Naive Bayes classifier (HNB) 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 Mallows for permutations. We consider two kinds of probabilistic models: one based on a Naive Bayes 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.

Efficient ensembles of distance‐based label ranking trees

“…Algorithms belonging to different machine learning paradigms (Zhou et al, 2014) have been proposed to tackle the LR problem: instance‐based learning (Cheng et al, 2009; Cheng et al, 2010), decision/regression trees (Cheng et al, 2009; de Sá et al, 2017; Plaia & Sciandra, 2019), neural networks (Ribeiro et al, 2012), association rules (de Sá et al, 2011), probabilistic graphical models (Rodrigo et al, 2021), and transformation methods (Brinker & Hüllermeier, 2020; Cheng et al, 2013; Hüllermeier et al, 2008). However, current state‐of‐the‐art methods are those based on the ensemble technique and, in particular, ensembles of Label Ranking Trees, which have been proposed for standard ensemble techniques: bagging (Aledo et al, 2017; Suchithra & Pai, 2022), boosting (Dery & Shmueli, 2020) and random forest (de Sá et al, 2017; Zhou & Qiu, 2018).…”

Ensemble learning for the partial label ranking problem

“…Several methods have been proposed to deal with the LR problem: Adaptation methods . The first group comprises the methods that adapt well‐known machine learning algorithms to cope with (possibly incomplete) rankings, such as decision tree induction , 4 instance‐based learning , 4 probabilistic graphical models , 7,8 association rules , 9 and neural networks 10 Transformation methods .…”

Heuristic Search for Rank Aggregation with Application to Label Ranking

“…The difference between the two rankings is usually measured by the distance. Among the distance measures available in the literature, the Kendall tau distance (or the Kendall distance) [9] is the most widely used in several real-world applications centered on the analysis of ranked data [6], [10]- [12].…”