Mixture-Based Probabilistic Graphical Models for the Label Ranking Problem

Area of Science:

• Machine Learning
• Artificial Intelligence
• Probabilistic Graphical Models

Background:

• Label Ranking (LR) aims to predict preferred label rankings for instances.
• Existing machine learning algorithms like k-nearest neighbors and decision trees perform well in LR.
• Probabilistic Graphical Models (PGMs) have not been widely used for LR due to challenges in modeling permutations.

Purpose of the Study:

• To propose a novel Hidden Naive Bayes classifier (HNB) for the Label Ranking problem.
• To address the difficulty of incorporating permutation modeling within Probabilistic Graphical Models.
• To develop a hybrid Bayesian network capable of handling diverse variable types and permutations.

Main Methods:

• Introduced a hidden variable within a Naive Bayes framework to create a hybrid Bayesian network.
• Combined multinomial, Gaussian, and Mallows distributions to model discrete, numerical, and permutation data, respectively.
• Developed two probabilistic models: one with a Naive Bayes structure and another allowing attribute interactions via multivariate Gaussian distributions.

Main Results:

• The proposed Hidden Naive Bayes classifier (HNB) effectively addresses the Label Ranking problem.
• The hybrid Bayesian network successfully integrates different distribution types, including Mallows for permutations.
• Experimental evaluations demonstrate that the HNB approach is competitive with state-of-the-art algorithms in terms of accuracy and computational time.

Conclusions:

• The Hidden Naive Bayes classifier offers a viable and effective solution for the Label Ranking problem.
• This work successfully extends the application of Probabilistic Graphical Models to Label Ranking by handling permutations.
• The proposed methods provide a competitive alternative to existing algorithms, balancing accuracy and efficiency.