Classification using belief functions: relationship between case-based and model-based approaches

Area of Science:

• Artificial Intelligence
• Machine Learning
• Uncertainty Quantification

Background:

• The transferable belief model (TBM) offers a framework for quantified uncertainty using belief functions, independent of probability models.
• Two TBM classification approaches exist: model-based (using general Bayesian theorem - GBT) and case-based (using pattern similarity).
• The relationship between these TBM classifiers and standard classification techniques was previously unclear.

Purpose of the Study:

• To demonstrate that both TBM classification methods stem from the same underlying principle, the general Bayesian theorem (GBT).
• To elucidate the differences between the TBM model-based and case-based classifiers based on information assumptions.
• To connect TBM classification to standard methods and identify potential new research avenues.

Main Methods:

• Analysis of the theoretical underpinnings of TBM model-based and case-based classifiers.
• Application of the general Bayesian theorem (GBT) to unify the two TBM classification approaches.
• Investigation of special cases, including precise/categorical data, to derive kernel rules and relationships between basic belief assignments.

Main Results:

• Both TBM classification methods are shown to derive from the general Bayesian theorem (GBT).
• The primary distinction between the methods lies in the nature of the assumed available information.
• Under specific conditions (precise/categorical data), both methods converge to a kernel rule, with a defined relationship between their basic belief assignments.

Conclusions:

• This work clarifies the theoretical connection between TBM classification methods and standard approaches.
• The findings provide insights into supervised learning within the TBM framework.
• The results aid in selecting appropriate TBM methods based on available information and suggest future research directions.