Stopping Criterion Design for Recursive Bayesian Classification: Analysis and Decision Geometry.

Area of Science:

• Machine Learning
• Bayesian Inference
• Pattern Recognition

Background:

• Recursive Bayesian updates are used for classification, with cost efficiency dependent on stopping criteria.
• Conventional criteria include thresholds on maximum posterior probability and posterior uncertainty.
• These methods have limitations, such as unnecessary evidence collection or premature termination.

Purpose of the Study:

• To propose a new stopping criterion for Bayesian classification systems based on a geometric interpretation of posterior progression.
• To analyze the disadvantages of conventional termination criteria using this geometric insight.
• To compare the proposed method against conventional ones in terms of decision accuracy and speed.

Main Methods:

• Developed a geometric interpretation of state posterior progression in Bayesian classification.
• Analyzed limitations of existing termination criteria (maximum posterior and uncertainty thresholds).
• Proposed a novel stopping criterion derived from the geometric insights.
• Validated the new criterion using simulations and real-world data from a brain-computer interface typing system.

Main Results:

• Demonstrated that conventional maximum posterior thresholds lead to 'stiffness' and excessive evidence collection.
• Showed that uncertainty-based thresholds are sensitive to the number of categories and can terminate prematurely.
• The proposed geometric criterion overcomes these limitations, offering improved decision accuracy and speed.

Conclusions:

• The geometric interpretation provides a deeper understanding of Bayesian classification dynamics.
• The novel stopping criterion offers a more robust and efficient alternative to conventional methods.
• The findings are validated on both simulated and real-world brain-computer interface data.