PAC-Bayes Unleashed: Generalisation Bounds with Unbounded Losses.

Area of Science:

• Machine Learning
• Statistical Learning Theory
• Computational Learning Theory

Background:

• The PAC-Bayes learning framework typically assumes bounded loss functions, limiting its applicability.
• Existing PAC-Bayes generalization bounds are often restricted to loss functions within a fixed interval, e.g., [0,1].
• Unbounded loss functions are common in real-world machine learning problems, necessitating more flexible theoretical tools.

Purpose of the Study:

• To extend the PAC-Bayes learning framework to handle learning problems with unbounded loss functions.
• To introduce a novel theoretical approach that relaxes the assumption of bounded loss.
• To provide a practical and broadly applicable PAC-Bayesian generalization bound.

Main Methods:

• Development of a new PAC-Bayesian generalization bound tailored for unbounded loss functions.
• Introduction of the HYPothesis-dependent rangE (HYPE) concept to model predictor-dependent loss ranges.
• Instantiation of the derived bound on a linear regression problem.

Main Results:

• A novel PAC-Bayesian generalization bound for learning with unbounded loss functions is derived.
• The HYPE concept effectively captures the relaxation of the bounded loss assumption.
• The theoretical framework is demonstrated through an application to linear regression.

Conclusions:

• The proposed PAC-Bayesian generalization bounds significantly broaden the applicability of the PAC-Bayes framework.
• The HYPE concept offers a more realistic way to model loss functions in machine learning.
• The study provides practical insights into computation, practicality, and limitations for wider adoption.