Convex Calibrated Surrogates for the Multi-Label F-Measure

Area of Science:

• Machine Learning
• Computer Science
• Data Science

Background:

• The F-measure is crucial for multi-label classification, balancing precision and recall.
• Directly optimizing the F-measure is computationally challenging due to its discrete nature.

Purpose of the Study:

• To design convex surrogate losses calibrated for the F-measure.
• To enable the optimization of F-measure in multi-label classification problems.

Main Methods:

• Deriving a rank bound for the F-measure loss matrix.
• Applying existing results to construct a family of convex calibrated surrogates.
• Decomposing the multi-label F-measure problem into binary classification tasks.

Main Results:

• A family of convex calibrated surrogates for the F-measure was designed.
• The learning problem is decomposed into s^2 + 1 binary probability estimation problems.
• A regret transfer bound was established, connecting binary and multi-label guarantees.

Conclusions:

• The proposed convex surrogates offer a computationally tractable approach to optimizing the F-measure.
• The decomposition strategy simplifies complex multi-label F-measure learning.
• Theoretical findings are supported by experimental validation.