Exploring the Learning Difficulty of Data Theory and Measure

TL;DR

This paper provides a rigorous theoretical foundation for understanding and measuring learning difficulty in machine learning, proposing a formal definition, properties, and a practical measure that outperforms existing heuristics.

Contribution

It introduces a formal theoretical definition of learning difficulty based on bias-variance trade-off, along with properties and a practical measure, filling a gap in existing heuristic approaches.

Findings

The proposed measure outperforms existing difficulty measures in experiments.

Classical weighting methods can be explained through the properties of the new difficulty measure.

Theoretical insights clarify the role of difficulty in weighting strategies.

Abstract

As learning difficulty is crucial for machine learning (e.g., difficulty-based weighting learning strategies), previous literature has proposed a number of learning difficulty measures. However, no comprehensive investigation for learning difficulty is available to date, resulting in that nearly all existing measures are heuristically defined without a rigorous theoretical foundation. In addition, there is no formal definition of easy and hard samples even though they are crucial in many studies. This study attempts to conduct a pilot theoretical study for learning difficulty of samples. First, a theoretical definition of learning difficulty is proposed on the basis of the bias-variance trade-off theory on generalization error. Theoretical definitions of easy and hard samples are established on the basis of the proposed definition. A practical measure of learning difficulty is given as well inspired by the formal definition. Second, the properties for learning difficulty-based weighting strategies are explored. Subsequently, several classical weighting methods in machine learning can be well explained on account of explored properties. Third, the proposed measure is evaluated to verify its reasonability and superiority in terms of several main difficulty factors. The comparison in these experiments indicates that the proposed measure significantly outperforms the other measures throughout the experiments.