Learning Theory Approach to Minimum Error Entropy Criterion
This work addresses theoretical foundations for a specific machine learning criterion, which is incremental as it builds on existing MEE methods.
The paper tackles the theoretical analysis of the minimum error entropy (MEE) criterion in regression by providing explicit error bounds and asymptotic analysis for generalization error, overcoming technical challenges compared to classical least squares.
We consider the minimum error entropy (MEE) criterion and an empirical risk minimization learning algorithm in a regression setting. A learning theory approach is presented for this MEE algorithm and explicit error bounds are provided in terms of the approximation ability and capacity of the involved hypothesis space when the MEE scaling parameter is large. Novel asymptotic analysis is conducted for the generalization error associated with Renyi's entropy and a Parzen window function, to overcome technical difficulties arisen from the essential differences between the classical least squares problems and the MEE setting. A semi-norm and the involved symmetrized least squares error are introduced, which is related to some ranking algorithms.