Statistical Mechanics of Online Learning of Drifting Concepts : A Variational Approach

TL;DR

This paper applies statistical mechanics to analyze online learning of drifting concepts, deriving optimal generalization bounds and proposing adaptive algorithms based on variational methods for large systems.

Contribution

It introduces a variational approach to exactly determine the best generalization ability and develops adaptive algorithms for learning drifting concepts.

Findings

Exact determination of optimal generalization performance

Development of an effective adaptive learning algorithm

Comparison of algorithms for different concept drift scenarios

Abstract

We review the application of Statistical Mechanics methods to the study of online learning of a drifting concept in the limit of large systems. The model where a feed-forward network learns from examples generated by a time dependent teacher of the same architecture is analyzed. The best possible generalization ability is determined exactly, through the use of a variational method. The constructive variational method also suggests a learning algorithm. It depends, however, on some unavailable quantities, such as the present performance of the student. The construction of estimators for these quantities permits the implementation of a very effective, highly adaptive algorithm. Several other algorithms are also studied for comparison with the optimal bound and the adaptive algorithm, for different types of time evolution of the rule.