Statistical Mechanics of On-Line Learning Under Concept Drift

Abstract

We introduce a modelling framework for the investigation of on-line machine learning processes in non-stationary environments. We exemplify the approach in terms of two specific model situations: In the first, we consider the learning of a classification scheme from clustered data by means of prototype-based Learning Vector Quantization (LVQ). In the second, we study the training of layered neural networks with sigmoidal activations for the purpose of regression. In both cases, the target, i.e. the classification or regression scheme, is considered to change continuously while the system is trained from a stream of labeled data. We extend and apply methods borrowed from statistical physics which have been used frequently for the exact description of training dynamics in stationary environments. Extensions of the approach allow for the computation of typical learning curves in the presence of concept drift in a variety of model situations. First results are presented and discussed for stochastic drift processes in classification and regression problems. They indicate that LVQ is capable of tracking a classification scheme under drift to a non-trivial extent. Furthermore, we show that concept drift can cause the persistence of sub-optimal plateau states in gradient based training of layered neural networks for regression.

Data-dependence of plateau phenomenon in learning with neural network—statistical mechanical analysis *

“…They derived the macroscopic behavior of learning dynamics in two-layered soft-committee machine and by analyzing it they pointed out the existence of plateau phenomenon. Nowadays, the statistical mechanical method is applied to analyze recent techniques (Hara et al 2016, Yoshida et al 2017, Takagi et al 2019and Straat and Biehl 2019, and generalization performance in over-parameterized setting (Goldt et al 2019) and environment with conceptual drift (Straat et al 2018). However, it is unknown how the property of input dataset itself can affect the learning dynamics, including plateaus.…”