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Paper details
Number 3 - September 2018
Volume 28 - 2018
Regression function and noise variance tracking methods for data streams with concept drift
Maciej Jaworski
Abstract
Two types of heuristic estimators based on Parzen kernels are presented. They are able to estimate the regression function
in an incremental manner. The estimators apply two techniques commonly used in concept-drifting data streams, i.e., the
forgetting factor and the sliding window. The methods are applicable for models in which both the function and the noise
variance change over time. Although nonparametric methods based on Parzen kernels were previously successfully applied
in the literature to online regression function estimation, the problem of estimating the variance of noise was generally
neglected. It is sometimes of profound interest to know the variance of the signal considered, e.g., in economics, but it can
also be used for determining confidence intervals in the estimation of the regression function, as well as while evaluating the
goodness of fit and in controlling the amount of smoothing. The present paper addresses this issue. Specifically, variance
estimators are proposed which are able to deal with concept drifting data by applying a sliding window and a forgetting
factor, respectively. A number of conducted numerical experiments proved that the proposed methods perform satisfactorily
well in estimating both the regression function and the variance of the noise.
Keywords
data streams, concept drift, Parzen kernels, regression, variance estimation