<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

Regression Function and Noise Variance Tracking Methods for Data Streams with Concept Drift

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Two types of heuristic estimators based on Parzen kernels are presented. They are able to estimate the regression function in an incremental manner. The...

Regression Function and Noise Variance Tracking Methods for Data Streams with Concept Drift

Published Online: Oct 03, 2018

Page range: 559 - 567

Received: Feb 16, 2018

Accepted: May 04, 2018

DOI: https://doi.org/10.2478/amcs-2018-0043

Keywords
data streams, concept drift, Parzen kernels, regression, variance estimation

© 2018 Maciej Jaworski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Regression Function and Noise Variance Tracking Methods for Data Streams with Concept Drift

Published Online: Oct 03, 2018

Page range: 559 - 567

Received: Feb 16, 2018

Accepted: May 04, 2018

DOI: https://doi.org/10.2478/amcs-2018-0043

Keywordsdata streams, concept drift, Parzen kernels, regression, variance estimation

© 2018 Maciej Jaworski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
data streams, concept drift, Parzen kernels, regression, variance estimation