Optimal Distance Function for Locally Weighted Average Prediction of Just‐in‐Time Methods

This paper discusses the optimal distance function for Just‐in‐Time prediction. We focus on the standard Locally Weighted Average (LWA) prediction with Mahalanobis distance, and find the optimal distance which minimizes the prediction error. The key idea of this work is to introduce an integral whic...

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Bibliographic Details
Published in:Asian journal of control 2018-11, Vol.20 (6), p.2055-2064
Main Authors: Fujimoto, Yusuke, Maruta, Ichiro, Sugie, Toshiharu
Format: Article
Language:English
Subjects:
Convexity
Integrals
Just‐in‐Time
lazy learning
Mathematical models
prediction
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Summary:This paper discusses the optimal distance function for Just‐in‐Time prediction. We focus on the standard Locally Weighted Average (LWA) prediction with Mahalanobis distance, and find the optimal distance which minimizes the prediction error. The key idea of this work is to introduce an integral which works as a model of the LWA prediction. This integral approximates the LWA prediction, and it becomes easier to discuss analytically. The main result of this paper is to show that the optimal distance function for such integral is constructed through a convex optimization. A numerical example and an experiment with a motor are shown to demonstrate the validity of the proposed distance function.
ISSN:1561-8625
1934-6093
DOI:10.1002/asjc.1698