Generalized \(\varepsilon \)—Loss Function-Based Regression

  • Pritam AnandEmail author
  • Reshma Rastogi (nee Khemchandani)
  • Suresh Chandra
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 748)


In this paper, we propose a new loss function termed as “generalized \(\varepsilon \)—loss function” to study the regression problem. Unlike the standard \(\varepsilon \)—insensitive loss function, the generalized \(\varepsilon \)—loss function penalizes even those data points which lie inside of the \(\varepsilon \)—tube so as to minimize the scatter within the tube. Also, the rate of penalization of data points lying outside of the \(\varepsilon \)—tube is much higher in comparison to the data points which lie inside of the \(\varepsilon \)—tube. Based on the proposed generalized \(\varepsilon \)—loss function, a new support vector regression model is formulated which is termed as “Penalizing \(\varepsilon \)—generalized SVR (Pen-\(\varepsilon \)—SVR).” Further, extensive numerical experiments are carried out to check the validity and efficacy of the proposed Pen-\(\varepsilon \)—SVR.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Pritam Anand
    • 1
    Email author
  • Reshma Rastogi (nee Khemchandani)
    • 1
  • Suresh Chandra
    • 2
  1. 1.Faculty of Mathematics and Computer ScienceSouth Asian UniversityNew DelhiIndia
  2. 2.Department of MathematicsIndian Institute of Technology DelhiNew DelhiIndia

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