Smooth ε-insensitive regression by loss symmetrization

Ofer Dekel*, Shai Shalev-Shwartz, Yoram Singer

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

7 Scopus citations


We describe a framework for solving regression problems by reduction to classification. Our reduction is based on symmetrization of margin-based loss functions commonly used in boosting algorithms, namely, the logistic loss and the exponential loss. Our construction yields a smooth version of the ε-insensitive hinge loss that is used in support vector regression. A byproduct of this construction is a new simple form of regularization for boosting-based classification and regression algorithms. We present two parametric families of batch learning algorithms for minimizing these losses. The first family employs a log-additive update and is based on recent boosting algorithms while the second family uses a new form of additive update. We also describe and analyze online gradient descent (GD) and exponentiated gradient (EG) algorithms for the ε-insensitive logistic loss. Our regression framework also has implications on classification algorithms, namely, a new additive batch algorithm for the log-loss and exp-loss used in boosting.

Original languageAmerican English
Pages (from-to)433-447
Number of pages15
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
StatePublished - 2003
Event16th Annual Conference on Learning Theory and 7th Kernel Workshop, COLT/Kernel 2003 - Washington, DC, United States
Duration: 24 Aug 200327 Aug 2003


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