# Linear dependency between epsilon and the input noise in epsilon-support vector regression

### James T. Kwok, Ivor W. Tsang

**Abstract:**
In using the epsilon-support vector regression (epsilon-SVR) algorithm, one
has to
decide a suitable value for the insensitivity parameter epsilon.
Smola et al. considered its ``optimal'' choice by studying
the statistical efficiency in a location parameter estimation problem.
While they successfully predicted a linear scaling
between the optimal
epsilon and the noise in the data,
their theoretically optimal value
does not have a close match with its experimentally observed
counterpart in the case of Gaussian noise.
In this paper, we attempt to better explain their experimental results by
studying the regression problem itself.
Our resultant predicted choice of epsilon is much closer to the
experimentally observed optimal value, while again demonstrating
a linear trend with the input noise.
*IEEE Transactions on Neural Networks*, 14(3):544-553, May 2003.

Postscript:
http://www.cs.ust.hk/~jamesk/papers/tnn03.ps.gz

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