Duality, Geometry, and Support Vector Regression

Part of Advances in Neural Information Processing Systems 14 (NIPS 2001)

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J. Bi, Kristin Bennett


We develop an intuitive geometric framework for support vector regression (SVR). By examining when (cid:15)-tubes exist, we show that SVR can be regarded as a classi(cid:12)cation problem in the dual space. Hard and soft (cid:15)-tubes are constructed by separating the convex or reduced convex hulls respectively of the training data with the response variable shifted up and down by (cid:15). A novel SVR model is proposed based on choosing the max-margin plane between the two shifted datasets. Maximizing the margin corresponds to shrinking the e(cid:11)ective (cid:15)-tube. In the proposed approach the e(cid:11)ects of the choices of all parameters become clear geometrically.