Interval regression analysis using support vector networks

Support vector machines (SVMs) have been very successful in pattern classification and function estimation problems for crisp data. In this paper, the v-support vector interval regression network (v-SVIRN) is proposed to evaluate interval linear and nonlinear regression models for crisp input and output data. As it is difficult to select an appropriate value of the insensitive tube width in epsilon-support vector regression network, the proposed v-SVIRN alleviates this problem by utilizing a new parametric-insensitive loss function. The proposed v-SVIRN automatically adjusts a flexible parametric-insensitive zone of arbitrary shape and minimal size to include the given data. Besides, the proposed method can achieve automatic accuracy control in the interval regression analysis task. For a priori chosen v, at most a fraction v of the data points lie outside the interval model constructed by the proposed v-SVIRN. To be more precise, v is an upper bound on the fraction of training errors and a lower bound on the fraction of support vectors. Hence, the selection of v is more intuitive. Moreover, the proposed algorithm here is a model-free method in the sense that we do not have to assume the underlying model function. Experimental results are then presented which show the proposed v-SVIRN is useful in practice, especially when the noise is heteroscedastic, that is, the noise strongly depends on the input value x. (c) 2008 Elsevier B.V. All rights reserved.