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 ε-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.