A Novel Method of Identifying Optimal Interval Regression Model Using Structural Risk Minimization and Approximation Error Minimization

Uncertain measurements derived from many practical applications tend to be constructed as interval regression model (IRM), consisted of upper regression model (URM) and lower regression model (LRM). Motivated by interval regression analysis, a novel method of identifying IRM is proposed in this paper by combining the principle of structural risk minimization with approximation error minimization. Taken the superiorities of model sparse representation and computational efficiency of linear programming support vector regression (LP-SVR) and some ideas from ℓ 1 -norm minimization on approximation error into consideration, the proposed method not only possesses the characteristics of adjusting a flexible interval spread, but also independently constructs URM and LRM, instead of adopting the traditional estimated center model and estimated radius of IRM which is the incapability of dealing with asymmetrical interval. More importantly, model complexity for IRM is under control by our approach. First, ℓ 1 -norms minimization on approximation error for URM and LRM are constructed, and the both optimization problems subject to respective constraints are integrated into LP-SVR to form new upper and lower optimization problems, respectively. Following that, optimization problems corresponding to URM and LRM are solved by linear programming and IRM is thus constructed. Finally, several simulations are provided to show the validity and applicability of the proposed method.