Robust support vector quantile regression with truncated pinball loss (RSVQR)

Support vector quantile regression (SVQR) adapts the flexible pinball loss function for empirical risk in regression problems. Furthermore, $$\varepsilon -$$ SVQR obtains sparsity by introducing the $$\varepsilon -$$ insensitive approach to SVQR. Despite their excellent generalisation performance, the employed loss functions of SVQR and $$\varepsilon -$$ SVQR still possess noise and outlier sensitivity. This paper suggests a new robust SVQR model called a robust support vector quantile regression with truncated pinball loss (RSVQR). RSVQR employs a truncated pinball loss function for reducing the impact of noise. The employed loss function takes a non-convex structure which might lead to a local optimum solution. Further, to solve the non-convex optimization problem formulated using the employed non-convex loss function, we apply the concave–convex procedure (CCCP) to the cost function of the proposed method which decomposes the total loss into one convex and one concave part. Few interesting artificial and real-world datasets are considered for the experimental analysis. Support vector regression (SVR), Huber loss-based SVR (HSVR), asymmetric HSVR (AHSVR), SVQR and $$\varepsilon -$$ SVQR are used to compare the results of the suggested model. The obtained results reveal the applicability of the proposed RSVQR model.