Fused Lasso Additive Quantile Regression

Additive quantile regression provides a flexible and robust approach for modeling nonlinear relationships. The usual method of fitting an additive quantile model is to approximate the components with a spline function, this method requires an a priori selection of knots and is computationally slow which makes it unsuitable for training large-scale data problems. We propose an adaptive additive quantile estimator by using the fused Lasso penalty. Utilizing the sparsity of the discrete first derivative matrix in the fused Lasso penalty enables fast computation of the model, adaptive selection of knots and prediction of desired quartiles or even extreme quartiles. Furthermore, we develop an algorithm that guarantees convergence to the global optimum. The experimental results show that the proposed model has significant advantages over other models.