XGBoost is often presented as the algorithm that wins every ML competition. Surprisingly, this is true even though predictions are piecewise constant. This might be justified in high dimensional input spaces, but when the number of features is low, a piecewise linear model is likely to perform better. XGBoost was extended into LinXGBoost that stores at each leaf a linear model. This extension, ...

A nonparametric regression method that blends key features of piecewise polynomial quantile regression and tree-structured regression based on adaptive recursive partitioning of the covariate space is investigated. Unlike least squares regression trees, which concentrate on modeling the relationship between the response and the covariates at the center of the response distribution, our quantile...

‎‎In this article‎, ‎a new method is introduced to give approximate solution to Van der Pol equation‎. ‎The proposed method is based on the combination of two different methods‎, ‎the spectral Adomian decomposition method (SADM) and piecewise method‎, ‎called the piecewise Adomian decomposition method (PSADM)‎. ‎The numerical results obtained from the proposed method show that this method is an...

We introduce herein a new class of autoregressive models in which the regression parameters and error variances may undergo changes at unknown time points while staying constant between adjacent change-points. Assuming conjugate priors, we derive closed-form recursive Bayes estimates of the regression parameters and error variances. Approximations to the Bayes estimates are developed that have ...

We consider nonparametric estimation of a one-dimensional piecewise-smooth function observed with white Gaussian noise on an interval. We propose a two-step estimation procedure, where one first detects jump points by a wavelet-based procedure and then estimates the function on each smooth segment separately by bridge regression splines. We prove the asymptotic optimality (in the minimax sense)...