This paper presents a fast and robust algorithm for trend filtering, a recently developed nonparametric regression tool. It has been shown that, for estimating functions whose derivatives are of bounded variation, trend filtering achieves the minimax optimal error rate, while other popular methods like smoothing splines and kernels do not. Standing in the way of a more widespread practical adop...

Given the concept of reliability-based design (RBD) and the growing risk management trend in geotechnical engineering, proper understanding and quantification of uncertainties are very important. The complexity of methods and a large volume of calculations of probabilistic design methods are the most critical reasons for civil engineers not to be comfortable using these approaches. In this rese...

In this study, the spatial and temporal variability of water quality including monthly series of TDS, EC, So4, Cl, Ca and Na in common statistical period 1993-2014 was evaluated for the Karun River. This assessment is based on qualitative data stations including Susan in the upstream of Gotvand reservoir, Gotvand, Mollasani and Ahvaz in the downstream. To determine the parameters trend process,...

We study trend filtering, a recently proposed tool of Kim et al. (2009) for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the penalty term sums the absolute kth order discrete derivatives over the input points. Perhaps not surprisingly, trend filtering estimates appear to have the structure of kth degree splin...