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SIAM Chapter Seminar

Veeranjaneyulu Sadhanala
Carnegie Melllon University
Title: Trend filtering: Some recent advances and challenges

Abstract: Trend filtering is a recently developed tool Steidl et al. (2006), Kim et al. (2009) for nonparametric regression. Given n points, the trend filtering estimate is defined as the minimizer of a penalized least squares, where the penalty is the l1-norm of the kth order discrete derivatives over the input points. We will give an overview of some interesting connections between these estimates and adaptive spline estimation, and also of the provable statistical superiority of trend filtering to other common nonparametric regression tools, such as smoothing splines and kernel smoothing.

We will present extensions of this method to generalized linear models such as logistic and Poisson models and our approach to address the computational challenges using a proximal Newton method with a specialized ADMM algorithm. We will also present a generalization of trend filtering to nonparametric estimation over graphs. This approach is more locally adaptive compared to the standard methods such as wavelet smoothing and Laplacian smoothing.

Finally, we will discuss a mostly heuristic but empirically promising method for tuning parameter selection in trend filtering using recent advances in high-dimensional inference.

Date: Tuesday, March 3, 2015
Time: 5:30 pm
Location: Wean Hall 8220