Title: Trend filtering on regular lattices with sub-exponential noise
Authors: Veeranjaneyulu Sadhanala - University of Chicago (United States) [presenting]
Daniel McDonald - University of British Columbia (Canada)
Robert Bassett - Naval Postgraduate School (United States)
James Sharpnack - University of California Davis (United States)
Abstract: Trend filtering is a locally adaptive nonparametric regression method that fits a piecewise polynomial to univariate data with automatically chosen knots. The statistical performance of trend filtering and its extensions to regular lattices was analyzed recently, assuming that the observations are corrupted by sub-gaussian noise. We study this problem with sub-exponential noise. We derive minimax optimal error bounds on mean which are same as in the sub-gaussian case but with an additional logarithmic factor. We also argue why it is hard to upper bound the KL divergence, which is a more natural quantity to bound in the exponential family setting.