A1760
Title: Online TV regression with dependent noise
Authors: Fabian Mies - Delft University of Technology (Netherlands) [presenting]
Ivan Krylov - Delft University of Technology (Netherlands)
Abstract: Via nonlinear regression procedures, signals of bounded variation can be recovered from noisy observations at the same asymptotic rate $n^{1/3}$, which is identical to the rate for Lipschitz signals, while allowing for spatially inhomogeneous smoothness. The problem is considered in a sequential setting and in the presence of temporally dependent error terms. Adaptivity is achieved by leveraging an online learning algorithm to choose the optimal restart times for running averages. The method achieves the optimal rate of convergence, up to log factors, for the online nonparametric regression problem with martingale difference errors, and the procedure is shown to be robust against small deviations from the martingale assumptions. To handle stronger autocorrelations, a thinning procedure is devised and shown to recover the optimal rate of convergence for signal denoising under total variation constraints.
