Element-wise estimation error of a total variation regularized estimator for change point detection

Abstract

This work studies the total variation regularized ${\ell }_2$ estimator (fused lasso) in the setting of a change point detection problem. Compared with existing works that focus on the sum of squared estimation errors, we give bound on the element-wise estimation error. Our bound is nearly optimal in the sense that the sum of squared error matches the best existing result, up to a logarithmic factor. This analysis of the element-wise estimation error allows a screening method that can approximately detect all the change points. We also generalize this method to the muitivariate setting, i.e., to the problem of group fused lasso.

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Cited by in corpus (3)

• A review on minimax rates in change point detection and localisation
• Multivariate extensions of isotonic regression and total variation denoising via entire monotonicity and Hardy-Krause variation
• Denoising and change point localisation in piecewise-constant high-dimensional regression coefficients