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arXiv · 1901.00914

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

Teng Zhang
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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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Teng Zhang. 2019-01-03. Element-wise estimation error of a total variation regularized estimator for change point detection. https://arxiv.org/abs/1901.00914

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