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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2019
- DOI:
- 10.48550/arXiv.1901.00914
- arXiv:
- arXiv:1901.00914
- Bibcode:
- 2019arXiv190100914Z
- Keywords:
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- Mathematics - Statistics Theory