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Title: A Sharp Error Analysis for the Fused Lasso, with Application to Approximate Changepoint Screening
In the 1-dimensional multiple changepoint detection problem, we derive a new fast error rate for the fused lasso estimator, under the assumption that the mean vector has a sparse number of changepoints. This rate is seen to be suboptimal (compared to the minimax rate) by only a factor of loglogn. Our proof technique is centered around a novel construction that we call a lower interpolant. We extend our results to misspecified models and exponential family distributions. We also describe the implications of our error analysis for the approximate screening of changepoints.
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Award ID(s):
Publication Date:
Journal Name:
Advances in neural information processing systems
Page Range or eLocation-ID:
6884 - 6893
Sponsoring Org:
National Science Foundation
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