A Sharp Error Analysis For The Fused Lasso, With Application To Approximate Changepoint Screening
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 30 (NIPS 2017)(2017)
摘要
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 log log n. 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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