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A Sharp Error Analysis for the Fused Lasso, with Application to Approximate Changepoint Screening
Kevin Lin · James Sharpnack · Alessandro Rinaldo · Ryan Tibshirani

Wed Dec 06 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #216 #None
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.

Author Information

Kevin Lin (Carnegie Mellon University)
James Sharpnack (UC Davis)
Alessandro Rinaldo (CMU)
Ryan Tibshirani (Carnegie Mellon University)

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