A Sharp Error Analysis for the Fused Lasso, with Application to Approximate Changepoint Screening
A Sharp Error Analysis for the Fused Lasso, with Application to Approximate Changepoint Screening
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发表时间：
2017
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通讯作者：
Kevin Lin;J. Sharpnack;A. Rinaldo;R. Tibshirani
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作者：
Kevin Lin;J. Sharpnack;A. Rinaldo;R. Tibshirani
在1维多变点检测问题中，我们推导出一个新的快速错误率的融合套索估计，假设平均向量有稀疏的变点。这个速率被认为是次优的（与极大极小化速率相比），只有$\log\log{n}$的因子。我们的证明技术是围绕着一个新的建设，我们称之为较低的插值。我们将我们的结果扩展到错误指定的模型和指数族分布。我们还描述了我们的误差分析的变化点的近似筛选的影响。
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.