Learning the Intensity of Time Events With Change-Points

Alaya Mokhtar Z.; Gaiffas Stephane; Guilloux Agathe

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Learning the Intensity of Time Events With Change-Points

机译：通过变化点学习时间事件的强度

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摘要

We consider the problem of learning the inhomogeneous intensity of a counting process, under a sparse segmentation assumption. We introduce a weighted total-variation penalization, using data-driven weights that correctly scale the penalization along the observation interval. We prove that this leads to a sharp tuning of the convex relaxation of the segmentation prior, by stating oracle inequalities with fast rates of convergence, and consistency for change-points detection. This provides first theoretical guarantees for segmentation with a convex proxy beyond the standard independent identically distributed signal + white noise setting. We introduce a fast algorithm to solve this convex problem. Numerical experiments illustrate our approach on simulated and on a high-frequency genomics data set.

机译：我们考虑在稀疏分割假设下学习计数过程的不均匀强度的问题。我们使用数据驱动的权重引入加权的总变异惩罚，该权重可沿着观察间隔正确缩放惩罚。通过证明具有快速收敛速度和变化点检测一致性的预言不等式，我们证明了这导致了分割之前凸松弛的急剧调整。这为超出标准独立的均匀分布信号+白噪声设置的凸代理进行分割提供了理论上的第一保证。我们介绍了一种快速算法来解决该凸问题。数值实验说明了我们在模拟和高频基因组数据集上的方法。

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来源
《Information Theory, IEEE Transactions on》 |2015年第9期|5148-5171|共24页
作者
Alaya Mokhtar Z.; Gaiffas Stephane; Guilloux Agathe;
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作者单位

Sorbonne Universit??s, Universit?? Pierre et Marie Curie???Paris 6, Paris, France;

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原文格式 PDF
正文语种 eng
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关键词
Change-Points; Counting Processes; Counting processes; Total-Variation; change-points; oracle inequalities; total-variation;

机译：变更点;计数过程;计数过程;总变化;变更点;oracle不等式;总变化;

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7. Learning the intensity of time events with change-points [O] . Alaya, Mokhtar Zahdi, Gaïffas, Stéphane, Guilloux, Agathe 2015

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Learning the Intensity of Time Events With Change-Points

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