A Kernel Multiple Change-point Algorithm via Model Selection
A Kernel Multiple Change-point Algorithm via Model Selection
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发表时间：
2012-02
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通讯作者：
Sylvain Arlot;Alain Celisse;Zaïd Harchaoui
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作者：
Sylvain Arlot;Alain Celisse;Zaïd Harchaoui
我们通过属于一般集合的数据解决了变更点问题。我们为选择基于内核的Harchaoui和Capp {\'E}（2007）的变更点的数量而建立了惩罚。这项惩罚概括了Lebarbier（2005）提出的一维信号的惩罚。由于希尔伯特空间有价值的随机变量的某些功能，我们证明了该方法的非反应性甲骨文不等式。关于合成数据的实验说明了我们方法的准确性，表明即使均值和方差是恒定的，它也可以检测数据的整体分布的变化。
We tackle the change-point problem with data belonging to a general set. We build a penalty for choosing the number of change-points in the kernel-based method of Harchaoui and Capp{\'e} (2007). This penalty generalizes the one proposed by Lebarbier (2005) for one-dimensional signals. We prove a non-asymptotic oracle inequality for the proposed method, thanks to a new concentration result for some function of Hilbert-space valued random variables. Experiments on synthetic data illustrate the accuracy of our method, showing that it can detect changes in the whole distribution of data, even when the mean and variance are constant.