一种计算效率高的非参数变点检测方法
A computationally efficient nonparametric approach for changepoint detection
摘要：
在本文中，我们基于Zou等人提出的方法。（2014）用于非参数变点检测。这种方法将数据集的最佳分割定义为使惩罚成本函数最小化的分割，其中成本函数根据每个段内的数据的非参数对数似然来定义。使用动态规划可以最小化这个成本函数，但是他们的算法的计算成本是数据集长度的立方。为了加快计算速度，Zou et al.（2014）采用了筛选过程，这意味着估计的分割不再保证是成本函数的全局最小值。我们表明，筛选过程对变点检测方法的准确性产生不利影响，并显示了一种更快的动态规划算法，修剪精确线性时间，PELT（Killick等人，2012），可以用于找到最佳分割，其计算成本在数据量上可以接近线性。PELT需要惩罚以避免模型拟合不足/过度，这可能对检测到的变化点的质量产生不利影响。为了克服这个问题，我们使用一种相对较新的方法，在惩罚范围内的变化点（CROPS）（Haynes等人，2015），其在连续范围内找到多个惩罚值的所有最优分割。我们应用我们的方法来检测身体活动期间心率的变化。
英文摘要：
In this paper we build on an approach proposed by Zou et al. (2014) for nonpara- metric changepoint detection. This approach defines the best segmentation for a data set as the one which minimises a penalised cost function, with the cost function defined in term of minus a non-parametric log-likelihood for data within each segment. Min- imising this cost function is possible using dynamic programming, but their algorithm had a computational cost that is cubic in the length of the data set. To speed up computation, Zou et al. (2014) resorted to a screening procedure which means that the estimated segmentation is no longer guaranteed to be the global minimum of the cost function. We show that the screening procedure adversely affects the accuracy of the changepoint detection method, and show how a faster dynamic programming algorithm, Pruned Exact Linear Time, PELT (Killick et al., 2012), can be used to find the optimal segmentation with a computational cost that can be close to linear in the amount of data. PELT requires a penalty to avoid under/over-fitting the model which can have a detrimental effect on the quality of the detected changepoints. To overcome this issue we use a relatively new method, Changepoints Over a Range of PenaltieS (CROPS) (Haynes et al., 2015), which finds all of the optimal segmentations for multiple penalty values over a continuous range. We apply our method to detect changes in heart rate during physical activity.
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