Optimal Detection of Changepoints With a Linear Computational Cost
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具有线性计算成本的最优变点检测
- 研究问题
- 当数据量与变点数量同时增长时，如何通过最小化分段成本，确定多个变点的数量与位置，并控制计算负担？
- 方法与思路
- 作者提出求解分段成本全局最小值的新方法，涵盖惩罚似然与最小描述长度，并称在温和条件下计算成本随观测数线性增长。
- 材料陈述的贡献
- 摘要称该方法在模拟中比其他精确算法快数个数量级；与二分分割相比，精确求解可明显改善所推断分段的准确性。
- 阅读关注点
- 应核对线性计算成本成立的具体条件、允许的成本函数与惩罚形式，以及模拟如何设置变点增长和分段准确性指标。
- 阅读边界
- 仅据未注明稿件版本的OpenAlex索引摘要；复杂度条件未说明，成本最优也不能直接解释为统计风险最优。
原文摘要
In this article, we consider the problem of detecting multiple changepoints in large datasets. Our focus is on applications where the number of changepoints will increase as we collect more data: for example, in genetics as we analyze larger regions of the genome, or in finance as we observe time series over longer periods. We consider the common approach of detecting changepoints through minimizing a cost function over possible numbers and locations of changepoints. This includes several established procedures for detecting changing points, such as penalized likelihood and minimum description length. We introduce a new method for finding the minimum of such cost functions and hence the optimal number and location of changepoints that has a computational cost, which, under mild conditions, is linear in the number of observations. This compares favorably with existing methods for the same problem whose computational cost can be quadratic or even cubic. In simulation studies, we show that our new method can be orders of magnitude faster than these alternative exact methods. We also compare with the binary segmentation algorithm for identifying changepoints, showing that the exactness of our approach can lead to substantial improvements in the accuracy of the inferred segmentation of the data. This article has supplementary materials available online.