论文标题
通过几何启发的映射检测高维更改点
High-Dimensional Changepoint Detection via a Geometrically Inspired Mapping
论文作者
论文摘要
高维更改点分析是一个不断增长的研究领域，并在广泛的领域中应用。目的是在时间序列和尺寸较大时准确有效地检测到时间序列数据中的变更点。现有方法通常汇总或将数据投影到较小数量的维度；通常一个。我们提出了一种高维更改点检测方法，该方法从几何形状到将高维时间序列映射到两个维度。我们从理论上和模拟中表明，如果输入系列是高斯，那么映射保留了数据的高斯性。将单变量更改点检测方法应用于两个映射系列，可以检测与原始时间序列的平均值和方差相对应的变更点。我们证明，就检测到的更改点和计算效率而言，这种方法的表现优于当前最新的多元变更点方法。我们以遗传和金融的应用结束。
High-dimensional changepoint analysis is a growing area of research and has applications in a wide range of fields. The aim is to accurately and efficiently detect changepoints in time series data when both the number of time points and dimensions grow large. Existing methods typically aggregate or project the data to a smaller number of dimensions; usually one. We present a high-dimensional changepoint detection method that takes inspiration from geometry to map a high-dimensional time series to two dimensions. We show theoretically and through simulation that if the input series is Gaussian then the mappings preserve the Gaussianity of the data. Applying univariate changepoint detection methods to both mapped series allows the detection of changepoints that correspond to changes in the mean and variance of the original time series. We demonstrate that this approach outperforms the current state-of-the-art multivariate changepoint methods in terms of accuracy of detected changepoints and computational efficiency. We conclude with applications from genetics and finance.
