论文标题
可扩展的贝叶斯多变更点通过辅助统一检测
Scalable Bayesian Multiple Changepoint Detection via Auxiliary Uniformization
论文作者
论文摘要
通过将辅助事件时间连接到按时间顺序排序的观测值中，我们将离散时间观察值的贝叶斯多个变更点问题提出到连续时间的观察值。提出了一种前向过滤向后采样（FFBS）算法的版本，以模拟倒塌的Gibbs采样方案中的变更点。理想情况下，FFBS算法的计算成本和记忆成本都可以二次缩放到更改点的数量，而不是观察值的数量，这对于长长的观察序列而言，这否则是令人难以置信的。新公式允许更改点的数量在新数据的到达中不受限制地产生。同样，假定各个段的随时间变化点的复发率可以表征变化点的运行长度的不同尺度。然后，我们建议一种连续的viterbi算法，用于获得更改点的最大后验（MAP）估计值。我们通过模拟研究和实际数据分析来证明方法。
By attaching auxiliary event times to the chronologically ordered observations, we formulate the Bayesian multiple changepoint problem of discrete-time observations into that of continuous-time ones. A version of forward-filtering backward-sampling (FFBS) algorithm is proposed for the simulation of changepoints within a collapsed Gibbs sampling scheme. Ideally, both the computational cost and memory cost of the FFBS algorithm can be quadratically scaled down to the number of changepoints, instead of the number of observations, which is otherwise prohibitive for a long sequence of observations. The new formulation allows the number of changepoints accrue unboundedly upon the arrivals of new data. Also, a time-varying changepoint recurrence rate across different segments is assumed to characterize diverse scales of run lengths of changepoints. We then suggest a continuous-time Viterbi algorithm for obtaining the Maximum A Posteriori (MAP) estimates of changepoints. We demonstrate the methods through simulation studies and real data analysis.
