A Fast Algorithm in Exponential Change-Points Model with Comparison

Abstract

The dynamic programming (DP) algorithm can be used to find an exact solution of the maximum likelihood estimation of change points in a sequence of data from exponential family. Since the algorithm has a quadratic complexity in data size n, it is computationally burdensome if the data size n is large. In this work, a fast two-stage (TS) algorithm by window method is proposed. The window method is simple and interesting. The first stage is to apply the window method based on the log likelihood ratio measure to find a subset of candidate change points, and use DP algorithm on the chosen subset to obtain good initial change points which will be proximate to the locations of the true change points. The second stage is to apply the segmental K-means (SKM) algorithm on the initial change points obtained in the first stage. Some simulated data sets are investigated for DP, SKM and TS three algorithms. We find that, in comparison of CPU times, the SKM algorithm is fastest than DP and TS algorithm with the largest error in the estimation of change points. For TS and DP algorithms, both yield the small errors, but in the speed of CPU times, our TS algorithm can be up to 18.94 times faster than the DP algorithm. The results show that our algorithm works very well. It substantially reduces the computation load for large data size n.