A computationally efficient nonparametric approach for changepoint detection

Statistics and Computing

Volumn 27, Issue 5, 2017, Pages 1293-1305

  Haynes, Kaylea ^a   Fearnhead, Paul ^b   Eckley, Idris A ^b  

^a LANCASTER UNIVERSITY   (United Kingdom)

^b LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Activity tracking; CROPS; Nonparametric maximum likelihood; PELT

Indexed keywords

EID: 84979966334     PISSN: 09603174     EISSN: 15731375     Source Type: Journal    
DOI: 10.1007/s11222-016-9687-5     Document Type: Article

References (42)

1. Aubert, A.E., Seps, B., Beckers, F.: Heart rate variability in athletes. Sports Med. 33(12), 889–919 (2003)
2. Aue, A., Horvth, L.: Structural breaks in time series. J. Time Ser. Anal. 34(1), 1–16 (2013)
3. Auger, I.E., Lawrence, C.E.: Algorithms for the optimal identification of segment neighborhoods. Bull. Math. Biol. 51(1), 39–54 (1989)
4. Bai, J., Perron, P.: Estimating and testing linear models with multiple structural changes. Econometrica 66(1), 47–78 (1998)
5. Baron, M.: Nonparametric adaptive change-point estimation and on-line detection. Sequ. Anal. 19, 1–23 (2000)
6. Bhattacharyya, G., Johnson, R.: Nonparametric tests for shift at an unknown time point. Ann. Math. Stat. 39(5), 1731–1743 (1968)
7. Billat, V.L., Mille-Hamard, L., Meyer, Y., Wesfreid, E.: Detection of changes in the fractal scaling of heart rate and speed in a marathon race. Physica A 388(18), 3798–3808 (2009)
8. Boysen, L., Kempe, A., Liebscher, V., Munk, A., Wittich, O.: Consistencies and rates of convergence of jump-penalized least squares estimators. Ann. Stat. 37(1), 157–183 (2009)
9. BrainMacSportsCoach: Heart rate training zones. http://www.brianmac.co.uk/hrm1.htm (2015)
10. Carlstein, E.: Nonparametric change-point estimation. Ann. Stat. 16(1), 188–197 (1988)
11. Davis, R.A., Lee, T.C.M., Rodriguez-Yam, G.A.: Structural break estimation for nonstationary time series models. J. Am. Stat. Assoc. 101(473), 223–239 (2006)
12. Dette, H., Wied, D.: Detecting relevant changes in time series models. J. R. Stat. Soc. Ser. B 78(2), 371–394 (2015)
13. Dumbgen, L.: The asymptotic behavior of some nonparametric change-point estimators. Ann. Stat. 19(3), 1471–1495 (1991)
14. Frick, K., Munk, A., Sieling, H.: Multiscale change-point inference. J. R. Stat. Soc. Ser. B. Methodol. with discussion and rejoinder by the authors 76, 495–580 (2014)
15. Fryzlewicz, P.: Wild binary segmentation for multiple change-point detection. Ann. Stat. 42(6), 2243–2281 (2014)
16. Galway, L., Zhang, S., Nugent, C., McClean, S., Finlay, D., Scotney, B.: Utilizing wearable sensors to investigate the impact of everyday activities on heart rate. In: Abdulrazak, B., Giroux, S., Bouchard, B., Pigot, H., Mokhtari, M. (eds.) Toward Useful Services for Elderly and People with Disabilities. Lecture Notes in Computer Science, vol. 6719, pp. 184–191. Berlin Heidelberg, Springer (2011)
17. Guarnaccia, C., Quartieri, J., Tepedino, C., Rodrigues, E.R.: An analysis of airport noise data using a non-homogeneous Poisson model with a change-point. Appl. Acoust. 91, 33–39 (2015)
18. Haynes, K.: changepoint.np: Methods for Nonparametric Changepoint Detection. R package version 0.0.2
19. Haynes, K., Eckley, I. A., and Fearnhead, P.: Computationally effieicnet changepoint detection for a range of penalties. J. Comput. Graph. Stat. (to appear) (2016)
20. Hocking, T., Rigaill, G., Vert, J.P., Bach, F.: Learning sparse penalties for change-point detection using max margin interval regression. In: ICML (3), vol. 28 of JMLR Proceedings, pp. 172–180 (2013)
21. Jackson, B., Sargle, J., Barnes, D., Arabhi, S., Alt, A., Gioumousis, P., Gwin, E., Sangtrakulcharoen, P., Tan, L., Tsai, T.: An algorithm for optimal partitioning of data on an interval. IEEE Signal Process. Lett. 12(2), 105–108 (2005)
22. James, N.A., Matteson, D.S.: Change points via probabilistically pruned objectives (2015). arXiv:1505.04302
23. Jandhyala, V., Fotopoulos, S., MacNeill, I., Liu, P.: Inference for single and multiple change-points in time series. J. Time Ser. Anal. 15, 453–472 (2013)
24. Khalfa, N., Bertandm, P.R., Boudet, G., Chamoux, A., Billat, V.: Heart rate regulation processed through wavelet analysis and change detection: some case studies. Acta. Biotheor. 60, 109–129 (2012)
25. Killick, R., Fearnhead, P., Eckley, I.A.: Optimal detection of changepoints with a linear computational cost. J. Am. Stat. Assoc. 107(500), 1590–1598 (2012)
26. Lavielle, M.: Using penalized contrasts for the change-point problem. Signal Process. 85(8), 1501–1510 (2005)
27. Lee, C.-B.: Nonparametric multiple change-point estimators. Stat. Probab. Lett. 27(4), 295–304 (1996)
28. Lu, L., Zhang, H.J.: Speaker change detection and tracking in real-time news broadcasting analysis. In: Proceedings of the Tenth ACM International Conference on Multimedia, pp. 602–610 (2002)
29. Matteson, D.S., James, N.A.: A nonparametric approach for multiple change point analysis of multivariate data. J. Am. Stat. Assoc. 109(505), 334–345 (2014)
30. Nam, C.F.H., Aston, J.A.D., Eckley, I.A., Killick, R.: The uncertainty of storm season changes: quantifying the uncertainty of autocovariance changepoints. Technometrics 57(2), 194–206 (2014)
31. Olshen, A.B., Venkatraman, E.S., Lucito, R., Wigler, M.: Circular binary segmentation for the analysis of array-based dna copy number data. Biostatistics 5(4), 557–572 (2004)
32. Page, E.: Continuous inspection schemes. Biometrika 41(1), 100–115 (1954)
33. Pettitt, A.: A non-parametric approach to the change-point problem. Appl. Stat. 28(2), 126–135 (1979)
34. Ross, G., Adams, N.M.: Two nonparametric control charts for detecting arbitrary distribution changes. J. Qual. Technol. 44(2), 102–116 (2012)
35. Schwarz, G.: Estimating the dimension of a model. Ann. Stat. 6(2), 461–464 (1978)
36. Scott, A.J., Knott, M.: A cluster analysis method for grouping means in the analysis of variance. Biometrics 30(3), 507–512 (1974)
37. Staudacher, M., Telser, S., Amann, A., Hinterhuber, H., Ritsch-Marte, M.: A new method for change-point detection developed for on-line analysis of the heart beat variability during sleep. Physica A 349(3), 582–596 (2005)
38. Yao, Y.-C.: Estimating the number of change-points via Schwarz’ criterion. Stat. Probab. Lett. 6(3), 181–189 (1988)
39. Zhang, J.: Powerful goodness-of-fit tests based on the likelihood ratio. J. R. Stat. Soc. Ser. B 64(2), 281–294 (2002)
40. Zhang, N.R., Siegmund, D.O.: A modified Bayes information criterion with applications to the analysis of comparative genomic hybridization data. Biometrics 63(1), 22–32 (2007)
41. Zou, C., Yin, G., Feng, L., Wang, Z.: Nonparametric maximum likelihood approach to multiple change-point problems. Ann. Stat. 42(3), 970–1002 (2014)
42. Zou, C., Zhange, L.: nmcdr: Non-parametric Multiple Change-Points Detection. R package version 0.3.0 (2014)