Abstract
We propose a novel approach for estimating the location of block boundaries (change-points) in a random matrix consisting of a block wise constant matrix observed in white noise. Our method consists in rephrasing this task as a variable selection issue. We use a penalized least-squares criterion with an \(\ell _1\)-type penalty for dealing with this problem. We first provide some theoretical results ensuring the consistency of our change-point estimators. Then, we explain how to implement our method in a very efficient way. Finally, we provide some empirical evidence to support our claims and apply our approach to data coming from molecular biology which can be used for better understanding the structure of the chromatin.
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Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C.J.: Classification and Regression Trees. Statistics/Probability Series. Wadsworth Publishing Company, Belmont (1984)
Brodsky, B., Darkhovsky, B.: Non-parametric statistical diagnosis: problems and methods. Kluwer Academic Publishers (2000)
Dixon, J.R., Selvaraj, S., Yue, F., Kim, A., Li, Y., Shen, Y., Hu, M., Liu, J.S., Ren, B.: Topological domains in mammalian genomes identified by analysis of chromatin interactions. Nature 485(7398), 376–380 (2012)
Efron, B., Hastie, T., Johnstone, I., Tibshirani, R., et al.: Least angle regression. The Annals of statistics 32(2), 407–499 (2004)
Harchaoui, Z., Lévy-Leduc, C.: Multiple change-point estimation with a total variation penalty. Journal of the American Statistical Association 105(492), 1480–1493 (2010)
Hoefling, H.: A path algorithm for the fused lasso signal approximator. J. Comput. Graph. Statist. 19(4), 984–1006 (2010)
Kay, S.: Fundamentals of statistical signal processing: detection theory. Prentice-Hall, Inc. (1993)
Lévy-Leduc, C., Delattre, M., Mary-Huard, T., Robin, S.: Two-dimensional segmentation for analyzing hi-c data. Bioinformatics 30(17), i386–i392 (2014)
Meinshausen, N., Bühlmann, P.: Stability selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72(4), 417–473 (2010)
Osborne, M.R., Presnell, B., Turlach, B.A.: A new approach to variable selection in least squares problems. IMA Journal of Numerical Analysis 20(3), 389–403 (2000)
R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2015). http://www.R-project.org/
Sanderson, C.: Armadillo: An open source C++ linear algebra library for fast prototyping and computationally intensive experiments. Tech. rep, NICTA (2010)
Tartakovsky, A., Nikiforov, I., Basseville, M.: Sequential Analysis: Hypothesis Testing and Changepoint Detection. CRC Press, Taylor & Francis Group (2014)
Tibshirani, R.J., Taylor, J.: The solution path of the generalized lasso. Ann. Statist. 39(3), 1335–1371 (2011)
Vert, J.P., Bleakley, K.: Fast detection of multiple change-points shared by many signals using group lars. In: Advances in Neural Information Processing Systems, pp. 2343–2351 (2010)
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Brault, V., Chiquet, J., Lévy-Leduc, C. (2016). Fast Detection of Block Boundaries in Block-Wise Constant Matrices. In: Perner, P. (eds) Machine Learning and Data Mining in Pattern Recognition. MLDM 2016. Lecture Notes in Computer Science(), vol 9729. Springer, Cham. https://doi.org/10.1007/978-3-319-41920-6_16
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DOI: https://doi.org/10.1007/978-3-319-41920-6_16
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