Detekce bodů změn v tenzorových datech

• Název práce v češtině: Detekce bodů změn v tenzorových datech
• Název v anglickém jazyce: Changepoint detection in tensor data
• Klíčová slova: bod změny|tenzor|tenzorová data|panelová data|bootstrap|testování hypotéz
• Klíčová slova anglicky: changepoint|tensor|tensor data|panel data|bootstrap|hypothesis testing
• Akademický rok vypsání: 2024/2025
• Typ práce: diplomová práce
• Jazyk práce: čeština
• Ústav: Katedra pravděpodobnosti a matematické statistiky (32-KPMS)
• Vedoucí / školitel: doc. RNDr. Michal Pešta, Ph.D.
• Řešitel: skrytý - zadáno a potvrzeno stud. odd.
• Datum přihlášení: 05.10.2024
• Datum zadání: 06.11.2024
• Datum potvrzení stud. oddělením: 06.11.2024
• Datum a čas obhajoby: 04.02.2025 08:30
• Datum odevzdání elektronické podoby: 09.01.2025
• Datum odevzdání tištěné podoby: 09.01.2025
• Datum proběhlé obhajoby: 04.02.2025
• Oponenti: prof. RNDr. Marie Hušková, DrSc.

Zásady pro vypracování

To know whether a change has happened is a task that not only interesting, but also desirable. Multidimensional data are prevalently and predominately represented through multiway arrays or tensors in current applications across various fields such as econometrics, psychometrics, chemometrics, genomics, image analysis, and signal processing. Handling structural breaks and changing developments in diverse data structures remains a priority task within a plethora of scientific areas, including the previously mentioned ones. The changepoint detection problem for a tensor data structure is considered, where the multivariate observations form a panel data. The multidimensional outcomes within each individual panel are permitted to be generally dependent and non-stationary. Simultaneously, the individual panels are weakly dependent and non-stationary among each other. The main goal is to detect whether an unknown change has occurred or not in the panels. The student's task will be to become familiar with the concept of changepoints and notion of tensors, explore some multivariate changepoint models, and demonstrate them on real/simulated data.

Seznam odborné literatury

[1] J. Antoch, J. Hanousek, L. Horváth, M. Hušková, and S. Wang, Structural breaks in panel data: Large number of panels and short length time series, Economet. Rev. 38 (2019), no. 7, 828–855.
[2] J. Bai, Common breaks in means and variances for panel data, J. Econometrics 157 (2010), no. 1, 78–92.
[3] B. H. Baltagi, Q. Feng, and C. Kao, Estimation of heterogeneous panels with structural breaks, J. Econometrics 191 (2016), no. 2016, 176–195.
[4] P. Comon, Tensors: A brief introduction, IEEE Signal Process. Mag. 31 (2014), no. 3, 44–53.
[5] N. Gaw, P. M. Pardalos, and M. R. Gahrooei, Applied Matrix and Tensor Variate Data Analysis, Springer Nature, New York, NY, 2024.
[6] L. Horváth and M. Hušková, Change-point detection in panel data, J. Time Ser. Anal. 33 (2012), no. 4, 631–648.
[7] T. G. Kolda and B. W. Bader, Tensor decompositions and applications, SIAM Rev. 51 (2009), no. 3, 455–500.
[8] Y. Liu, J. Liu, Z. Long, and C. Zhu, Tensor Computation for Data Analysis, Springer, New York, NY, 2022.
[9] M. Maciak, M. Pešta, and B. Peštová, Changepoint in dependent and non-stationary panels, Stat. Pap. 61 (2020), no. 4, 1385–1407.
[10] M. Maciak, B. Peštová, and M. Pešta, Structural breaks in dependent, heteroscedastic, and extremal panel data, Kybernetika 54 (2018), no. 6, 1106–1121.
[11] P. McCullagh, Tensor Methods in Statistics, 2nd edn., Dover Publications, Mineola, NY, 2018.
[12] K. Naskovska, B. Sokal, A. L. F. de Almeida, and M. Haardt, Using tensor contractions to derive the structure of slice-wise multiplications of tensors with applications to space-time Khatri-Rao coding for MIMO-OFDM systems, EURASIP J. Adv. Signal Process. 1 (2022), 109.
[13] M. Pešta, B. Peštová, and M. Maciak, Changepoint estimation for dependent and non-stationary panels, Appl. Math.-Czech. 65 (2020), no. 3, 29–310.
[14] M. Pešta and M. Wendler, Nuisance-parameter-free changepoint detection in non-stationary series, TEST 29 (2020), no. 2, 379–408.
[15] B. Peštová and M. Pešta, Testing structural changes in panel data with small fixed panel size and bootstrap, Metrika 78 (2015), no. 6, 665–689.
[16] B. Peštová and M. Pešta, Erratum to: Testing structural changes in panel data with small fixed panel size and bootstrap, Metrika 79 (2016), no. 2, 237–238.
[17] B. Peštová and M. Pešta, Change point estimation in panel data without boundary issue, Risks 5 (2017), no. 1, 7.
[18] T. Sakata, Applied Matrix and Tensor Variate Data Analysis, Springer, New York, NY, 2016.