Bayesian online change point detection with Hilbert space approximate Student-t process

Jeremy Sellier, Petros Dellaportas
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:30553-30569, 2023.

Abstract

In this paper, we introduce a variant of Bayesian online change point detection with a reducedrank Student-t process (TP) and dependent Student-t noise, as a nonparametric time series model. Our method builds and improves upon the state-of-the-art Gaussian process (GP) change point model benchmark of Saatci et al. (2010). The Student-t process generalizes the concept of a GP and hence yields a more flexible alternative. Additionally, unlike a GP, the predictive variance explicitly depends on the training observations, while the use of an entangled Student-t noise model preserves analytical tractability. Our approach also uses a Hilbert space reduced-rank representation of the TP kernel, derived from an eigenfunction expansion of the Laplace operator (Solin & Sarkka, 2020), to alleviate its computational complexity. Improvements in prediction and training time are demonstrated with real-world data-sets

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-sellier23a, title = {{B}ayesian online change point detection with {H}ilbert space approximate Student-t process}, author = {Sellier, Jeremy and Dellaportas, Petros}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {30553--30569}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/sellier23a/sellier23a.pdf}, url = {https://proceedings.mlr.press/v202/sellier23a.html}, abstract = {In this paper, we introduce a variant of Bayesian online change point detection with a reducedrank Student-t process (TP) and dependent Student-t noise, as a nonparametric time series model. Our method builds and improves upon the state-of-the-art Gaussian process (GP) change point model benchmark of Saatci et al. (2010). The Student-t process generalizes the concept of a GP and hence yields a more flexible alternative. Additionally, unlike a GP, the predictive variance explicitly depends on the training observations, while the use of an entangled Student-t noise model preserves analytical tractability. Our approach also uses a Hilbert space reduced-rank representation of the TP kernel, derived from an eigenfunction expansion of the Laplace operator (Solin & Sarkka, 2020), to alleviate its computational complexity. Improvements in prediction and training time are demonstrated with real-world data-sets} }
Endnote
%0 Conference Paper %T Bayesian online change point detection with Hilbert space approximate Student-t process %A Jeremy Sellier %A Petros Dellaportas %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-sellier23a %I PMLR %P 30553--30569 %U https://proceedings.mlr.press/v202/sellier23a.html %V 202 %X In this paper, we introduce a variant of Bayesian online change point detection with a reducedrank Student-t process (TP) and dependent Student-t noise, as a nonparametric time series model. Our method builds and improves upon the state-of-the-art Gaussian process (GP) change point model benchmark of Saatci et al. (2010). The Student-t process generalizes the concept of a GP and hence yields a more flexible alternative. Additionally, unlike a GP, the predictive variance explicitly depends on the training observations, while the use of an entangled Student-t noise model preserves analytical tractability. Our approach also uses a Hilbert space reduced-rank representation of the TP kernel, derived from an eigenfunction expansion of the Laplace operator (Solin & Sarkka, 2020), to alleviate its computational complexity. Improvements in prediction and training time are demonstrated with real-world data-sets
APA
Sellier, J. & Dellaportas, P.. (2023). Bayesian online change point detection with Hilbert space approximate Student-t process. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:30553-30569 Available from https://proceedings.mlr.press/v202/sellier23a.html.

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