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Probabilistic sequential matrix factorization
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Akyildiz, Ömer Deniz, van den Burg, Gerrit J. J., Damoulas, Theodoros and Steel, Mark F. J. (2021) Probabilistic sequential matrix factorization. In: The 24th International Conference on Artificial Intelligence and Statistics (AISTATS 2021), Virtual, 13-15 Apr 2021. Published in: Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, 130 pp. 3484-3492. ISSN 2640-3498.
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Official URL: https://proceedings.mlr.press/v130/akyildiz21a.htm...
Abstract
We introduce the probabilistic sequential matrix factorization (PSMF) method for factorizing time-varying and non-stationary datasets consisting of high-dimensional time-series. In particular, we consider nonlinear Gaussian state-space models where sequential approximate inference results in the factorization of a data matrix into a dictionary and time-varying coefficients with potentially nonlinear Markovian dependencies. The assumed Markovian structure on the coefficients enables us to encode temporal dependencies into a low-dimensional feature space. The proposed inference method is solely based on an approximate extended Kalman filtering scheme, which makes the resulting method particularly efficient. PSMF can account for temporal nonlinearities and, more importantly, can be used to calibrate and estimate generic differentiable nonlinear subspace models. We also introduce a robust version of PSMF, called rPSMF, which uses Student-t filters to handle model misspecification. We show that PSMF can be used in multiple contexts: modeling time series with a periodic subspace, robustifying changepoint detection methods, and imputing missing data in several high-dimensional time-series, such as measurements of pollutants across London.
Item Type: | Conference Item (Paper) | |||||||||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science Faculty of Science, Engineering and Medicine > Science > Statistics |
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Library of Congress Subject Headings (LCSH): | Statistics, Artificial intelligence, Probabilities -- Mathematical models, Data mining, Machine learning | |||||||||||||||
Series Name: | Proceedings of Machine Learning Research | |||||||||||||||
Journal or Publication Title: | Proceedings of The 24th International Conference on Artificial Intelligence and Statistics | |||||||||||||||
Publisher: | PMLR | |||||||||||||||
ISSN: | 2640-3498 | |||||||||||||||
Official Date: | 2021 | |||||||||||||||
Dates: |
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Volume: | 130 | |||||||||||||||
Page Range: | pp. 3484-3492 | |||||||||||||||
Status: | Peer Reviewed | |||||||||||||||
Publication Status: | Published | |||||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||||||||
Date of first compliant deposit: | 2 September 2021 | |||||||||||||||
Date of first compliant Open Access: | 2 September 2021 | |||||||||||||||
RIOXX Funder/Project Grant: |
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Conference Paper Type: | Paper | |||||||||||||||
Title of Event: | The 24th International Conference on Artificial Intelligence and Statistics (AISTATS 2021) | |||||||||||||||
Type of Event: | Conference | |||||||||||||||
Location of Event: | Virtual | |||||||||||||||
Date(s) of Event: | 13-15 Apr 2021 | |||||||||||||||
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