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Mazhar, Othmane
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Mazhar, O., Rojas, C. R., Fischione, C. & Hesamzadeh, M. R. (2018). Bayesian model selection for change point detection and clustering. In: 35th International Conference on Machine Learning, ICML 2018: . Paper presented at 35th International Conference on Machine Learning, ICML 2018, 10 July 2018 through 15 July 2018 (pp. 5497-5520). International Machine Learning Society (IMLS)
Open this publication in new window or tab >>Bayesian model selection for change point detection and clustering
2018 (English)In: 35th International Conference on Machine Learning, ICML 2018, International Machine Learning Society (IMLS) , 2018, p. 5497-5520Conference paper, Published paper (Refereed)
Abstract [en]

We address a generalization of change point detection with the purpose of detecting the change locations and the levels of clusters of a piece- wise constant signal. Our approach is to model it as a nonparametric penalized least square model selection on a family of models indexed over the collection of partitions of the design points and propose a computationally efficient algorithm to approximately solve it. Statistically, minimizing such a penalized criterion yields an approximation to the maximum a-posteriori probability (MAP) estimator. The criterion is then ana-lyzed and an oracle inequality is derived using a Gaussian concentration inequality. The oracle inequality is used to derive on one hand conditions for consistency and on the other hand an adaptive upper bound on the expected square risk of the estimator, which statistically motivates our approximation. Finally, we apply our algorithm to simulated data to experimentally validate the statistical guarantees and illustrate its behavior.

Place, publisher, year, edition, pages
International Machine Learning Society (IMLS), 2018
Keywords
Artificial intelligence, Bayesian networks, Least squares approximations, Probability distributions, Bayesian model selection, Change point detection, Computationally efficient, Concentration inequality, Maximum A posteriori probabilities, Penalized least-squares, Piece-wise constants, Statistical guarantee, Learning systems
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-247470 (URN)2-s2.0-85057285830 (Scopus ID)9781510867963 (ISBN)
Conference
35th International Conference on Machine Learning, ICML 2018, 10 July 2018 through 15 July 2018
Note

QC20190405

Available from: 2019-04-05 Created: 2019-04-05 Last updated: 2019-04-05Bibliographically approved
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