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Bayesian Model Selection for Change Point Detection and Clustering
othmane mazhar · Cristian R. Rojas · Inst. of Technology Carlo Fischione · Mohammad Reza Hesamzadeh

Fri Jul 13 09:15 AM -- 12:00 PM (PDT) @ Hall B #91

We address a generalization of change point detection with the purpose of detecting the change locations and the levels of clusters of a piecewise 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 analyzed 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.

Author Information

othmane mazhar (KTH Royal Institute of Technology)
Cristian R. Rojas (KTH Royal Institute of Technology)
Inst. of Technology Carlo Fischione (Royal Inst. of Technology, KTH)
Mohammad Reza Hesamzadeh (KTH Royal Institute of Technology)

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