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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 12:50 AM -- 01:00 AM (PDT) @ K11

We address a generalization of change point detectionwith the purpose of detecting the changelocations and the levels of clusters of a piecewiseconstant signal. Our approach is to model itas a nonparametric penalized least square modelselection on a family of models indexed over thecollection of partitions of the design points andpropose a computationally efficient algorithm toapproximately solve it. Statistically, minimizingsuch a penalized criterion yields an approximationto the maximum a-posteriori probability(MAP) estimator. The criterion is then analyzedand an oracle inequality is derived usinga Gaussian concentration inequality. The oracleinequality is used to derive on one hand conditionsfor consistency and on the other hand anadaptive upper bound on the expected square riskof the estimator, which statistically motivates ourapproximation. Finally, we apply our algorithmto simulated data to experimentally validate thestatistical 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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