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Article Dans Une Revue Statistical Inference for Stochastic Processes Année : 2015

Cox process functional learning

Résumé

This article addresses the problem of supervised classification of Cox process trajectories, whose random intensity is driven by some exogenous random covariable. The classification task is achieved through a regularized convex empirical risk minimization procedure, and a nonasymptotic oracle inequality is derived. We show that the algorithm provides a Bayes-risk consistent classifier. Furthermore, it is proved that the classifier converges at a rate which adapts to the unknown regularity of the intensity process. Our results are obtained by taking advantage of martingale and stochastic calculus arguments, which are natural in this context and fully exploit the functional nature of the problem.
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Dates et versions

hal-00820838 , version 1 (06-05-2013)

Identifiants

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Gérard Biau, Benoît Cadre, Quentin Paris. Cox process functional learning. Statistical Inference for Stochastic Processes, 2015, 18 (3), pp.257-277. ⟨10.1007/s11203-015-9115-z⟩. ⟨hal-00820838⟩
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