Quantifying the Closeness to a Set of Random Curves via the Mean Marginal Likelihood

Cédric Rommel 1, 2, 3, * Frédéric Bonnans 1, 3 Baptiste Gregorutti 2 Pierre Martinon 1, 3
* Corresponding author
3 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
Abstract : In this paper, we tackle the problem of quantifying the closeness of a newly observed curve to a given sample of random functions, supposed to have been sampled from the same distribution. We define a probabilistic criterion for such a purpose, based on the marginal density functions of an underlying random process. For practical applications, a class of estimators based on the aggregation of multivariate density estimators is introduced and proved to be consistent. We illustrate the effectiveness of our estimators, as well as the practical usefulness of the proposed criterion, by applying our method to a dataset of real aircraft trajectories.
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Cédric Rommel, Frédéric Bonnans, Baptiste Gregorutti, Pierre Martinon. Quantifying the Closeness to a Set of Random Curves via the Mean Marginal Likelihood. 2018. ⟨hal-01816407⟩

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