Dirichlet process mixtures under affine transformations of the data

Abstract : Location-scale Dirichlet process mixtures of Gaussians (DPM-G) have proved extremely useful in dealing with density estimation and clustering problems in a wide range of domains. Motivated by an astronomical application, in this work we address the robustness of DPM-G models to affine transformations of the data, a natural requirement for any sensible statistical method for density estimation. First, we devise a coherent prior specification of the model which makes posterior inference invariant with respect to affine transformation of the data. Second, we formalise the notion of asymptotic robustness under data transformation and show that mild assumptions on the true data generating process are sufficient to ensure that DPM-G models feature such a property. Our investigation is supported by an extensive simulation study and illustrated by the analysis of an astronomical dataset consisting of physical measurements of stars in the field of the globular cluster NGC 2419.
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https://hal.archives-ouvertes.fr/hal-01950652
Contributeur : Julyan Arbel <>
Soumis le : mardi 11 décembre 2018 - 03:13:11
Dernière modification le : lundi 4 février 2019 - 10:22:01
Document(s) archivé(s) le : mardi 12 mars 2019 - 12:54:32

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  • HAL Id : hal-01950652, version 1

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Julyan Arbel, Riccardo Corradin, Bernardo Nipoti. Dirichlet process mixtures under affine transformations of the data. 2018. 〈hal-01950652〉

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