تقرير
A Wasserstein index of dependence for random measures
| العنوان: | A Wasserstein index of dependence for random measures |
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| المؤلفون: | Catalano, Marta, Lavenant, Hugo, Lijoi, Antonio, Prünster, Igor |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Statistics Theory, Mathematics - Probability |
| الوصف: | Optimal transport and Wasserstein distances are flourishing in many scientific fields as a means for comparing and connecting random structures. Here we pioneer the use of an optimal transport distance between L\'{e}vy measures to solve a statistical problem. Dependent Bayesian nonparametric models provide flexible inference on distinct, yet related, groups of observations. Each component of a vector of random measures models a group of exchangeable observations, while their dependence regulates the borrowing of information across groups. We derive the first statistical index of dependence in $[0,1]$ for (completely) random measures that accounts for their whole infinite-dimensional distribution, which is assumed to be equal across different groups. This is accomplished by using the geometric properties of the Wasserstein distance to solve a max-min problem at the level of the underlying L\'{e}vy measures. The Wasserstein index of dependence sheds light on the models' deep structure and has desirable properties: (i) it is $0$ if and only if the random measures are independent; (ii) it is $1$ if and only if the random measures are completely dependent; (iii) it simultaneously quantifies the dependence of $d \ge 2$ random measures, avoiding the need for pairwise comparisons; (iv) it can be evaluated numerically. Moreover, the index allows for informed prior specifications and fair model comparisons for Bayesian nonparametric models. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2109.06646 |
| رقم الأكسشن: | edsarx.2109.06646 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |