تقرير
Weak limits of entropy regularized Optimal Transport; potentials, plans and divergences
| العنوان: | Weak limits of entropy regularized Optimal Transport; potentials, plans and divergences |
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| المؤلفون: | Gonzalez-Sanz, Alberto, Loubes, Jean-Michel, Niles-Weed, Jonathan |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematics - Statistics Theory |
| الوصف: | This work deals with the asymptotic distribution of both potentials and couplings of entropic regularized optimal transport for compactly supported probabilities in $\R^d$. We first provide the central limit theorem of the Sinkhorn potentials -- the solutions of the dual problem -- as a Gaussian process in $\Cs$. Then we obtain the weak limits of the couplings -- the solutions of the primal problem -- evaluated on integrable functions, proving a conjecture of \cite{ChaosDecom}. In both cases, their limit is a real Gaussian random variable. Finally we consider the weak limit of the entropic Sinkhorn divergence under both assumptions $H_0:\ {\rm P}={\rm Q}$ or $H_1:\ {\rm P}\neq{\rm Q}$. Under $H_0$ the limit is a quadratic form applied to a Gaussian process in a Sobolev space, while under $H_1$, the limit is Gaussian. We provide also a different characterisation of the limit under $H_0$ in terms of an infinite sum of an i.i.d. sequence of standard Gaussian random variables. Such results enable statistical inference based on entropic regularized optimal transport. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2207.07427 |
| رقم الأكسشن: | edsarx.2207.07427 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |