We consider the problem of estimating the Fr{é}chet and conditional Fr{é}chet mean from data taking values in separable metric spaces. Unlike Euclidean spaces, where well-established methods are available, there is no practical estimator that works universally for all metric spaces. Therefore, we introduce a computable estimator for the Fr{é}chet mean based on random quantization techniques and establish its universal consistency across any separable metric spaces. Additionally, we propose another estimator for the conditional Fr{é}chet mean, leveraging data-driven partitioning and quantization, and demonstrate its universal consistency when the output space is any Banach space.

翻译：我们考虑从取值于可分度量空间的数据中估计弗雷歇均值与条件弗雷歇均值的问题。与欧几里得空间不同，后者已有成熟的方法可用，而对于所有度量空间，目前尚无普遍适用的实用估计量。为此，我们基于随机量化技术提出了一种可计算的弗雷歇均值估计量，并证明了其在任意可分度量空间中的普适一致性。此外，我们利用数据驱动的划分与量化方法，提出了另一种条件弗雷歇均值的估计量，并证明了当输出空间为任意巴拿赫空间时，该估计量具有普适一致性。