Statistics on metric spaces
Most of statistics and ML happens in Euclidean space. How can do statistics on data valued in a general metric space?
Basic statistics
Using the Fréchet mean , the mean and variance can be generalized to random variables in metric spaces. Examples of this methodology:
- Panaretos & Zemel, 2019: Statistical aspects of Wasserstein distances (doi,
arxiv)
- Fréchet mean of random measures (measure-valued data)
- Commentary at optimal transport, see also statistical distances
- Dubey & Müller, 2017: Fréchet analysis of variance for random objects (arxiv)