Biodiversity studies rely heavily on estimates of species' distributions often obtained through ecological niche modelling. Numerous software packages exist that allow users to model ecological niches using machine learning and statistical methods. However, no existing package with a graphical user interface allows users to perform model calibration and selection based on convex forms such as ellipsoids, which may match fundamental ecological niche shapes better, incorporating tools for exploring, modelling, and evaluating niches and distributions that are intuitive for both novice and proficient users. Here we describe an The method is explained in detail and tested via modelling the threatened feline species Using
Optimal transport (OT) methods seek a transformation map (or plan) between two probability measures, such that the transformation has the minimum transportation cost. Such a minimum transport cost, with a certain power transform, is called the Wasserstein distance. Recently, OT methods have drawn great attention in statistics, machine learning, and computer science, especially in deep generative neural networks. Despite its broad applications, the estimation of high‐dimensional Wasserstein distances is a well‐known challenging problem owing to the curse‐of‐dimensionality. There are some cutting‐edge projection‐based techniques that tackle high‐dimensional OT problems. Three major approaches of such techniques are introduced, respectively, the slicing approach, the iterative projection approach, and the projection robust OT approach. Open challenges are discussed at the end of the review.
This article is categorized under: Statistical and Graphical Methods of Data Analysis > Dimension Reduction Statistical Learning and Exploratory Methods of the Data Sciences > Manifold Learning
- NSF-PAR ID:
- 10443887
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- WIREs Computational Statistics
- Volume:
- 15
- Issue:
- 2
- ISSN:
- 1939-5108
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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