Hypothesis Test and Confidence Analysis with Wasserstein Distance on General Dimension

We develop a general framework for statistical inference with the 1-Wasserstein distance. Recently, the Wasserstein distance has attracted considerable attention and has been widely applied to various machine learning tasks because of its excellent properties. However, hypothesis tests and a confidence analysis for it have not been established in a general multivariate setting. This is because the limit distribution of the empirical distribution with the Wasserstein distance is unavailable without strong restriction. To address this problem, in this study, we develop a novel nonasymptotic gaussian approximation for the empirical 1-Wasserstein distance. Using the approximation method, we develop a hypothesis test and confidence analysis for the empirical 1-Wasserstein distance. We also provide a theoretical guarantee and an efficient algorithm for the proposed approximation. Our experiments validate its performance numerically.

Characterizing spatial distributions of astrocytes in the mammalian retina

MOTIVATION

In addition to being involved in retinal vascular growth, astrocytes play an important role in diseases and injuries, such as glaucomatous neuro-degeneration and retinal detachment. Studying astrocytes, their morphological cell characteristics and their spatial relationships to the surrounding vasculature in the retina may elucidate their role in these conditions.

RESULTS

Our results show that in normal healthy retinas, the distribution of observed astrocyte cells does not follow a uniform distribution. The cells are significantly more densely packed around the blood vessels than a uniform distribution would predict. We also show that compared with the distribution of all cells, large cells are more dense in the vicinity of veins and toward the optic nerve head whereas smaller cells are often more dense in the vicinity of arteries. We hypothesize that since veinal astrocytes are known to transport toxic metabolic waste away from neurons they may be more critical than arterial astrocytes and therefore require larger cell bodies to process waste more efficiently.

AVAILABILITY AND IMPLEMENTATION

A 1/8th size down-sampled version of the seven retinal image mosaics described in this article can be found on BISQUE (Kvilekval et al., 2010) at http://bisque.ece.ucsb.edu/client_service/view?resource=http://bisque.ece.ucsb.edu/data_service/dataset/6566968.