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Defining multivariate generalizations of the classical univariate ranks has been a long-standing open problem in statistics. Optimal transport has been shown to offer a solution in which multivariate ranks are obtained by transporting data points to a grid that approximates a uniformreference measure (Chernozhukov et al. 2017; Hallin, 2017; Hallin et al. 2021). We take up this new perspective to develop and study multivariate analogues of the sign covariance/quadrant statistic, Kendall’s tau, and Spearman’s rho. The resulting tests of multivariate independence are genuinely distribution-free, hence uniformly valid irrespective of the actual (absolutely continuous) distributions of the observations. Our results provide asymptotic distribution theory for these new test statistics, with asymptotic approximations to critical values to be used for testing independence as well as a power analysis of the resulting tests. This includes a multivariate elliptical Chernoff–Savage property, which guarantees that, under ellipticity, our nonparametric tests of independence enjoy an asymptotic relative efficiency of one or larger with respect to theclassical Gaussian procedures., info:eu-repo/semantics/published

Defining multivariate generalizations of the classical univariate ranks has been a long-standing open problem in statistics. Optimal transport has been showed to offer a solution by transporting data points to grid approximating a reference measure (Chernozhukov et al. 2017;Hallin, 2017; Hallin et al. 2021a). We take up this new perspective to develop and study multivariate analogues of popular correlations measures including the sign covariance, Kendall's tau and Spearman's rho. Our tests are genuinely distribution-free, hence valid irrespective of the actual (absolutely continuous) distributions of the observations. We present asymptotic distribution theory for these new statistics, providing asymptotic approximations to critical values to be used for testing independence as well as an analysis of power of the resulting tests. Interestingly, we are able to establish a multivariate elliptical Chernoff-Savage property, which guarantees that, under ellipticity, our nonparametric tests of independence when compared to Gaussian procedures enjoy an asymptotic relative efficiency of one or larger. Hence, the nonparametric tests constitute a safe replacement for procedures based on multivariate Gaussianity., info:eu-repo/semantics/published

Rank correlations have found many innovative applications in the last decade. In particular,suitable versions of rank correlations have been used for consistent tests of independence between pairs of random variables. The use of ranks is especially appealing for continuous data as tests become distribution-free. However, the traditional concept of ranks relies on ordering data and is, thus, tied to univariate observations. As a result it has long remained unclear how one may construct distribution-free yet consistent tests of independence between multivariate random vectors. This is the problem we address in this paper, in which we lay out a general framework for designing dependence measures that give tests of multivariate independence that are not only consistent and distribution-free but which we also prove to be statistically efficient. Our framework leverages the recently introduced concept of center-outward ranks and signs, a multivariate generalization of traditional ranks, and adopts a common standard form for dependence measures that encompasses many popular measures from the literature. In a unified study, we derive a general asymptotic representation of center-outward test statistics under independence, extending to the multivariate setting the classical Hájek asymptotic representation results. This representation permits a direct calculation of limiting null distributions for the proposed test statistics. Moreover, it facilitates a local power analysis that provides strong support for the center-outward approach to multivariate ranks by establishing, for the first time, the rate-optimality of center-outward tests within families of Konijn alternatives., info:eu-repo/semantics/published

In this paper, we focus on three problems in deep learning based medical image segmentation. Firstly, U-net, as a popular model for medical image segmentation, is difficult to train when convolutional layers increase even though a deeper network usually has a better generalization ability because of more learnable parameters. Secondly, the exponential ReLU (ELU), as an alternative of ReLU, is not much different from ReLU when the network of interest gets deep. Thirdly, the Dice loss, as one of the pervasive loss functions for medical image segmentation, is not effective when the prediction is close to ground truth and will cause oscillation during training. To address the aforementioned three problems, we propose and validate a deeper network that can fit medical image datasets that are usually small in the sample size. Meanwhile, we propose a new loss function to accelerate the learning process and a combination of different activation functions to improve the network performance. Our experimental results suggest that our network is comparable or superior to state-of-the-art methods.

Pupil tracking is an important branch of object tracking which require high precision. We investigate head mounted pupil tracking which is often more convenient and precise than remote pupil tracking, but also more challenging. When pupil tracking suffers from noise like bad illumination, detection precision dramatically decreases. Due to the appearance of head mounted recording device and public benchmark image datasets, head mounted tracking algorithms have become easier to design and evaluate. In this paper, we propose a robust head mounted pupil detection algorithm which uses a Convolutional Neural Network (CNN) to combine different features of pupil. Here we consider three features of pupil. Firstly, we use three pupil feature-based algorithms to find pupil center independently. Secondly, we use a CNN to evaluate the quality of each result. Finally, we select the best result as output. The experimental results show that our proposed algorithm performs better than the present state-of-art., Comment: It's out of date and not STOA any more