The paper obtains the general form of the cross-covariance function of vector fractional Brownian motion with correlated components having different self-similarity indices.

Abstract: In this note, we establish an asymptotic expansion for the centering parameter appearing in the central limit theorems for linear spectral statistic of large-dimensional sample covariance matrices when the population has a spiked covariance structure. As an application, we provide an asymptotic power function for the corrected likelihood ratio statistic for testing the presence of spi...

We investigated the meridional circulation of photospheric faculae throughout cycle 19. Together with the rotation observed in a companion paper (Meunier et al. 1996), we were able to address the problem of the existence of the observed differential rotation. Themeridional circulation is characterized by a strong north-south asymmetry. The distribution of meridional circulation around the mean ...

We describe a method for causal inference that measures the strength of statistical dependence by the Hilbert-Schmidt norm of kernelbased conditional cross-covariance operators. We consider the increase of the dependence of two variables X and Y by conditioning on a third variable Z as a hint for Z being a common effect of X and Y . Based on this assumption, we collect “votes” for hypothetical ...

Outdoor positioning for Unmanned Aerial Vehicles (UAVs) commonly relies on GPS signals, which might be reflected or blocked in urban areas. In such cases, additional on-board sensors such as Light Detection and Ranging (LiDAR) are desirable. To fuse GPS and LiDAR measurements, it is important, yet challenging, to accurately characterize the error covariance of the sensor measurements. In this p...

Covariance matrices are an effective way to capture global spread across local interest points in images. Often, these image descriptors are more compact, robust and informative than, for example, bags of visual words. However, they are symmetric and positive definite (SPD) and therefore live on a non-Euclidean Riemannian manifold, which gives rise to non-Euclidean metrics. These are slow to co...

Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of the unknown data generating density. This paper contributes to the mathematical understanding of this phenomenon and helps define better justified sampling algorithms for deep learning based on auto-encoder variants. We consider an MCMC where each step samples from a Gaussian whose me...

This paper presents a strategy for achieving practical mapping navigation using a wheeled mobile robot equipped with an advanced sonar sensor. The original mapping navigation experiment, carried out with the same robot configuration, builds a feature map consisting of commonplace indoor landmarks crucial for localisation, namely planes, corners and edges. The map exhaustively maintains covarian...

We prove a universality theorem for learning with random features. Our result shows that, in terms of training and generalization errors, feature model nonlinear activation function is asymptotically equivalent to surrogate linear Gaussian matching covariance matrix. This settles so-called equivalence conjecture based on which several recent papers develop their results. method proving the buil...

We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also considered.