Related papers: On the Christoffel function and classification in …
In many applications including financial risk measurement, copulas have shown to be a powerful building block to reflect multivariate dependence between several random variables including the mapping of tail dependencies. A famous key…
The replacement of indicator functions by integrated beta kernels in the definition of the empirical stable tail dependence function is shown to produce a smoothed version of the latter estimator with the same asymptotic distribution but…
Galaxy surveys provide finite catalogs of objects observed within bounded volumes, yet clustering statistics are often interpreted using theoretical frameworks developed for infinite point processes. In this work, we formulate key…
Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…
Clustering techniques applied to multivariate data are a very useful tool in Statistics and have been fully studied in the literature. Nevertheless, these clustering methodologies are less well known when dealing with functional data. Our…
Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first…
Speculative optimisation relies on the estimation of the probabilities that certain properties of the control flow are fulfilled. Concrete or estimated branch probabilities can be used for searching and constructing advantageous speculative…
The use of a hypothetical generative model was been suggested for causal analysis of observational data. The very assumption of a particular model is a commitment to a certain set of variables and therefore to a certain set of possible…
The purpose of the present paper is to give unified expressions to the characteristic functions of all elliptical and related distributions. Those distributions including the multivariate elliptical symmetric distributions and some…
With the ubiquity of sensors in the IoT era, statistical observations are becoming increasingly available in the form of massive (multivariate) time-series. Formulated as unsupervised anomaly detection tasks, an abundance of applications…
Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has…
Two central objects in constructive approximation, the Christoffel-Darboux kernel and the Christoffel function, are encoding ample information about the associated moment data and ultimately about the possible generating measures. We…
Selecting diverse and important items, called landmarks, from a large set is a problem of interest in machine learning. As a specific example, in order to deal with large training sets, kernel methods often rely on low rank matrix Nystr\"om…
In this note we provide a quick proof of the Sklar's Theorem on the existence of copulas by using the generalized inverse functions as in the one dimensional case, but a little more sophisticated.
This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and…
We establish Krylov-Safonov type H\"older regularity theory for solutions to quite general discrete dynamic programming equations or equivalently discrete stochastic processes on random geometric graphs. Such graphs arise for example from…
Hypergraph spectral analysis has emerged as an effective tool processing complex data structures in data analysis. The surface of a three-dimensional (3D) point cloud and the multilateral relationship among their points can be naturally…
Stochastic variational inference makes it possible to approximate posterior distributions induced by large datasets quickly using stochastic optimization. The algorithm relies on the use of fully factorized variational distributions.…
First-order statistics of scattered light is described using the representation of probability density cloud which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail…
As a popular representation of 3D data, point cloud may contain noise and need to be filtered before use. Existing point cloud filtering methods either cannot preserve sharp features or result in uneven point distribution in the filtered…