Related papers: Choosing among notions of multivariate depth stati…
Closeness centrality, first considered by Bavelas (1948), is an importance measure of a node in a network which is based on the distances from the node to all other nodes. The classic definition, proposed by Bavelas (1950), Beauchamp…
A multivariate signal denoising method is proposed which employs a novel multivariate goodness of fit (GoF) test that is applied at multiple data scales obtained from discrete wavelet transform (DWT). In the proposed multivariate GoF test,…
This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…
Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing…
When several models have similar training scores, classical model selection heuristics follow Occam's razor and advise choosing the ones with least capacity. Yet, modern practice with large neural networks has often led to situations where…
To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…
The concept of depth represents methods to measure how deep an arbitrary point is positioned in a dataset and can be seen as the opposite of outlyingness. It has proved very useful and a wide range of methods have been developed based on…
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…
Distance metric learning is of fundamental interest in machine learning because the distance metric employed can significantly affect the performance of many learning methods. Quadratic Mahalanobis metric learning is a popular approach to…
Is there a natural way to order data in dimension greater than one? The approach based on the notion of data depth, often associated with John Tukey, is among the most popular. Tukey's depth has found applications in robust statistics,…
Multidimensional scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures embed data points in low-dimensional Euclidean (flat) domains, such that…
Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…
In this paper, a novel Bayesian nonparametric test for assessing multivariate normal models is presented. While there are extensive frequentist and graphical methods for testing multivariate normality, it is challenging to find Bayesian…
Functional magnetic resonance imaging (fMRI) data contain high levels of noise and artifacts. To avoid contamination of downstream analyses, fMRI-based studies must identify and remove these noise sources prior to statistical analysis. One…
With the rapid advancements in autonomous driving and robot navigation, there is a growing demand for lifelong learning models capable of estimating metric (absolute) depth. Lifelong learning approaches potentially offer significant cost…
Multivariate location and scatter matrix estimation is a cornerstone in multivariate data analysis. We consider this problem when the data may contain independent cellwise and casewise outliers. Flat data sets with a large number of…
We introduce two new measures for the dependence of $n \ge 2$ random variables: distance multivariance and total distance multivariance. Both measures are based on the weighted $L^2$-distance of quantities related to the characteristic…
With the massive data challenges nowadays and the rapid growing of technology, stream mining has recently received considerable attention. To address the large number of scenarios in which this phenomenon manifests itself suitable tools are…
The problem of overdispersion in multivariate count data is a challenging issue. Nowadays, it covers a central role mainly due to the relevance of modern technologies data, such as Next Generation Sequencing and textual data from the web or…
A robust mean value is often a good alternative to the standard mean value when dealing with data containing many outliers. An efficient method for samples of one-dimensional features and the truncated quadratic error norm is presented and…