Related papers: Choosing among notions of multivariate depth stati…
Statistical depths have been well studied for multivariate and functional data over the past few decades, but remain under-explored for point processes. A first attempt on the notion of point process depth was conducted recently where the…
Data depth is a powerful nonparametric tool originally proposed to rank multivariate data from center outward. In this context, one of the most archetypical depth notions is Tukey's halfspace depth. In the last few decades notions of depth…
During the past two decades there has been a lot of interest in developing statistical depth notions that generalize the univariate concept of ranking to multivariate data. The notion of depth has also been extended to regression models and…
The purpose of this article is to extend the notion of statistical depth to the case of sample paths of a Markov chain. Initially introduced to define a center-outward ordering of points in the support of a multivariate distribution, depth…
Statistical data depth plays an important role in the analysis of multivariate data sets. The main outcome is a center-outward ordering of the observations that can be used both to highlight features of the underlying distribution of the…
Data depths are score functions that quantify in an unsupervised fashion how central is a point inside a distribution, with numerous applications such as anomaly detection, multivariate or functional data analysis, arising across various…
The Oja depth (simplicial volume depth) is one of the classical statistical techniques for measuring the central tendency of data in multivariate space. Despite the widespread emergence of object data like images, texts, matrices or graphs,…
We present single imputation method for missing values which borrows the idea of data depth---a measure of centrality defined for an arbitrary point of a space with respect to a probability distribution or data cloud. This consists in…
The concept of statistical depth extends the notions of the median and quantiles to other statistical models. These procedures aim to formalize the idea of identifying deeply embedded fits to a model that are less influenced by…
Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…
Statistical tools which satisfy rigorous privacy guarantees are necessary for modern data analysis. It is well-known that robustness against contamination is linked to differential privacy. Despite this fact, using multivariate medians for…
This paper proposes a clustering procedure for samples of multivariate functions in $(L^2(I))^{J}$, with $J\geq1$. This method is based on a k-means algorithm in which the distance between the curves is measured with a metrics that…
In the field of machine learning, model performance is usually assessed by randomly splitting data into training and test sets. Different random splits, however, can yield markedly different performance estimates, so a genuinely good model…
We present analytical expressions for the means and covariances of the sample distribution of the cross-validated Mahalanobis distance. This measure has proven to be especially useful in the context of representational similarity analysis…
Statistical depth measures the centrality of a point with respect to a given distribution or data cloud. It provides a natural center-outward ordering of multivariate data points and yields a systematic nonparametric multivariate analysis…
Statistical models are inherently uncertain. Quantifying or at least upper-bounding their uncertainties is vital for safety-critical systems such as autonomous vehicles. While standard neural networks do not report this information, several…
Anomaly detection is a branch of data analysis and machine learning which aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…
This work introduces the Matrix Minimum Covariance Determinant (MMCD) method, a novel robust location and covariance estimation procedure designed for data that are naturally represented in the form of a matrix. Unlike standard robust…
Data depth is a well-known and useful nonparametric tool for analyzing functional data. It provides a novel way of ranking a sample of curves from the center outwards and defining robust statistics, such as the median or trimmed means. It…
For the purpose of explaining multivariate outlyingness, it is shown that the squared Mahalanobis distance of an observation can be decomposed into outlyingness contributions originating from single variables. The decomposition is obtained…