Related papers: The random Tukey depth

We study families of depth measures defined by natural sets of axioms. We show that any such depth measure is a constant factor approximation of Tukey depth. We further investigate the dimensions of depth regions, showing that the Cascade…

A new multivariate concept of quantile, based on a directional version of Koenker and Bassett's traditional regression quantiles, is introduced for multivariate location and multiple-output regression problems. In their empirical version,…

We introduce a novel projection depth for data lying in a general Hilbert space, called the regularized projection depth, with a focus on functional data. By regularizing projection directions, the proposed depth does not suffer from the…

We show how random subspace methods can be adapted to estimating local projections with many controls. Random subspace methods have their roots in the machine learning literature and are implemented by averaging over regressions estimated…

There exist multiple methods to detect outliers in multivariate data in the literature, but most of them require to estimate the covariance matrix. The higher the dimension, the more complex the estimation of the matrix becoming impossible…

The halfspace depth is a prominent tool of nonparametric multivariate analysis. The upper level sets of the depth, termed the trimmed regions of a measure, serve as a natural generalization of the quantiles and inter-quantile regions to…

This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…

The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…

Monocular depth prediction plays a crucial role in understanding 3D scene geometry. Although recent methods have achieved impressive progress in evaluation metrics such as the pixel-wise relative error, most methods neglect the geometric…

We give examples of different multivariate probability distributions whose halfspace depths coincide at all points of the sample space.

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…

Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…

Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…

Despite the renewed interest in the Newey and Powell (1987) concept of expectiles in fields such as econometrics, risk management, and extreme value theory, expectile regression---or, more generally, M-quantile regression---unfortunately…

Among their competitors, projection depth and its induced estimators are very favorable because they can enjoy very high breakdown point robustness without having to pay the price of low efficiency, meanwhile providing a promising…

We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution,…

Quantitative assessment of the uncertainties tainting the results of computer simulations is nowadays a major topic of interest in both industrial and scientific communities. One of the key issues in such studies is to get information about…

As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…

This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…

1) We introduce random discrete Morse theory as a computational scheme to measure the complicatedness of a triangulation. The idea is to try to quantify the frequence of discrete Morse matchings with a certain number of critical cells. Our…