Related papers: High-Dimensional Density Estimation via SCA: An Ex…
Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high-dimensional data. However, classical PCA is very sensitive to…
We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the number of observations is of the same magnitude as the number of variables…
This study proposes a radically alternate approach for extracting quantitative information from schlieren images. The method uses a scaled, derivative enhanced Gaussian process model to obtain true density estimates from two corresponding…
The availability of reliable, high-resolution climate and weather data is important to inform long-term decisions on climate adaptation and mitigation and to guide rapid responses to extreme events. Forecasting models are limited by…
We introduce a novel two-step approach for estimating a probability density function (pdf) given its samples, with the second and important step coming from a geometric formulation. The procedure involves obtaining an initial estimate of…
This work proposes a sampling-based (non-intrusive) approach within the context of low-rank separated representations to tackle the issue of curse-of-dimensionality associated with the solution of models, e.g., PDEs/ODEs, with…
As part of a project to develop more accurate estimates of the risks due to tropical cyclones, we describe a non-parametric method for the statistical simulation of the location of tropical cyclone genesis. The method avoids the use of…
We propose two ways of estimating the current source density (CSD) from measurements of voltage on a Cartesian grid with missing recording points using the inverse CSD method. The simplest approach is to substitute local averages (LA) in…
High-dimensional astronomical data cubes provide a wealth of spectral and structural information that can be used to study astrophysical and chemical processes. The complexity and sheer size of these datasets pose significant challenges in…
A stylized feature of high-dimensional data is that many variables have heavy tails, and robust statistical inference is critical for valid large-scale statistical inference. Yet, the existing developments such as Winsorization,…
This article focuses on the robust principal component analysis (PCA) of high-dimensional data with elliptical distributions. We investigate the PCA of the sample spatial-sign covariance matrix in both nonsparse and sparse contexts,…
In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a…
Multidimensional data is often associated with uncertainties that are not well-described by normal distributions. In this work, we describe how such distributions can be projected to a low-dimensional space using uncertainty-aware principal…
This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for…
Particularly important to hurricane risk assessment for coastal regions is finding accurate approximations of return probabilities of maximum windspeeds. Since extremes in maximum windspeed have a direct relationship to minimums in the…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions…
We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…
We propose a method for the unsupervised clustering of hyperspectral images based on spatially regularized spectral clustering with ultrametric path distances. The proposed method efficiently combines data density and geometry to…
We describe results from the second stage of a project to build a statistical model for hurricane tracks. In the first stage we modelled the unconditional mean track. We now attempt to model the unconditional variance of fluctuations around…