Related papers: Compositional regression using principal nested sp…

High-dimensional compositional data are commonplace in the modern omics sciences amongst others. Analysis of compositional data requires a proper choice of orthonormal coordinate representation as their relative nature is not compatible…

Compositional observations are an increasingly prevalent data source in spatial statistics. Analysis of such data is typically done on log-ratio transformations or via Dirichlet regression. However, these approaches often make unnecessarily…

The method of Principal Nested Spheres (PNS) is a non-linear dimension reduction technique for spherical data. The method is a backwards fitting procedure, starting with fitting a high-dimensional sphere and then successively reducing…

Molecular dynamics simulations produce huge datasets of temporal sequences of molecules. It is of interest to summarize the shape evolution of the molecules in a succinct, low-dimensional representation. However, Euclidean techniques such…

Compositional data, also referred to as simplicial data, naturally arise in many scientific domains such as geochemistry, microbiology, and economics. In such domains, obtaining sensible lower-dimensional representations and modes of…

Statistical analysis on compositional data has gained a lot of attention due to their great potential of applications. A feature of these data is that they are multivariate vectors that lie in the simplex, that is, the components of each…

Simplicial-simplicial regression refers to the regression setting where both the responses and predictor variables lie within the simplex space, i.e. they are compositional. For this setting, constrained least squares, where the regression…

Compositional data, such as human gut microbiomes, consist of non-negative variables whose only the relative values to other variables are available. Analyzing compositional data such as human gut microbiomes needs a careful treatment of…

Over the past decades, the increasing dimensionality of data has increased the need for effective data decomposition methods. Existing approaches, however, often rely on linear models or lack sufficient interpretability or flexibility. To…

Compositional data arise in many real-life applications and versatile methods for properly analyzing this type of data in the regression context are needed. When parametric assumptions do not hold or are difficult to verify, non-parametric…

In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…

We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other…

We propose a principal components regression method based on maximizing a joint pseudo-likelihood for responses and predictors. Our method uses both responses and predictors to select linear combinations of the predictors relevant for the…

In compositional data, an observation is a vector with non-negative components which sum to a constant, typically 1. Data of this type arise in many areas, such as geology, archaeology, biology, economics and political science amongst…

Conformal prediction provides distribution-free coverage guaranties for regression; yet existing methods assume Euclidean output spaces and produce prediction regions that are poorly calibrated when responses lie on Riemannian manifolds. We…

Regression on manifolds, and, more broadly, statistics on manifolds, has garnered significant importance in recent years due to the vast number of applications for non Euclidean data. Circular data is a classic example, but so is data in…

We discuss Bayesian nonparametric procedures for the regression analysis of compositional responses, that is, data supported on a multivariate simplex. The procedures are based on a modified class of multivariate Bernstein polynomials and…

We propose a supervised principal component regression method for relating functional responses with high dimensional predictors. Unlike the conventional principal component analysis, the proposed method builds on a newly defined expected…

Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to…

For sequences of random backward nested subspaces as occur, say, in dimension reduction for manifold or stratified space valued data, asymptotic results are derived. In fact, we formulate our results more generally for backward nested…