Related papers: Metric space valued Fr\'echet regression

Estimating the mean of a random vector from i.i.d. data has received considerable attention, and the optimal accuracy one may achieve with a given confidence is fairly well understood by now. When the data take values in more general metric…

Fr\'echet means, conceptually appealing, generalize the Euclidean expectation to general metric spaces. We explore how well Fr\'echet means can be estimated from independent and identically distributed samples and uncover a fundamental…

Fr\'echet mean and variance provide a way of obtaining mean and variance for general metric space valued random variables and can be used for statistical analysis of data objects that lie in abstract spaces devoid of algebraic structure and…

Increasingly, statisticians are faced with the task of analyzing complex data that are non-Euclidean and specifically do not lie in a vector space. To address the need for statistical methods for such data, we introduce the concept of…

Non-Euclidean data that are indexed with a scalar predictor such as time are increasingly encountered in data applications, while statistical methodology and theory for such random objects are not well developed yet. To address the need for…

The Fr\'echet mean generalizes the concept of a mean to a metric space setting. In this work we consider equivariant estimation of Fr\'echet means for parametric models on metric spaces that are Riemannian manifolds. The geometry and…

We address the problem of testing hypotheses about a specific value of the Fr\'echet mean in metric spaces, extending classical mean testing from Euclidean spaces to more general settings. We extend an Euclidean testing procedure…

This paper introduces a novel uncertainty quantification framework for regression models where the response takes values in a separable metric space, and the predictors are in a Euclidean space. The proposed algorithms can efficiently…

In this article, we study the consistency of the template estimation with the Fr\'echet mean in quotient spaces. The Fr\'echet mean in quotient spaces is often used when the observations are deformed or transformed by a group action. We…

The Fr\'echet mean (or barycenter) generalizes the expectation of a random variable to metric spaces by minimizing the expected squared distance to the random variable. Similarly, the median can be generalized by its property of minimizing…

Fr\'echet regression, or conditional Barycenters, is a flexible framework for modeling relationships between covariates (usually Euclidean) and response variables on general metric spaces, e.g., probability distributions or positive…

Random objects are complex non-Euclidean data taking value in general metric space, possibly devoid of any underlying vector space structure. Such data are getting increasingly abundant with the rapid advancement in technology. Examples…

Local Fr\'echet regression is a nonparametric regression method for metric space valued responses and Euclidean predictors, which can be utilized to obtain estimates of smooth trajectories taking values in general metric spaces from noisy…

Fr\'echet regression extends the principles of linear regression to accommodate responses valued in generic metric spaces. While this approach has primarily focused on exploring relationships between Euclidean predictors and non-Euclidean…

Across many scientific disciplines, multiple observations are collected from the same experimental units, and in modern datasets these observations often arise as non-Euclidean random objects. In such settings, the incorporation of random…

The Frechet mean is a useful description of location for a probability distribution on a metric space that is not necessarily a vector space. This article considers simultaneous estimation of multiple Frechet means from a decision-theoretic…

Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for…

The Fr\'echet regression is a useful method for modeling random objects in a general metric space given Euclidean covariates. However, the conventional approach could be sensitive to outlying objects in the sense that the distance from the…

Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional…

Advancements in data collection have led to increasingly common repeated observations with complex structures in biomedical studies. Treating these observations as random objects, rather than summarizing features as vectors, avoids feature…