Related papers: Convex generalized Fr\'echet means in a metric tre…
The distance on a set is a comparative function. The smaller the distance between two elements of that set, the closer, or more similar, those elements are. Fr\'echet axiomatized the distance into what is today known as a metric. In this…
While there exists a well-developed asymptotic theory of Fr\'echet means of random variables taking values in a general "finite-dimensional" metric space, there are only a few known results in which the random variables can take values in…
A Fr\'echet mean of a random variable $Y$ with values in a metric space $(\mathcal Q, d)$ is an element of the metric space that minimizes $q \mapsto \mathbb E[d(Y,q)^2]$. This minimizer may be non-unique. We study strong laws of large…
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…
This paper investigates the computational geometry relevant to calculations of the Frechet mean and variance for probability distributions on the phylogenetic tree space of Billera, Holmes and Vogtmann, using the theory of probability…
To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Fr\'echet mean. In this…
Recent interest in treespaces as well-founded mathematical domains for phylogenetic inference and statistical analysis for populations of anatomical trees has motivated research into efficient and rigorous methods for optimization problems…
For $1\le p \le \infty$, the Fr\'echet $p$-mean of a probability measure on a metric space is an important notion of central tendency that generalizes the usual notions in the real line of mean ($p=2$) and median ($p=1$). In this work we…
Fr\'echet means of samples from a probability measure $\mu$ on any smoothly stratified metric space M with curvature bounded above are shown to satisfy a central limit theorem (CLT). The methods and results proceed by introducing and…
This article introduces a new class of models for multiple networks. The core idea is to parametrize a distribution on labelled graphs in terms of a Fr\'{e}chet mean graph (which depends on a user-specified choice of metric or graph…
Complex data objects arise in many areas of modern science including evolutionary biology, nueroscience, dynamics of gene expression and medical imaging. Object oriented data analysis (OODA) is the statistical analysis of datasets of…
This paper introduces a novel extension of Fr\'{e}chet means, called \textit{generalized Fr\'{e}chet means} as a comprehensive framework for characterizing features in probability distributions in general topological spaces. The generalized…
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…
We study a generalization of the Fr\'echet mean on metric spaces, which we call $\phi$-means. Our generalization is indexed by a convex function $\phi$. We find necessary and sufficient conditions for $\phi$-means to be finite and provide a…
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…
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…
Samples of phylogenetic trees arise in a variety of evolutionary and biomedical applications, and the Fr\'echet mean in Billera-Holmes-Vogtmann tree space is a summary tree shown to have advantages over other mean or consensus trees.…
Fr\'echet regression is becoming a mainstay in modern data analysis for analyzing non-traditional data types belonging to general metric spaces. This novel regression method is especially useful in the analysis of complex health data such…
Fr\'echet means are a popular type of average for non-Euclidean datasets, defined as those points which minimise the average squared distance to a set of data points. We consider the behaviour of sample Fr\'echet means on normed spaces…
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…