Related papers: On metric choice in dimension reduction for Fr\'ec…
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…
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…
Global Fr\'echet regression is addressed from the observation of a strictly stationary bivariate curve process, evaluated in a finite--dimensional compact differentiable Riemannian manifold, with bounded positive smooth sectional curvature.…
Distance metrics and their nonlinear variant play a crucial role in machine learning based real-world problem solving. We demonstrated how Euclidean and cosine distance measures differ not only theoretically but also in real-world medical…
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…
The \emph{Fr\'echet distance} is a well studied similarity measures between curves. The \emph{discrete Fr\'echet distance} is an analogous similarity measure, defined for a sequence $A$ of $m$ points and a sequence $B$ of $n$ points, where…
Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which…
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…
It has previously been shown that response transformations can be very effective in improving dimension reduction outcomes for a continuous response. The choice of transformation used can make a big difference in the visualization of the…
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…
We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in generalized regression models on metric spaces based on…
Few-shot learning is a relatively new technique that specializes in problems where we have little amounts of data. The goal of these methods is to classify categories that have not been seen before with just a handful of samples. Recent…
Dimension reduction lies at the heart of many statistical methods. In regression, dimension reduction has been linked to the notion of sufficiency whereby the relation of the response to a set of predictors is explained by a lower…
Local Fr'echet Regression (LFR) is a nonparametric regression method for settings in which the explanatory variable lies in a Euclidean space and the response variable lies in a metric space. It is used to estimate smooth trajectories in…
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…
Object-oriented data analysis is a fascinating and evolving field in modern statistical science, with the potential to make significant contributions to biomedical applications. This statistical framework facilitates the development of new…
Recent advances in generative modeling have led to an increased interest in the study of statistical divergences as means of model comparison. Commonly used evaluation methods, such as the Frechet Inception Distance (FID), correlate well…
This paper proposes a method to detect change points in dynamic social networks using Fr\'echet statistics. We address two main questions: (1) what metric can quantify the distances between graph Laplacians in a dynamic network and enable…
To consider model uncertainty in global Fr\'{e}chet regression and improve density response prediction, we propose a frequentist model averaging method. The weights are chosen by minimizing a cross-validation criterion based on Wasserstein…
Signal averaging is the process that consists in computing a mean shape from a set of noisy signals. In the presence of geometric variability in time in the data, the usual Euclidean mean of the raw data yields a mean pattern that does not…