Related papers: Metric space valued Fr\'echet regression
Fr\'echet means on non-Euclidean spaces may exhibit nonstandard asymptotic rates rendering quantile-based asymptotic inference inapplicable. We show here that this affects, among others, all circular distributions whose support exceeds a…
We consider two statistical problems at the intersection of functional and non-Euclidean data analysis: the determination of a Fr\'echet mean in the Wasserstein space of multivariate distributions; and the optimal registration of deformed…
Combining several independent measurements of the same physical quantity is one of the most important tasks in metrology. Small samples, biased input estimates, not always adequate reported uncertainties, and unknown error distribution make…
We show that the Fr\'echet distance of two-dimensional parametrised surfaces in a metric space is computable in the bit-model of real computation. An analogous result in the real RAM model for piecewise-linear surfaces has recently been…
This paper is concerned with a new approach to coorbit space theory. Usually, coorbit spaces are defined by collecting all distributions for which the voice transform associated with a square-integrable group representation possesses a…
Data visualization and dimension reduction for regression between a general metric space-valued response and Euclidean predictors is proposed. Current Fr\'ech\'et dimension reduction methods require that the response metric space be…
In this paper we investigate algorithmic randomness on more general spaces than the Cantor space, namely computable metric spaces. To do this, we first develop a unified framework allowing computations with probability measures. We show…
The existing Fr\'echet regression is actually defined within a linear framework, since the weight function in the Fr\'echet objective function is linearly defined, and the resulting Fr\'echet regression function is identified to be a linear…
Existing concentration bounds for bounded vector-valued random variables include extensions of the scalar Hoeffding and Bernstein inequalities. While the latter is typically tighter, it requires knowing a bound on the variance of the random…
Estimation of a conditional mean (linking a set of features to an outcome of interest) is a fundamental statistical task. While there is an appeal to flexible nonparametric procedures, effective estimation in many classical nonparametric…
We propose an efficient algorithm for learning mappings between two metric spaces, $\X$ and $\Y$. Our procedure is strongly Bayes-consistent whenever $\X$ and $\Y$ are topologically separable and $\Y$ is "bounded in expectation" (our term;…
There is growing interest in developing statistical estimators that achieve exponential concentration around a population target even when the data distribution has heavier than exponential tails. More recent activity has focused on…
Advancements in modern science have led to the increasing availability of non-Euclidean data in metric spaces. This paper addresses the challenge of modeling relationships between non-Euclidean responses and multivariate Euclidean…
Single index models provide an effective dimension reduction tool in regression, especially for high dimensional data, by projecting a general multivariate predictor onto a direction vector. We propose a novel single-index model for…
In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fr\'echet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means.…
Linear regression is widely used to model relationships between responses and predictors. In modern applications, one encounters data where the responses are non-Euclidean random objects situated in a metric space, paired with Euclidean…
This article provides an exposition of recent methodologies for nonparametric analysis of digital observations on images and other non-Euclidean objects. Fr\'echet means of distributions on metric spaces, such as manifolds and stratified…
In applied research, Lee (2009) bounds are widely applied to bound the average treatment effect in the presence of selection bias. This paper extends the methodology of Lee bounds to accommodate outcomes in a general metric space, such as…
The extension of bivariate measures of dependence to non-Euclidean spaces is a challenging problem. The non-linear nature of these spaces makes the generalisation of classical measures of linear dependence (such as the covariance) not…
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…