Related papers: The Fr\'echet correlation coefficient for heteroge…
As a growing number of problems involve variables that are random objects, the development of models for such data has become increasingly important. This paper introduces a novel varying-coefficient Fr\'echet regression model that extends…
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…
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…
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…
Fr\'echet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables. However, its practical applicability has been hindered by its reliance on ideal scenarios with abundant and…
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 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…
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…
Fr\'echet regression extends classical regression methods to non-Euclidean metric spaces, enabling the analysis of data relationships on complex structures such as manifolds and graphs. This work establishes a rigorous theoretical analysis…
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…
We present a novel framework for variable selection in Fr\'echet regression with responses in general metric spaces, a setting increasingly relevant for analyzing non-Euclidean data such as probability distributions and covariance matrices.…
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…
Nonlinear sufficient dimension reduction\citep{libing_generalSDR}, which constructs nonlinear low-dimensional representations to summarize essential features of high-dimensional data, is an important branch of representation learning.…
We consider the problem of estimating the Fr\'echet and conditional Fr\'echet mean from data taking values in separable metric spaces. Unlike Euclidean spaces, where well-established methods are available, there is no practical estimator…
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…
Modern-day problems in statistics often face the challenge of exploring and analyzing complex non-Euclidean object data that do not conform to vector space structures or operations. Examples of such data objects include covariance matrices,…
With the increasing availability of non-Euclidean data objects, statisticians are faced with the task of developing appropriate statistical methods for their analysis. For regression models in which the predictors lie in $\mathbb{R}^p$ and…
Distribution-as-response regression problems are gaining wider attention, especially within biomedical settings where observation-rich patient specific data sets are available, such as feature densities in CT scans (Petersen et al., 2021)…
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…
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…