Related papers: Varying-Coefficient Fr\'echet Regression
Variational autoencoders (VAEs) have been used extensively to discover low-dimensional latent factors governing neural activity and animal behavior. However, without careful model selection, the uncovered latent factors may reflect noise in…
This paper investigates the integration of gradient boosted decision trees and varying coefficient models. We introduce the tree boosted varying coefficient framework which justifies the implementation of decision tree boosting as the…
We address the problem of constructing varying-coefficient models based on basis expansions along with the technique of regularization. A crucial point in our modeling procedure is the selection of smoothing parameters in the regularization…
We consider covariate adjusted regression (CAR), a regression method for situations where predictors and response are observed after being distorted by a multiplicative factor. The distorting factors are unknown functions of an observable…
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…
In this paper we introduce new estimators of the coefficient functions in the varying coefficient regression model. The proposed estimators are obtained by projecting the vector of the full-dimensional kernel-weighted local polynomial…
This paper concerns the robust regression model when the number of predictors and the number of observations grow in a similar rate. Theory for M-estimators in this regime has been recently developed by several authors [El Karoui et al.,…
Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…
Motivated by recent work studying massive imaging data in the neuroimaging literature, we propose multivariate varying coefficient models (MVCM) for modeling the relation between multiple functional responses and a set of covariates. We…
An increasing array of biomedical and computer vision applications requires the predictive modeling of complex data, for example images and shapes. The main challenge when predicting such objects lies in the fact that they do not comply to…
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…
We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other…
This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient…
This study examines the varying coefficient model in tail index regression. The varying coefficient model is an efficient semiparametric model that avoids the curse of dimensionality when including large covariates in the model. In fact,…
Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data…
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…
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…
A nonparametric regression setting is considered with a real-valued covariate and responses from a metric space. One may approach this setting via Fr\'echet regression, where the value of the regression function at each point is estimated…
This paper develops a flexible method for decreasing the variance of estimators for complex experiment effect metrics (e.g. ratio metrics) while retaining asymptotic unbiasedness. This method uses the auxiliary information about the…
We consider the problem of variable selection in varying-coefficient functional linear models, where multiple predictors are functions and a response is a scalar and depends on an exogenous variable. The varying-coefficient functional…