Related papers: Additive Models for Symmetric Positive-Definite Ma…
In this paper, we study an additive model where the response variable is Hilbert-space-valued and predictors are multivariate Euclidean, and both are possibly imperfectly observed. Considering Hilbert-space-valued responses allows to cover…
In this paper, we target the problem of sufficient dimension reduction with symmetric positive definite matrices valued responses. We propose the intrinsic minimum average variance estimation method and the intrinsic outer product gradient…
Regression analysis for responses taking values in general metric spaces has received increasing attention, particularly for settings with Euclidean predictors $X \in \mathbb{R}^p$ and non-Euclidean responses $Y$ in metric spaces. While…
The "shape" of a planar curve and/or landmark configuration is considered its equivalence class under translation, rotation and scaling, its "form" its equivalence class under translation and rotation while scale is preserved. We extend…
Symmetric Positive Definite (SPD) matrices have received wide attention in machine learning due to their intrinsic capacity to encode underlying structural correlation in data. Many successful Riemannian metrics have been proposed to…
We present a new Riemannian metric, termed Log-Cholesky metric, on the manifold of symmetric positive definite (SPD) matrices via Cholesky decomposition. We first construct a Lie group structure and a bi-invariant metric on Cholesky space,…
Modeling non-Euclidean data is drawing extensive attention along with the unprecedented successes of deep neural networks in diverse fields. Particularly, a symmetric positive definite matrix is being actively studied in computer vision,…
Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-valued features, researchers have started extending Euclidean…
In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…
This paper presents a Bayesian regression model relating scalar outcomes to brain functional connectivity represented as symmetric positive definite (SPD) matrices. Unlike many proposals that simply vectorize the matrix-valued connectivity…
Symmetric Positive Definite (SPD) matrix learning methods have become popular in many image and video processing tasks, thanks to their ability to learn appropriate statistical representations while respecting Riemannian geometry of…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
In many complex applications, data heterogeneity and homogeneity exist simultaneously. Ignoring either one will result in incorrect statistical inference. In addition, coping with complex data that are non-Euclidean becomes more common. To…
Inspired by logistic regression, we introduce a regression model for data tuples consisting of a binary response and a set of covariates residing in a metric space without vector structures. Based on the proposed model we also develop a…
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
Consider a multinomial regression model where the response, which indicates a unit's membership in one of several possible unordered classes, is associated with a set of predictor variables. Such models typically involve a matrix of…
Similar to variable selection in the linear regression model, selecting significant components in the popular additive regression model is of great interest. However, such components are unknown smooth functions of independent variables,…
Ensemble of regression trees have become popular statistical tools for the estimation of conditional mean given a set of predictors. However, quantile regression trees and their ensembles have not yet garnered much attention despite the…
In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…
In this article, we develop a semiparametric Bayesian estimation and model selection approach for partially linear additive models in conditional quantile regression. The asymmetric Laplace distribution provides a mechanism for Bayesian…