Related papers: Generalized Linear Models for Geometrical Current …
Regression analysis of correlated data, where multiple correlated responses are recorded on the same unit, is ubiquitous in many scientific areas. With the advent of new technologies, in particular high-throughput omics profiling assays,…
Statistical modeling of high-dimensional matrix-valued data motivates the use of a low-rank representation that simultaneously summarizes key characteristics of the data and enables dimension reduction. Low-rank representations commonly…
A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear…
A regression model is proposed for the analysis of an ordinal response variable depending on a set of multiple covariates containing ordinal and potentially other variables. The proportional odds model (McCullagh (1980)) is used for the…
This article develops flexible methodology to study the association between scalar outcomes and functional predictors observed over time, at many instances, in longitudinal studies. We propose a parsimonious modeling framework to study…
This paper introduces a new objective measure for assessing treatment response in asthmatic patients using computed tomography (CT) imaging data. For each patient, CT scans were obtained before and after one year of monoclonal antibody…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
Modeling dynamical systems with ordinary differential equations implies a mechanistic view of the process underlying the dynamics. However in many cases, this knowledge is not available. To overcome this issue, we introduce a general…
Standard geostatistical models assume second order stationarity of the underlying Random Function. In some instances, there is little reason to expect the spatial dependence structure to be stationary over the whole region of interest. In…
This paper develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of…
Deep Gaussian Processes (DGPs) leverage a compositional structure to model non-stationary processes. DGPs typically rely on local inducing point approximations across intermediate GP layers. Recent advances in DGP inference have shown that…
A general formulation of the linear model with functional (random) explanatory variable $X = X(t), t \in T$ , and scalar response Y is proposed. It includes the standard functional linear model, based on the inner product in the space…
In statistical learning, identifying underlying structures of true target functions based on observed data plays a crucial role to facilitate subsequent modeling and analysis. Unlike most of those existing methods that focus on some…
Undirected graphical models are widely used to model the conditional independence structure of vector-valued data. However, in many modern applications, for example those involving EEG and fMRI data, observations are more appropriately…
We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The task is estimating/tracking nonlinear functions which are supposed…
We present a prediction framework for ordinal models: we introduce optimal predictions using loss functions and give the explicit form of the Least-Absolute-Deviation prediction for these models. Then, we reformulate an ordinal model with…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
We present a low-order modeling technique for actuated flows based on the regularization of an inverse problem. The inverse problem aims at minimizing the error between the model predictions and some reference simulations. The parameters to…
This paper generalizes regularized regression problems in a hyper-reproducing kernel Hilbert space (hyper-RKHS), illustrates its utility for kernel learning and out-of-sample extensions, and proves asymptotic convergence results for the…
Purpose: To quantify the ability of correlation and regression analysis to extract the normal lung dose-response function from dose volume histogram (DVH) data. Methods: A local injury model is adopted, in which radiation-induced damage…