Related papers: Nonlinear Multivariate Function-on-function Regres…
This paper studies the case of possibly high-dimensional covariates in the regression discontinuity design (RDD) analysis. In particular, we propose estimation and inference methods for the RDD models with covariate selection which perform…
Applications of functional data with large numbers of predictors have grown precipitously in recent years, driven, in part, by rapid advances in genotyping technologies. Given the large numbers of genetic mutations encountered in genetic…
We propose estimators based on kernel ridge regression for nonparametric causal functions such as dose, heterogeneous, and incremental response curves. Treatment and covariates may be discrete or continuous in general spaces. Due to a…
The prevalence of spatially referenced multivariate data has impelled researchers to develop a procedure for the joint modeling of multiple spatial processes. This ordinarily involves modeling marginal and cross-process dependence for any…
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…
Regression models with a response variable taking values in a Hilbert space and hybrid covariates are considered. This means two sets of regressors are allowed, one of finite dimension and a second one functional with values in a Hilbert…
In this paper we propose a multivariate ordinal regression model which allows the joint modeling of three-dimensional panel data containing both repeated and multiple measurements for a collection of subjects. This is achieved by a…
We propose a Bayesian modeling framework for jointly analyzing multiple functional responses of different types (e.g. binary and continuous data). Our approach is based on a multivariate latent Gaussian process and models the dependence…
To characterize the function space explored by neural networks (NNs) is an important aspect of learning theory. In this work, noticing that a multi-layer NN generates implicitly a hierarchy of reproducing kernel Hilbert spaces (RKHSs) -…
In this work we propose a generalized additive functional regression model for partially observed functional data. Our approach accommodates functional predictors of varying dimensions without requiring imputation of missing observations.…
We consider the problem of constructing a regression model with a functional predictor and a functional response. We extend the functional linear model to the quadratic model, where the quadratic term also takes the interaction between the…
In nonparametric regression analysis, errors are possibly correlated in practice, and neglecting error correlation can undermine most bandwidth selection methods. When no prior knowledge or parametric form of the correlation structure is…
In this work, we address optimization problems where the objective function is a nonlinear function of an expected value, i.e., compositional stochastic {strongly convex programs}. We consider the case where the decision variable is not…
In this paper we estimate the dynamic parameters of a time-varying coefficient model through radial kernel functions in the context of a longitudinal study. Our proposal is based on a linear combination of weighted kernel functions…
We propose a novel distributional regression model for a multivariate response vector based on a copula process over the covariate space. It uses the implicit copula of a Gaussian multivariate regression, which we call a ``regression…
Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data, and thus, a key enabler for safe learning-based control. In this domain, kernel methods such as Gaussian process…
This paper derives a new class of vector-valued reproducing kernel Hilbert spaces (vRKHS) defined in terms of operator-valued kernels for the representation of functional uncertainty arising in nonparametric adaptive control methods. These…
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…
We investigate structured sparsity methods for variable selection in regression problems where the target depends nonlinearly on the inputs. We focus on general nonlinear functions not limiting a priori the function space to additive…
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…