Related papers: Nonlinear global Fr\'echet regression for random o…

In this paper, we propose a dimension reduction model for spatially dependent variables. Namely, we investigate an extension of the \emph{inverse regression} method under strong mixing condition. This method is based on estimation of the…

We propose a novel Riemannian geometric framework for variational inference in Bayesian models based on the nonparametric Fisher-Rao metric on the manifold of probability density functions. Under the square-root density representation, the…

The functional generalized additive model (FGAM) provides a more flexible nonlinear functional regression model than the well-studied functional linear regression model. This paper restricts attention to the FGAM with identity link and…

The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…

We prove weak convergence in a separable Hilbert space for estimators of high-dimensional regression coefficients, which yields asymptotic normality and enables direct use of standard asymptotic tools such as the continuous mapping theorem.…

The goal of nonparametric regression is to recover an underlying regression function from noisy observations, under the assumption that the regression function belongs to a pre-specified infinite dimensional function space. In the online…

Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational…

We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…

Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear…

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…

In this paper, we present an efficient algorithm for solving a class of chance constrained optimization under non-parametric uncertainty. Our algorithm is built on the possibility of representing arbitrary distributions as functions in…

Refining low-resolution (LR) spatial fields with high-resolution (HR) information, often known as statistical downscaling, is challenging as the diversity of spatial datasets often prevents direct matching of observations. Yet, when LR…

We study distribution-on-distribution regression problems in which a response distribution depends on multiple distributional predictors. Such settings arise naturally in applications where the outcome distribution is driven by several…

As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be…

The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of…

This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the…

This paper extends a conventional, general framework for online adaptive estimation problems for systems governed by unknown nonlinear ordinary differential equations. The central feature of the theory introduced in this paper represents…

Incomplete covariate vectors are known to be problematic for estimation and inferences on model parameters, but their impact on prediction performance is less understood. We develop an imputation-free method that builds on a random…

This paper derives error bounds for regression in continuous time over subsets of certain types of Riemannian manifolds.The regression problem is typically driven by a nonlinear evolution law taking values on the manifold, and it is cast as…

We present an operator-free, measure-theoretic approach to the conditional mean embedding (CME) as a random variable taking values in a reproducing kernel Hilbert space. While the kernel mean embedding of unconditional distributions has…