Related papers: Variable Selection for Additive Global Fr\'echet R…
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…
Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…
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 presents new results on Functional Analysis of Variance for fixed effect models with correlated Hilbert-valued Gaussian error components. The geometry of the Reproducing Kernel Hilbert Space (RKHS) of the error term is considered…
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…
Fr\'echet regression extends linear regression to model complex responses in metric spaces, making it particularly relevant for multi-label regression, where eachinstance can have multiple associated labels. However, addressing noise and…
In multivariate regression, when covariates are numerous, it is often reasonable to assume that only a small number of them has predictive information. In some medical applications for instance, it is believed that only a few genes out of…
Consider the problem: given the data pair $(\mathbf{x}, \mathbf{y})$ drawn from a population with $f_*(x) = \mathbf{E}[\mathbf{y} | \mathbf{x} = x]$, specify a neural network model and run gradient flow on the weights over time until…
This paper combines vector-valued reproducing kernel Hilbert space (vRKHS) embedding with robust adaptive observation, yielding an algorithm that is both non-parametric and robust. The main contribution of this paper lies in the ability of…
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…
Modern regression analysis often involves responses and predictors taking values in the same or distinct metric spaces. To rank non-Euclidean heterogeneous predictors in regression by explanatory strength, analogous to the classical $R^2$,…
We propose a nonlinear function-on-function regression model where both the covariate and the response are random functions. The nonlinear regression is carried out in two steps: we first construct Hilbert spaces to accommodate the…
Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional…
We consider the problem of variable selection in high-dimensional sparse additive models. We focus on the case that the components belong to nonparametric classes of functions. The proposed method is motivated by geometric considerations in…
In partially linear additive models the response variable is modelled with a linear component on a subset of covariates and an additive component in which the rest of the covariates enter to the model as a sum of univariate unknown…
Recently, some works have suggested methods to combine variational probabilistic inference with Monte Carlo sampling. One promising approach is via local optimal transport. In this approach, a gradient steepest descent method based on local…
Learning with Reproducing Kernel Hilbert Spaces (RKHS) has been widely used in many scientific disciplines. Because a RKHS can be very flexible, it is common to impose a regularization term in the optimization to prevent overfitting.…
In this paper, an adaptive non-parametric method is proposed to estimate the scalar-valued nonlinear function that appears in uncertain systems governed by ordinary differential equations (ODEs). By employing an infinite-dimensional…
Structured additive distributional regression models offer a versatile framework for estimating complete conditional distributions by relating all parameters of a parametric distribution to covariates. Although these models efficiently…
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…