Related papers: Kernel dimension reduction in regression

We introduce a class of dimension reduction estimators based on an ensemble of the minimum average variance estimates of functions that characterize the central subspace, such as the characteristic functions, the Box--Cox transformations…

Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…

We introduce a principal support vector machine (PSVM) approach that can be used for both linear and nonlinear sufficient dimension reduction. The basic idea is to divide the response variables into slices and use a modified form of support…

This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…

Accurate and efficient environment representation is crucial for robotic applications such as motion planning, manipulation, and navigation. Signed distance functions (SDFs) have emerged as a powerful representation for encoding distance to…

We employ distribution regression (DR) to estimate the joint distribution of two outcome variables conditional on chosen covariates. While Bivariate Distribution Regression (BDR) is useful in a variety of settings, it is particularly…

We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…

Dirichlet regression models are suitable for compositional data, in which the response variable represents proportions that sum to one. However, there are still no well-established methods for constructing valid prediction sets in this…

Non-linear systems of differential equations have attracted the interest in fields like system biology, ecology or biochemistry, due to their flexibility and their ability to describe dynamical systems. Despite the importance of such models…

A model for the prediction of functional time series is introduced, where observations are assumed to be continuous random functions. We model the dependence of the data with a nonstandard autoregressive structure, motivated in terms of the…

The strategy of early stopping is a regularization technique based on choosing a stopping time for an iterative algorithm. Focusing on non-parametric regression in a reproducing kernel Hilbert space, we analyze the early stopping strategy…

We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as…

In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…

Dimensionality reduction (DR) is a popular method for preparing and analyzing high-dimensional data. Reduced data representations are less computationally intensive and easier to manage and visualize, while retaining a significant…

When facing multivariate covariates, general semiparametric regression techniques come at hand to propose flexible models that are unexposed to the curse of dimensionality. In this work a semiparametric copula-based estimator for…

In a high-dimensional regression framework, we study consequences of the naive two-step procedure where first the dimension of the input variables is reduced and second, the reduced input variables are used to predict the output variable…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

Simultaneous variable selection and statistical inference is challenging in high-dimensional data analysis. Most existing post-selection inference methods require explicitly specified regression models, which are often linear, as well as…

In the regression problem, L1 and L2 are the most commonly used loss functions, which produce mean predictions with different biases. However, the predictions are neither robust nor adequate enough since they only capture a few conditional…

We derive and prove the path-kernel formula for the linear response (parameter-derivative of averaged statistics) of SDEs. The parameter may affect the drift coefficient, the diffusion coefficient, and the initial condition. The formula…