相关论文: Fr\'echet Sufficient Dimension Reduction for Rando…

Sufficient dimension reduction [J. Amer. Statist. Assoc. 86 (1991) 316-342] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an…

As a fundamental task in natural language processing, word embedding converts each word into a representation in a vector space. A challenge with word embedding is that as the vocabulary grows, the vector space's dimension increases, which…

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…

A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…

Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including…

In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…

Nonparametric mean function regression with repeated measurements serves as a cornerstone for many statistical branches, such as longitudinal/panel/functional data analysis. In this work, we investigate this problem using fully connected…

The weighted Euclidean norm $\|x\|_w$ of a vector $x\in \mathbb{R}^d$ with weights $w\in \mathbb{R}^d$ is the Euclidean norm where the contribution of each dimension is scaled by a given weight. Approaches to dimensionality reduction that…

Machine learning techniques always aim to reduce the generalized prediction error. In order to reduce it, ensemble methods present a good approach combining several models that results in a greater forecasting capacity. The Random Machines…

In this paper, we target the problem of sufficient dimension reduction with symmetric positive definite matrices valued responses. We propose the intrinsic minimum average variance estimation method and the intrinsic outer product gradient…

We consider a class of inverse problems where it is possible to aggregate the results of multiple experiments. This class includes problems where the forward model is the solution operator to linear ODEs or PDEs. The tremendous size of such…

This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression under the covariate shift assumption, utilizing vector-valued reproducing kernel Hilbert spaces (vRKHS). Covariate…

We explore the application of volumetric reconstruction from structured-light sensors in cognitive neuroscience, specifically in the quantification of the size-weight illusion, whereby humans tend to systematically perceive smaller objects…

Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a…

Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…

We study the problem of identifying change points in high-dimensional generalized linear models, and propose an approach based on sample-weighted empirical risk minimization. Our method, Weighted ERM, encodes priors on the change points via…

In this paper, we introduce a wavelet-based method for estimating the EDR space in Li's semiparametric regression model for achieving dimension reduction. This method is obtained by using linear wavelet estimators of the density and…

In this paper, we consider the problem of non-linear dimensionality reduction under uncertainty, both from a theoretical and algorithmic perspectives. Since real-world data usually contain measurements with uncertainties and artifacts, the…

Most data sets comprise of measurements on continuous and categorical variables. In regression and classification Statistics literature, modeling high-dimensional mixed predictors has received limited attention. In this paper we study the…

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.…