Related papers: Sliced Inverse Moment Regression Using Weighted Ch…
In the regression setting, dimension reduction allows for complicated regression structures to be detected via visualization in a low-dimension framework. However, some popular dimension reduction methodologies fail to achieve this aim when…
Dimension reduction techniques, such as Sufficient Dimension Reduction (SDR), are indispensable for analyzing high-dimensional datasets. This paper introduces a novel SDR method named Principal Square Response Forward Regression (PSRFR) for…
A major family of sufficient dimension reduction (SDR) methods, called inverse regression, commonly require the distribution of the predictor $X$ to have a linear $E(X|\beta^\mathsf{T}X)$ and a degenerate $\mathrm{var}(X|\beta^\mathsf{T}X)$…
This work focuses on the issue of variable selection in functional regression. Unlike most work in this framework, our approach does not select isolated points in the definition domain of the predictors, nor does it rely on the expansion of…
In this paper, we prove that functional sliced inverse regression (FSIR) achieves the optimal (minimax) rate for estimating the central space in functional sufficient dimension reduction problems. First, we provide a concentration…
We consider forecasting a single time series using a large number of predictors in the presence of a possible nonlinear forecast function. Assuming that the predictors affect the response through the latent factors, we propose to first…
This paper presents a unified framework for sufficient dimension reduction (SDR) that generalizes several existing SDR techniques and offers new insights into the connection between inverse conditional moment independence and dimension…
The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…
We study the following basic machine learning task: Given a fixed set of $d$-dimensional input points for a linear regression problem, we wish to predict a hidden response value for each of the points. We can only afford to attain the…
Data visualization and dimension reduction for regression between a general metric space-valued response and Euclidean predictors is proposed. Current Fr\'ech\'et dimension reduction methods require that the response metric space be…
Sufficient dimension reduction (SDR) provides a framework for reducing the predictor space dimension in regression problems. We consider SDR in the context of deterministic functions of several variables such as those arising in computer…
We introduce a new sparse sliced inverse regression estimator called Cholesky matrix penalization and its adaptive version for achieving sparsity in estimating the dimensions of the central subspace. The new estimators use the Cholesky…
The ``curse of dimensionality'' has remained a challenge for high-dimensional data analysis in statistics. The sliced inverse regression (SIR) and canonical correlation (CANCOR) methods aim to reduce the dimensionality of data by replacing…
Based on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS-based Double SIR) to nonlinear dimension reduction for survival data is proposed and discussed. An…
We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of small variation in the response. These directions span the orthogonal complement of the minimal space relevant for the…
We present a new and general method of weighted least square univariate regression where the dependent variable is expanded as a series of suitably chosen functions of the independent variables. Each term of the series is obtained by an…
In this paper, we address the inference problem in high-dimensional linear expectile regression. We transform the expectile loss into a weighted-least-squares form and apply a de-biased strategy to establish Wald-type tests for multiple…
We propose a supervised principal component regression method for relating functional responses with high dimensional predictors. Unlike the conventional principal component analysis, the proposed method builds on a newly defined expected…
Online dimension reduction is a common method for high-dimensional streaming data processing. Online principal component analysis, online sliced inverse regression, online kernel principal component analysis and other methods have been…
The central subspace of a pair of random variables $(y,x) \in \mathbb{R}^{p+1}$ is the minimal subspace $\mathcal{S}$ such that $y \perp \hspace{-2mm} \perp x\mid P_{\mathcal{S}}x$. In this paper, we consider the minimax rate of estimating…