Related papers: Sufficient dimension reduction for regression with…
We present a new methodology for sufficient dimension reduction (SDR). Our methodology derives directly from the formulation of SDR in terms of the conditional independence of the covariate $X$ from the response $Y$, given the projection of…
As its name suggests, sufficient dimension reduction (SDR) targets to estimate a subspace from data that contains all information sufficient to explain a dependent variable. Ample approaches exist to SDR, some of the most recent of which…
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…
Sufficient dimension reduction (SDR) is a popular class of regression methods which aim to find a small number of linear combinations of covariates that capture all the information of the responses i.e., a central subspace. The majority of…
Parameter reduction can enable otherwise infeasible design and uncertainty studies with modern computational science models that contain several input parameters. In statistical regression, techniques for sufficient dimension reduction…
Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the…
Prediction, in regression and classification, is one of the main aims in modern data science. When the number of predictors is large, a common first step is to reduce the dimension of the data. Sufficient dimension reduction (SDR) is a well…
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…
Sufficient dimension reduction (SDR) is continuing an active research field nowadays for high dimensional data. It aims to estimate the central subspace (CS) without making distributional assumption. To overcome the large-$p$-small-$n$…
This is a tutorial and survey paper on various methods for Sufficient Dimension Reduction (SDR). We cover these methods with both statistical high-dimensional regression perspective and machine learning approach for dimensionality…
Given observations of a collection of covariates and responses $(Y, X) \in \mathbb{R}^p \times \mathbb{R}^q$, sufficient dimension reduction (SDR) techniques aim to identify a mapping $f: \mathbb{R}^q \rightarrow \mathbb{R}^k$ with $k \ll…
Causal inference plays an important role in under standing the underlying mechanisation of the data generation process across various domains. It is challenging to estimate the average causal effect and individual causal effects from…
We review sufficient dimension reduction (SDR) estimators with multivariate response in this paper. A wide range of SDR methods are characterized as inverse regression SDR estimators or forward regression SDR estimators. The inverse…
In this article, we propose a general nonlinear sufficient dimension reduction (SDR) framework when both the predictor and response lie in some general metric spaces. We construct reproducing kernel Hilbert spaces whose kernels are fully…
Considering the case where the response variable is a categorical variable and the predictor is a random function, two novel functional sufficient dimensional reduction (FSDR) methods are proposed based on mutual information and square loss…
Sufficient dimension reduction (SDR) in regression, which reduces the dimension by replacing original predictors with a minimal set of their linear combinations without loss of information, is very helpful when the number of predictors is…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
We consider the problem of sufficient dimensionality reduction (SDR), where the high-dimensional observation is transformed to a low-dimensional sub-space in which the information of the observations regarding the label variable is…
In this work, we develop a new theory and method for sufficient dimension reduction (SDR) in single-index models, where SDR is a sub-field of supervised dimension reduction based on conditional independence. Our work is primarily motivated…
We introduce a novel sufficient dimension-reduction (SDR) method which is robust against outliers using $\alpha$-distance covariance (dCov) in dimension-reduction problems. Under very mild conditions on the predictors, the central subspace…