Related papers: Sufficient dimension reduction for regression with…
Sufficient dimension reduction (SDR) methods aim to identify a dimension reduction subspace (DRS) that preserves all the information about the conditional distribution of a response given its predictor. Traditional SDR methods determine the…
Nowadays, massive datasets are typically dispersed across multiple locations, encountering dual challenges of high dimensionality and huge sample size. Therefore, it is necessary to explore sufficient dimension reduction (SDR) methods 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 $\mathrm{var}(X|\beta^\mathsf{T}X)$…
A bottleneck of sufficient dimension reduction (SDR) in the modern era is that, among numerous methods, only the sliced inverse regression (SIR) is generally applicable under the high-dimensional settings. The higher-order inverse…
Sufficient dimension reduction (SDR) is a popular tool in regression analysis, which replaces the original predictors with a minimal set of their linear combinations. However, the estimated linear combinations generally contain all original…
Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when…
There has been a lot of interest in sufficient dimension reduction (SDR) methodologies as well as nonlinear extensions in the statistics literature. In this note, we use classical results regarding metric spaces and positive definite…
In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The linear subspace spanned by these…
Sufficient dimension reduction (SDR), which seeks a lower-dimensional subspace of the predictors containing regression or classification information has been popular in a machine learning community. In this work, we present a new R software…
We explore two primary classes of approaches to dimensionality reduction (DR): Independent Dimensionality Reduction (IDR) and Simultaneous Dimensionality Reduction (SDR). In IDR methods, of which Principal Components Analysis is a…
Supervised dimension reduction (SDR) has been a topic of growing interest in data science, as it enables the reduction of high-dimensional covariates while preserving the functional relation with certain response variables of interest.…
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…
The purpose of sufficient dimension reduction (SDR) is to find the low-dimensional subspace of input features that is sufficient for predicting output values. In this paper, we propose a novel distribution-free SDR method called sufficient…
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…
Sufficient dimension reduction (SDR) methods, which often rely on class precision matrices, are widely used in supervised statistical classification problems. However, when class-specific sample sizes are small relative to the original…
Sufficient dimension reduction (SDR) using distance covariance (DCOV) was recently proposed as an approach to dimension-reduction problems. Compared with other SDR methods, it is model-free without estimating link function and does not…
In this paper, we propose a dimension reduction model for spatially dependent variables. Namely, we investigate an extension of the \emph{inverse regression} method under strong mixing condition. This method is based on estimation of the…
With the rapid development of data collection techniques, complex data objects that are not in the Euclidean space are frequently encountered in new statistical applications. Fr\'echet regression model (Peterson & M\"uller 2019) provides a…
For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if $\rho=\lim\frac{p}{n}=0$, where $p$ is the dimension…
Many machine learning applications deal with high dimensional data. To make computations feasible and learning more efficient, it is often desirable to reduce the dimensionality of the input variables by finding linear combinations of the…