相关论文: Contour regression: A general approach to dimensio…

For the regression model where the errors follow the elliptically contoured distribution (ECD), we consider the least squares (LS), restricted LS (RLS), preliminary test (PT), Stein-type shrinkage (S) and positive-rule shrinkage (PRS)…

Convex regression (CR) is an approach for fitting a convex function to a finite number of observations. It arises in various applications from diverse fields such as statistics, operations research, economics, and electrical engineering.…

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…

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 introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead…

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…

Contrastive dimension reduction (CDR) methods aim to extract signal unique to or enriched in a treatment (foreground) group relative to a control (background) group. This setting arises in many scientific domains, such as genomics, imaging,…

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.…

Deep neural networks have exhibited remarkable performance in image super-resolution (SR) tasks by learning a mapping from low-resolution (LR) images to high-resolution (HR) images. However, the SR problem is typically an ill-posed problem…

Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity…

We propose a novel Fr\'echet sufficient dimension reduction (SDR) method based on kernel distance covariance, tailored for metric space-valued responses such as count data, probability densities, and other complex structures. The method…

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…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

Scene coordinate regression (SCR) methods have emerged as a promising area of research due to their potential for accurate visual localization. However, many existing SCR approaches train on samples from all image regions, including dynamic…

Computer experiments with quantitative and qualitative inputs are widely used to study many scientific and engineering processes. Much of the existing work has focused on design and modeling or process optimization for such experiments.…

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…

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…

Based on the theory of reproducing kernel Hilbert space (RKHS) and semiparametric method, we propose a new approach to nonlinear dimension reduction. The method extends the semiparametric method into a more generalized domain where both 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…

We introduce data structures for solving robust regression through stochastic gradient descent (SGD) by sampling gradients with probability proportional to their norm, i.e., importance sampling. Although SGD is widely used for large scale…