Related papers: Enhancing Sufficient Dimension Reduction via Helli…

The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…

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…

Sufficient dimension reduction (SDR) is an effective tool for regression models, offering a viable approach to address and analyze the nonlinear nature of regression problems. This paper introduces the itdr R package, a comprehensive and…

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…

Dimensionality reduction is a topic of recent interest. In this paper, we present the classification constrained dimensionality reduction (CCDR) algorithm to account for label information. The algorithm can account for multiple classes as…

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.…

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…

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,…

Identifying low-dimensional sufficient structures in nonlinear sufficient dimension reduction (SDR) has long been a fundamental yet challenging problem. Most existing methods lack theoretical guarantees of exhaustiveness in identifying…

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…

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…

We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…

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…

We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…

Dimension reduction lies at the heart of many statistical methods. In regression, dimension reduction has been linked to the notion of sufficiency whereby the relation of the response to a set of predictors is explained by a lower…

Learning representations that capture both intrinsic data geometry and target-relevant structure remains a fundamental challenge, particularly in settings where data reduction must balance compression with predictive fidelity. While…

This paper investigates the connection between neural networks and sufficient dimension reduction (SDR), demonstrating that neural networks inherently perform SDR in regression tasks under appropriate rank regularizations. Specifically, the…

We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…

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…

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…