English
Related papers

Related papers: Robust Sufficient Dimension Reduction via $\alpha$…

200 papers

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…

Machine Learning · Statistics 2024-02-28 Xinyu Li , Jianjun Xu , Wenquan Cui , Haoyang Cheng

The singular value decomposition (SVD) is a crucial tool in machine learning and statistical data analysis. However, it is highly susceptible to outliers in the data matrix. Existing robust SVD algorithms often sacrifice speed for…

Machine Learning · Statistics 2024-02-16 Sangil Han , Kyoowon Kim , Sungkyu Jung

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…

Methodology · Statistics 2023-07-18 Tharindu P. De Alwis , S. Yaser Samadi , Jiaying Weng

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…

Statistics Theory · Mathematics 2012-11-15 Xin Chen , Changliang Zou , R. Dennis Cook

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…

Methodology · Statistics 2024-09-05 Zheng Li , Yunhao Wang , Wei Gao , Hon Keung Tony Ng

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…

Computation · Statistics 2020-12-16 Lei Yan , Xin Chen

Nonlinear sufficient dimension reduction\citep{libing_generalSDR}, which constructs nonlinear low-dimensional representations to summarize essential features of high-dimensional data, is an important branch of representation learning.…

Machine Learning · Statistics 2025-02-24 Hang Yuan , Christina Dan Wang , Zhou Yu

Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…

Optimization and Control · Mathematics 2023-11-01 Shiyi Jiang , Jianqiang Cheng , Kai Pan , Zuo-Jun Max Shen

We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of negligible variation for the response surface. These directions span the orthogonal complement of the minimal space…

Machine Learning · Computer Science 2014-08-15 Bing Li , Hongyuan Zha , Francesca Chiaromonte

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…

Methodology · Statistics 2025-09-16 Hongying Li , Minyi Zhu , Yaqi Cao , Xinyi Xu

Sufficient dimension reduction is used pervasively as a supervised dimension reduction approach. Most existing sufficient dimension reduction methods are developed for data with a continuous response and may have an unsatisfactory…

Machine Learning · Computer Science 2021-02-03 Cheng Meng , Jun Yu , Jingyi Zhang , Ping Ma , Wenxuan Zhong

Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has…

Statistics Theory · Mathematics 2023-09-26 Xing Yang , Jianjun Xu

A new dimension reduction (DR) method for data sets is proposed by autonomous deforming of data manifolds. The deformation is guided by the proposed deforming vector field, which is defined by two kinds of virtual interactions between data…

Machine Learning · Computer Science 2021-10-22 Xiaodong Zhuang

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…

Methodology · Statistics 2022-02-03 Yuexiao Dong , Abdul-Nasah Soale , Michael D. Power

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…

Methodology · Statistics 2020-10-29 Youngjoo Cho , Debashis Ghosh

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…

Machine Learning · Computer Science 2021-06-04 Quanming Yao , Hangsi Yang , En-Liang Hu , James Kwok

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…

Machine Learning · Computer Science 2026-05-28 Sai-Aakash Ramesh , Archit Sood , Andrew Corbett , Tim Dodwell

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…

Methodology · Statistics 2022-12-08 Qi Zhang , Lingzhou Xue , Bing Li

Sliced inverse regression (SIR, Li 1991) is a pioneering work and the most recognized method in sufficient dimension reduction. While promising progress has been made in theory and methods of high-dimensional SIR, two remaining challenges…

Methodology · Statistics 2023-04-14 Qing Mai , Xiaofeng Shao , Runmin Wang , Xin Zhang

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…

Numerical Analysis · Mathematics 2018-12-12 Andrew T. Glaws , Paul G. Constantine , R. Dennis Cook