scholarly journals Cumulative Median Estimation for Sufficient Dimension Reduction

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 138-145
Author(s):  
Stephen Babos ◽  
Andreas Artemiou
Keyword(s):  
Dimension Reduction ◽  
Real Data ◽  
Sufficient Dimension Reduction

In this paper, we present the Cumulative Median Estimation (CUMed) algorithm for robust sufficient dimension reduction. Compared with non-robust competitors, this algorithm performs better when there are outliers present in the data and comparably when outliers are not present. This is demonstrated in simulated and real data experiments.

Sparse sufficient dimension reduction with heteroscedasticity

2021 ◽  
pp. 2150037
Author(s):  
Haoyang Cheng ◽  
Wenquan Cui
Keyword(s):  
Data Analysis ◽  
Dimension Reduction ◽  
High Dimensional Data ◽  
Real Data ◽  
Dimensional Subspace ◽  
High Dimensional ◽  
Sufficient Dimension Reduction ◽  
Lasso Regression ◽  
High Dimension Data ◽  
Reduction Problem

Heteroscedasticity often appears in the high-dimensional data analysis. In order to achieve a sparse dimension reduction direction for high-dimensional data with heteroscedasticity, we propose a new sparse sufficient dimension reduction method, called Lasso-PQR. From the candidate matrix derived from the principal quantile regression (PQR) method, we construct a new artificial response variable which is made up from top eigenvectors of the candidate matrix. Then we apply a Lasso regression to obtain sparse dimension reduction directions. While for the “large [Formula: see text] small [Formula: see text]” case that [Formula: see text], we use principal projection to solve the dimension reduction problem in a lower-dimensional subspace and projection back to the original dimension reduction problem. Theoretical properties of the methodology are established. Compared with several existing methods in the simulations and real data analysis, we demonstrate the advantages of our method in the high dimension data with heteroscedasticity.

scholarly journals Learning Heterogeneity in Causal Inference Using Sufficient Dimension Reduction

2019 ◽  
Vol 7 (1) ◽  
Author(s):  
Wei Luo ◽  
Wenbo Wu ◽  
Yeying Zhu
Keyword(s):  
Causal Inference ◽  
Dimension Reduction ◽  
Causal Effect ◽  
Real Data ◽  
Potential Outcomes ◽  
Estimation Accuracy ◽  
Sufficient Dimension Reduction ◽  
Simulation Studies ◽  
The Mean ◽  
The Individual

AbstractOften the research interest in causal inference is on the regression causal effect, which is the mean difference in the potential outcomes conditional on the covariates. In this paper, we use sufficient dimension reduction to estimate a lower dimensional linear combination of the covariates that is sufficient to model the regression causal effect. Compared with the existing applications of sufficient dimension reduction in causal inference, our approaches are more efficient in reducing the dimensionality of covariates, and avoid estimating the individual outcome regressions. The proposed approaches can be used in three ways to assist modeling the regression causal effect: to conduct variable selection, to improve the estimation accuracy, and to detect the heterogeneity. Their usefulness are illustrated by both simulation studies and a real data example.

scholarly journals Predicting tipping points in mutualistic networks through dimension reduction

2018 ◽  
Vol 115 (4) ◽  
pp. E639-E647 ◽  
Author(s):  
Junjie Jiang ◽  
Zi-Gang Huang ◽  
Thomas P. Seager ◽  
Wei Lin ◽  
Celso Grebogi ◽  
...  
Keyword(s):  
Dimension Reduction ◽  
Reduction Process ◽  
Real Data ◽  
Tipping Point ◽  
Networked Systems ◽  
Weighted Averaging ◽  
Dynamical Mechanism ◽  
Point Of No Return ◽  
2D System ◽  
Mutualistic Networks

Complex networked systems ranging from ecosystems and the climate to economic, social, and infrastructure systems can exhibit a tipping point (a “point of no return”) at which a total collapse of the system occurs. To understand the dynamical mechanism of a tipping point and to predict its occurrence as a system parameter varies are of uttermost importance, tasks that are hindered by the often extremely high dimensionality of the underlying system. Using complex mutualistic networks in ecology as a prototype class of systems, we carry out a dimension reduction process to arrive at an effective 2D system with the two dynamical variables corresponding to the average pollinator and plant abundances. We show, using 59 empirical mutualistic networks extracted from real data, that our 2D model can accurately predict the occurrence of a tipping point, even in the presence of stochastic disturbances. We also find that, because of the lack of sufficient randomness in the structure of the real networks, weighted averaging is necessary in the dimension reduction process. Our reduced model can serve as a paradigm for understanding and predicting the tipping point dynamics in real world mutualistic networks for safeguarding pollinators, and the general principle can be extended to a broad range of disciplines to address the issues of resilience and sustainability.

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