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 ...
Sufficient dimension reduction (SDR) is a successive tool for reducing the dimensionality of predictors by finding the central subspace, a minimal subspace of predictors that preserves all the regression information. When predictor dimension is large, it is often assumed that only a small number of ...
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 large. The standard SDR methods suffer because the estimated li...
Efficient Sparse Estimate of Sufficient Dimension Reduction in High DimensionDistance covarianceGrassmann manifoldsLarge p small nSufficient variable selectionWe propose a new and simple framework for dimension reduction in the large p, small n setting. The framework decomposes the data into pieces, ...
Assuming that the regression falls into a single-index structure, we propose a method called the sparse group sufficient dimension reduction to conduct group and within-group variable selections simultaneously without assuming a specific link function. Simulation studies show that our method is comparable...
. . , vd⊤X sufficient predictorsimportant origi nal predictors - H ilafu and Safo BMC Bioinformatics (2022) 23:168 Page 3 of 19 shrinkage sliced inverse regression introduced by [3]; the sparse sufficient dimension reduction method due to [4]; and the general shrinkage strategy for...
Finally, we apply our proposed method in the context of sparse sufficient dimension reduction to two gene expression data sets.doi:10.1111/rssb.12291Kean Ming TanZhaoran WangHan LiuTong ZhangJournal of the Royal Statistical Society Series B (Statistical Methodology)...
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 脧 =limpn=0 , where p is the dimension and n is the sample size. Thus, when p is of the same or ...
Sufficient dimension reduction, replacing the original predictors with a few linear combinations while keeping all the regression information, has been widely studied. A key goal is to find the central mean subspace, the intersection of all subspaces that provide such a reduction. To this end, a ...
In order to mitigate the curse of dimensionality, this paper proposes a novel surrogate modeling method, which involves seeking a sufficient dimension reduction space and approximating the original high-dimensional model with a low-dimensional PCE. The proposed surrogate modeling method benefits from both...