scholarly journals A robust variable screening procedure for ultra-high dimensional data

2021 ◽  
pp. 096228022110172
Author(s):  
Abhik Ghosh ◽  
Magne Thoresen
Keyword(s):  
Penalized Regression ◽  
Screening Procedure ◽  
Small Samples ◽  
High Dimensional ◽  
Simulation Studies ◽  
Robust Methods ◽  
Density Power Divergence ◽  
Variable Screening ◽  
Regression Problems ◽  
Power Divergence

Variable selection in ultra-high dimensional regression problems has become an important issue. In such situations, penalized regression models may face computational problems and some pre-screening of the variables may be necessary. A number of procedures for such pre-screening has been developed; among them the Sure Independence Screening (SIS) enjoys some popularity. However, SIS is vulnerable to outliers in the data, and in particular in small samples this may lead to faulty inference. In this paper, we develop a new robust screening procedure. We build on the density power divergence (DPD) estimation approach and introduce DPD-SIS and its extension iterative DPD-SIS. We illustrate the behavior of the methods through extensive simulation studies and show that they are superior to both the original SIS and other robust methods when there are outliers in the data. Finally, we illustrate its use in a study on regulation of lipid metabolism.

scholarly journals IPF-LASSO: Integrative L1-Penalized Regression with Penalty Factors for Prediction Based on Multi-Omics Data

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Anne-Laure Boulesteix ◽  
Riccardo De Bin ◽  
Xiaoyu Jiang ◽  
Mathias Fuchs
Keyword(s):  
Cross Validation ◽  
Real Life ◽  
Penalized Regression ◽  
R Package ◽  
Molecular Data ◽  
Regression Method ◽  
Data Driven ◽  
High Dimensional ◽  
Omics Data ◽  
Simulation Studies

As modern biotechnologies advance, it has become increasingly frequent that different modalities of high-dimensional molecular data (termed “omics” data in this paper), such as gene expression, methylation, and copy number, are collected from the same patient cohort to predict the clinical outcome. While prediction based on omics data has been widely studied in the last fifteen years, little has been done in the statistical literature on the integration of multiple omics modalities to select a subset of variables for prediction, which is a critical task in personalized medicine. In this paper, we propose a simple penalized regression method to address this problem by assigning different penalty factors to different data modalities for feature selection and prediction. The penalty factors can be chosen in a fully data-driven fashion by cross-validation or by taking practical considerations into account. In simulation studies, we compare the prediction performance of our approach, called IPF-LASSO (Integrative LASSO with Penalty Factors) and implemented in the R package ipflasso, with the standard LASSO and sparse group LASSO. The use of IPF-LASSO is also illustrated through applications to two real-life cancer datasets. All data and codes are available on the companion website to ensure reproducibility.

Category-Adaptive Variable Screening for Ultra-High Dimensional Heterogeneous Categorical Data

2019 ◽  
Vol 115 (530) ◽  
pp. 747-760 ◽  
Author(s):  
Jinhan Xie ◽  
Yuanyuan Lin ◽  
Xiaodong Yan ◽  
Niansheng Tang
Keyword(s):  
Categorical Data ◽  
High Dimensional ◽  
Variable Screening

scholarly journals Bézier Simplex Fitting: Describing Pareto Fronts of´ Simplicial Problems with Small Samples in Multi-Objective Optimization

2019 ◽  
Vol 33 ◽  
pp. 2304-2313 ◽  
Author(s):  
Ken Kobayashi ◽  
Naoki Hamada ◽  
Akiyoshi Sannai ◽  
Akinori Tanaka ◽  
Kenichi Bannai ◽  
...  
Keyword(s):  
Sample Size ◽  
Optimization Problems ◽  
Solution Set ◽  
Small Samples ◽  
High Dimensional ◽  
Large Sample Size ◽  
Multi Objective Optimization ◽  
Dimensional Solution ◽  
Multi Objective ◽  
Simplex Model

Multi-objective optimization problems require simultaneously optimizing two or more objective functions. Many studies have reported that the solution set of an M-objective optimization problem often forms an (M − 1)-dimensional topological simplex (a curved line for M = 2, a curved triangle for M = 3, a curved tetrahedron for M = 4, etc.). Since the dimensionality of the solution set increases as the number of objectives grows, an exponentially large sample size is needed to cover the solution set. To reduce the required sample size, this paper proposes a Bézier simplex model and its fitting algorithm. These techniques can exploit the simplex structure of the solution set and decompose a high-dimensional surface fitting task into a sequence of low-dimensional ones. An approximation theorem of Bézier simplices is proven. Numerical experiments with synthetic and real-world optimization problems demonstrate that the proposed method achieves an accurate approximation of high-dimensional solution sets with small samples. In practice, such an approximation will be conducted in the postoptimization process and enable a better trade-off analysis.

scholarly journals Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 399 ◽  
Author(s):  
Marco Riani ◽  
Anthony C. Atkinson ◽  
Aldo Corbellini ◽  
Domenico Perrotta
Keyword(s):  
Robust Regression ◽  
Robust Statistics ◽  
Estimation Method ◽  
Estimation Procedure ◽  
Breakdown Point ◽  
Parameter Estimates ◽  
Normal Density ◽  
Density Power Divergence ◽  
Numerical Minimization ◽  
Power Divergence

Minimum density power divergence estimation provides a general framework for robust statistics, depending on a parameter α , which determines the robustness properties of the method. The usual estimation method is numerical minimization of the power divergence. The paper considers the special case of linear regression. We developed an alternative estimation procedure using the methods of S-estimation. The rho function so obtained is proportional to one minus a suitably scaled normal density raised to the power α . We used the theory of S-estimation to determine the asymptotic efficiency and breakdown point for this new form of S-estimation. Two sets of comparisons were made. In one, S power divergence is compared with other S-estimators using four distinct rho functions. Plots of efficiency against breakdown point show that the properties of S power divergence are close to those of Tukey’s biweight. The second set of comparisons is between S power divergence estimation and numerical minimization. Monitoring these two procedures in terms of breakdown point shows that the numerical minimization yields a procedure with larger robust residuals and a lower empirical breakdown point, thus providing an estimate of α leading to more efficient parameter estimates.

Minimum density power divergence estimator for GARCH models

Test ◽  
2008 ◽  
Vol 18 (2) ◽  
pp. 316-341 ◽  
Author(s):  
Sangyeol Lee ◽  
Junmo Song
Keyword(s):  
Garch Models ◽  
Density Power Divergence ◽  
Minimum Density ◽  
Power Divergence
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