ExSIS: Extended sure independence screening for ultrahigh-dimensional linear models

Ahmed, Talal; Bajwa, Waheed U.

doi:10.1016/j.sigpro.2019.01.018

Cited by 9 publications

(6 citation statements)

References 52 publications

(98 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Gaussian assumptions in Condition 3(a) guarantee the desirable properties of SURE screening for the non-informative auxiliary studies. In fact, the Gaussian assumption can be relaxed to be sub-Gaussian random variables according to some recent studies (Ahmed and Bajwa, 2019). For the conciseness of the proof, we consider Gaussian distributed random variables.…”

Section: Theoretical Properties Of Trans-lassomentioning

confidence: 99%

Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality

Cai

2020

Preprint

View full text Add to dashboard Cite

This paper considers the estimation and prediction of a high-dimensional linear regression in the setting of transfer learning, using samples from the target model as well as auxiliary samples from different but possibly related regression models. When the set of "informative" auxiliary samples is known, an estimator and a predictor are proposed and their optimality is established. The optimal rates of convergence for prediction and estimation are faster than the corresponding rates without using the auxiliary samples. This implies that knowledge from the informative auxiliary samples can be transferred to improve the learning performance of the target problem. In the case that the set of informative auxiliary samples is unknown, we propose a data-driven procedure for transfer learning, called Trans-Lasso, and reveal its robustness to non-informative auxiliary samples and its efficiency in knowledge transfer. The proposed procedures are demonstrated in numerical studies and are applied to a dataset concerning the associations among gene expressions. It is shown that Trans-Lasso leads to improved performance in gene expression prediction in a target tissue by incorporating the data from multiple different tissues as auxiliary samples.

show abstract

Section: Theoretical Properties Of Trans-lassomentioning

confidence: 99%

Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality

Cai

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…In fact, the largest eigenvalue of

Σ^{false(k false)}

k \in {frakturA}^{c}

can grow as

O (n_{*}^{τ})

for some τ ≥ 0 and τ + α < 1 following the proof in Fan and Lv (2008). The Gaussian assumption can be relaxed to be sub‐Gaussian random variables according to some recent studies (Ahmed & Bajwa, 2019). For the conciseness of the proof, we consider Gaussian distributed random variables with bounded eigenvalues.…”

Section: Unknown Set Of Informative Auxiliary Samplesmentioning

confidence: 99%

Transfer Learning for High-Dimensional Linear Regression: Prediction, Estimation and Minimax Optimality

Cai

2021

Journal of the Royal Statistical Society Series B: Statistical Methodology

View full text Add to dashboard Cite

This paper considers estimation and prediction of a highdimensional linear regression in the setting of transfer learning where, in addition to observations from the target model, auxiliary samples from different but possibly related regression models are available. When the set of informative auxiliary studies is known, an estimator and a predictor are proposed and their optimality is established. The optimal rates of convergence for prediction and estimation are faster than the corresponding rates without using the auxiliary samples. This implies that knowledge from the informative auxiliary samples can be transferred to improve the learning performance of the target problem. When the set of informative auxiliary samples is unknown, we propose a data-driven procedure for transfer learning, called Trans-Lasso, and show its robustness to non-informative auxiliary samples and its efficiency in knowledge transfer. The proposed procedures are demonstrated in numerical studies and are applied to a dataset concerning the associations among gene expressions. It is shown that Trans-Lasso leads to improved performance in gene expression prediction in a target tissue by incorporating data from multiple different tissues as auxiliary samples.

show abstract

“…Li et al (2012) and Fan et al (2009) presented feature screening-based distance correlations. The extended ultrahigh dimensional sure independence screening for the generalized linear model was discussed in Saldana and Feng (2018) and Ahmed and Bajwa (2019). However, since the preceding studies created a synergy between the Lasso type estimators and the sure screening methods for ultrahigh dimensional data, the Lasso type based sure screening methods had been studied by Ghaoui et al (2010), Tibshirani et al (2012), Xiang and Ramadge (2012) as cited in Ahmed and Bajwa (2019).…”

Section: Introductionmentioning

confidence: 99%

Penalized LAD-SCAD Estimator Based on Robust Wrapped Correlation Screening Method for High Dimensional Models

Baba¹,

Midi²,

June³

et al. 2021

JST

View full text Add to dashboard Cite

The widely used least absolute deviation (LAD) estimator with the smoothly clipped absolute deviation (SCAD) penalty function (abbreviated as LAD-SCAD) is known to produce corrupt estimates in the presence of outlying observations. The problem becomes more complicated when the number of predictors diverges. To overcome these problems, the LAD-SCAD based on sure independence screening (SIS) technique is put forward. The SIS method uses the rank correlation screening (RCS) algorithm in the pre-screening step and the traditional Pathwise coordinate descent algorithm for computing the sequence of the regularization parameters in the post screening step for onward model selection. It is now evident that the rank correlation is less robust against outliers. Motivated by these inadequacies, we propose to improvise the LAD-SCAD estimator using robust wrapped correlation screening (WCS) method by replacing the rank correlation in the SIS method with robust wrapped correlation. The proposed estimator is denoted as WCS+LAD-SCAD and will be employed for variable selection. The simulation study and real-life data examples show that the proposed procedure produces more efficient results compared to the existing methods.

show abstract

ExSIS: Extended sure independence screening for ultrahigh-dimensional linear models

Cited by 9 publications

References 52 publications

Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality

Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality

Transfer Learning for High-Dimensional Linear Regression: Prediction, Estimation and Minimax Optimality

Penalized LAD-SCAD Estimator Based on Robust Wrapped Correlation Screening Method for High Dimensional Models

Contact Info

Product

Resources

About