A new estimator for efficient dimension reduction in regression

Luo, Wei; Cai, Xizhen

doi:10.1016/j.jmva.2015.12.014

Cited by 3 publications

(7 citation statements)

References 16 publications

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“…This amounts to studying the theoretical properties of β dist,1 . Ma and Zhu (2014), Luo et al (2014) and Luo and Cai (2016) have already studied the theoretical properties of β pool,1 thoroughly. We first present regularity conditions to establish the theoretical properties of β dist,1 .…”

Section: Theoretical Properties Of the First Distributed Algorithmmentioning

confidence: 99%

Distributed Mean Dimension Reduction Through Semi-parametric Approaches

Zhu¹,

Xu²,

Zhu³

2025

STAT SINICA

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In the present article we recast the semi-parametric mean dimension reduction approaches under a least squares framework, which turns the problem of recovering the central mean subspace into a series of problems of estimating slopes in linear regressions. It also facilitates to incorporate penalties to produce sparse solutions. We further adapt the semi-parametric mean dimension reduction approaches to distributed settings when massive data are scattered at various locations and cannot be aggregated or processed through a single machine. We propose three communication-efficient distributed algorithms, the first yields a dense solution, the second produces a sparse estimation, and the third provides an orthonormal basis. The distributed algorithms reduce the computational complexities of the pooled ones substantially. In addition, the distributed algorithms attain oracle rates after a finite number of iterations. We conduct extensive numerical studies to demonstrate the finite-sample performance of the distributed estimates and to compare with the pooled algorithms.

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Section: Theoretical Properties Of the First Distributed Algorithmmentioning

confidence: 99%

Distributed Mean Dimension Reduction Through Semi-parametric Approaches

Zhu¹,

Xu²,

Zhu³

2025

STAT SINICA

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“…The MAVE approach of Xia et al (2002) is another flexible estimator and has been shown to be highly effective in estimating the central mean subspace. More recent approaches such as Luo et al (2014) and Luo and Cai (2016) are also quite promising and have connections to the framework of Ma and Zhu (2012). In particular, Luo and Cai (2016) proposes an efficient estimator based on Luo et al (2014) that refines and improves the performance of semiparametric estimators of the central mean subspace.…”

Section: S Nonementioning

confidence: 99%

“…More recent approaches such as Luo et al (2014) and Luo and Cai (2016) are also quite promising and have connections to the framework of Ma and Zhu (2012). In particular, Luo and Cai (2016) proposes an efficient estimator based on Luo et al (2014) that refines and improves the performance of semiparametric estimators of the central mean subspace. The principles we develop in this article can be straightforwardly extended to incorporate the particular estimation methods of these works, such as Xia et al (2002), Luo et al (2014), andCai (2016).…”

Section: S Nonementioning

confidence: 99%

“…(2014) and Luo and Cai (2016) are also quite promising and have connections to the framework of Ma and Zhu (2012). In particular, Luo and Cai (2016) proposes an efficient estimator based on Luo et al. (2014) that refines and improves the performance of semiparametric estimators of the central mean subspace.…”

Section: Introductionmentioning

confidence: 99%

“…More recent approaches such as Luo et al. (2014) and Luo and Cai (2016) are also quite promising and have connections to the framework of Ma and Zhu (2012). In particular, Luo and Cai (2016) proposes an efficient estimator based on Luo et al.…”

Section: Introductionmentioning

confidence: 99%

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Sufficient dimension reduction for populations with structured heterogeneity

Huling

Yu²

2021

Biometrics

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A key challenge in building effective regression models for large and diverse populations is accounting for patient heterogeneity. An example of such heterogeneity is in health system risk modeling efforts where different combinations of comorbidities fundamentally alter the relationship between covariates and health outcomes. Accounting for heterogeneity arising combinations of factors can yield more accurate and interpretable regression models. Yet, in the presence of high‐dimensional covariates, accounting for this type of heterogeneity can exacerbate estimation difficulties even with large sample sizes. To handle these issues, we propose a flexible and interpretable risk modeling approach based on semiparametric sufficient dimension reduction. The approach accounts for patient heterogeneity, borrows strength in estimation across related subpopulations to improve both estimation efficiency and interpretability, and can serve as a useful exploratory tool or as a powerful predictive model. In simulated examples, we show that our approach often improves estimation performance in the presence of heterogeneity and is quite robust to deviations from its key underlying assumptions. We demonstrate our approach in an analysis of hospital admission risk for a large health system and demonstrate its predictive power when tested on further follow‐up data.

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