ADMM for High-Dimensional Sparse Penalized Quantile Regression

Gu, Yuwen; Fan, Jun; Kong, Lingchen; Ma, Shiqian; Zou, Hui

doi:10.1080/00401706.2017.1345703

Cited by 96 publications

(101 citation statements)

References 42 publications

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“…3 Computational Algorithm Koenker and D'Orey (1987) developed parametric linear programming to compute a quantile regression function for all τ ∈ (0, 1). Many algorithms have been recently introduced for high-dimensional sparse penalized quantile regression approaches; see Gu et al (2018) for an overview. For problem (2), there are C t p candidate submodels to fit the data for a given t, where C t p denotes the number of t-combinations from a given set of p elements.…”

Section: Sparse Composite Quantile Regressionmentioning

confidence: 99%

Sparse Composite Quantile Regression with Ultra-high Dimensional Heterogeneous Data

Qu¹,

Hao²,

Sun³

2022

STAT SINICA

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Quantile regression is widely employed in heterogeneous data, but to select covariates that globally affect the response and estimate coefficients simultaneously are very challenging. In this article, we introduce a novel sparse composite quantile regression screening method for the analysis of ultra-high dimensional heterogeneous data. The proposed method enjoys the sure screening property, provides a consistent selection path, and yields consistent estimates of coefficients simultaneously across a continuous range of quantile levels. An extended Bayesian information criterion is employed to select the "best" candidate from the path. Extensive simulation studies demonstrate the effectiveness of the proposed method, and an application to a gene expression dataset is provided.

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Section: Sparse Composite Quantile Regressionmentioning

confidence: 99%

Sparse Composite Quantile Regression with Ultra-high Dimensional Heterogeneous Data

Qu¹,

Hao²,

Sun³

2022

STAT SINICA

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“…Comparison with ADMM. Recently, researchers have developed new optimization techniques based on alternating direction method of multiplier (ADMM) for solving QR problems (see, e.g., Yu, Lin and Wang (2017); Gu et al (2018)). We refer the readers to Boyd et al (2011) for more details on ADMM.…”

Section: In Particularmentioning

confidence: 99%

Quantile regression under memory constraint

Chen¹,

Liu²,

Zhang³

2019

Ann. Statist.

112

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This paper studies the inference problem in quantile regression (QR) for a large sample size n but under a limited memory constraint, where the memory can only store a small batch of data of size m. A natural method is the naïve divide-and-conquer approach, which splits data into batches of size m, computes the local QR estimator for each batch, and then aggregates the estimators via averaging. However, this method only works when n = o(m 2 ) and is computationally expensive. This paper proposes a computationally efficient method, which only requires an initial QR estimator on a small batch of data and then successively refines the estimator via multiple rounds of aggregations. Theoretically, as long as n grows polynomially in m, we establish the asymptotic normality for the obtained estimator and show that our estimator with only a few rounds of aggregations achieves the same efficiency as the QR estimator computed on all the data. Moreover, our result allows the case that the dimensionality p goes to infinity. The proposed method can also be applied to address the QR problem under distributed computing environment (e.g., in a large-scale sensor network) or for real-time streaming data.

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“…Equations (4.7) and (4.9) complete the algorithm for the proposed estimation in a linear expectile model. Note that we add the proximal mapping of ρ τ in the Z step, so we call the algorithm the proximal ADMM algorithm, summarized as follows: Note that the convergence of the proximal ADMM algorithm can be established similarly to Section 3.3 in Gu et al [5]. As discussed in Gu et al [5], the worst case convergence rate of the proximal ADMM algorithm is at least of order 1/t at each communication round, where t is the iteration number.…”

Section: Proximal Admm Algorithmmentioning

confidence: 99%

Large-Scale Expectile Regression With Covariates Missing at Random

2020

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Analysis of large volumes of data is very complex due to not only a high level of skewness and heteroscedasticity of variance but also the phenomenon of missing data. Expectile regression is a popular alternative method of analyzing heterogeneous data. In this paper, we consider fitting a linear expectile regression model for estimating conditional expectiles based on a large quantity of data with covariates missing at random. We construct a communication-efficient surrogate loss (CSL) function to estimate model parameters. The asymptotic normality of the proposed estimator is established. A proximal alternating direction method of multipliers (ADMM) algorithm is developed for distributed statistical optimization on a large quantity of data. Simulation studies are performed to assess the finite-sample performance of the proposed method. Survey data from the Behavioral Risk Factor Surveillance System (BRFSS) is used to demonstrate the utility of the proposed method in practice. INDEX TERMS CSL function, expectile regression, large-scale data, missing at random, proximal ADMM algorithm.

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ADMM for High-Dimensional Sparse Penalized Quantile Regression

Cited by 96 publications

References 42 publications

Sparse Composite Quantile Regression with Ultra-high Dimensional Heterogeneous Data

Sparse Composite Quantile Regression with Ultra-high Dimensional Heterogeneous Data

Quantile regression under memory constraint

Large-Scale Expectile Regression With Covariates Missing at Random

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