Adaptive Bayesian SLOPE : Model Selection With Incomplete Data
(2022) In Journal of Computational and Graphical Statistics 31(1). p.113-137- Abstract
We consider the problem of variable selection in high-dimensional settings with missing observations among the covariates. To address this relatively understudied problem, we propose a new synergistic procedure—adaptive Bayesian SLOPE with missing values—which effectively combines SLOPE (sorted l 1 regularization) with the spike-and-slab LASSO (SSL) and is accompanied by an efficient stochastic approximation of expected maximization (SAEM) algorithm to handle missing data. Similarly as in SSL, the regression coefficients are regarded as arising from a hierarchical model consisting of two groups: the spike for the inactive and the slab for the active. However, instead of assigning independent spike and slab Laplace priors for... (More)
We consider the problem of variable selection in high-dimensional settings with missing observations among the covariates. To address this relatively understudied problem, we propose a new synergistic procedure—adaptive Bayesian SLOPE with missing values—which effectively combines SLOPE (sorted l 1 regularization) with the spike-and-slab LASSO (SSL) and is accompanied by an efficient stochastic approximation of expected maximization (SAEM) algorithm to handle missing data. Similarly as in SSL, the regression coefficients are regarded as arising from a hierarchical model consisting of two groups: the spike for the inactive and the slab for the active. However, instead of assigning independent spike and slab Laplace priors for each covariate, here we deploy a joint SLOPE “spike-and-slab” prior which takes into account the ordering of coefficient magnitudes in order to control for false discoveries. We position our approach within a Bayesian framework which allows for simultaneous variable selection and parameter estimation while handling missing data. Through extensive simulations, we demonstrate satisfactory performance in terms of power, false discovery rate (FDR) and estimation bias under a wide range of scenarios including complete data and existence of missingness. Finally, we analyze a real dataset consisting of patients from Paris hospitals who underwent severe trauma, where we show competitive performance in predicting platelet levels. Our methodology has been implemented in C++ and wrapped into open source R programs for public use. Supplemental files for this article are available online.
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- author
- Jiang, Wei ; Bogdan, Małgorzata LU ; Josse, Julie ; Majewski, Szymon ; Miasojedow, Błażej and Ročková, Veronika
- author collaboration
- organization
- publishing date
- 2022
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- FDR control, Health data, Incomplete data, Penalized regression, Spike and slab prior, Stochastic approximation EM
- in
- Journal of Computational and Graphical Statistics
- volume
- 31
- issue
- 1
- pages
- 113 - 137
- publisher
- American Statistical Association
- external identifiers
-
- scopus:85117475479
- ISSN
- 1061-8600
- DOI
- 10.1080/10618600.2021.1963263
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2021 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.
- id
- ad1a2291-e9e2-4a7c-aa10-00ffa6e0b75b
- date added to LUP
- 2021-11-22 09:20:21
- date last changed
- 2022-06-29 18:19:43
@article{ad1a2291-e9e2-4a7c-aa10-00ffa6e0b75b,
abstract = {{<p>We consider the problem of variable selection in high-dimensional settings with missing observations among the covariates. To address this relatively understudied problem, we propose a new synergistic procedure—adaptive Bayesian SLOPE with missing values—which effectively combines SLOPE (sorted l <sub>1</sub> regularization) with the spike-and-slab LASSO (SSL) and is accompanied by an efficient stochastic approximation of expected maximization (SAEM) algorithm to handle missing data. Similarly as in SSL, the regression coefficients are regarded as arising from a hierarchical model consisting of two groups: the spike for the inactive and the slab for the active. However, instead of assigning independent spike and slab Laplace priors for each covariate, here we deploy a joint SLOPE “spike-and-slab” prior which takes into account the ordering of coefficient magnitudes in order to control for false discoveries. We position our approach within a Bayesian framework which allows for simultaneous variable selection and parameter estimation while handling missing data. Through extensive simulations, we demonstrate satisfactory performance in terms of power, false discovery rate (FDR) and estimation bias under a wide range of scenarios including complete data and existence of missingness. Finally, we analyze a real dataset consisting of patients from Paris hospitals who underwent severe trauma, where we show competitive performance in predicting platelet levels. Our methodology has been implemented in C++ and wrapped into open source R programs for public use. Supplemental files for this article are available online.</p>}},
author = {{Jiang, Wei and Bogdan, Małgorzata and Josse, Julie and Majewski, Szymon and Miasojedow, Błażej and Ročková, Veronika}},
issn = {{1061-8600}},
keywords = {{FDR control; Health data; Incomplete data; Penalized regression; Spike and slab prior; Stochastic approximation EM}},
language = {{eng}},
number = {{1}},
pages = {{113--137}},
publisher = {{American Statistical Association}},
series = {{Journal of Computational and Graphical Statistics}},
title = {{Adaptive Bayesian SLOPE : Model Selection With Incomplete Data}},
url = {{http://dx.doi.org/10.1080/10618600.2021.1963263}},
doi = {{10.1080/10618600.2021.1963263}},
volume = {{31}},
year = {{2022}},
}