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We propose a scalable variational Bayes method for statistical inference for a single or pre-specified low-dimensional subset of the coordinates of a high-dimensional parameter in sparse linear regression.
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Castillo, I. & van der Vaart, A. (2012), ‘Needles and straw in a haystack: Posterior concentration for possibly sparse sequences’, Ann. Statist
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Javanmard, A. & Montanari, A. (2014), ‘Confidence intervals and hypothesis testing for high-dimensional regression’, J. Mach. Learn. Res
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van de Geer, S., Bühlmann, P., Ritov, Y. & Dezeure, R. (2014), ‘On asymptotically optimal confidence regions and tests for high-dimensional models’, Ann. Statist
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Zhang, C.-H. & Zhang, S. S. (2014), ‘Confidence intervals for low dimensional parameters in high dimensional linear models’, J. R. Statist. Soc. B
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Ormerod, J. T., You, C. & Müller, S. (2017), ‘A variational Bayes approach to variable selection’, Electron. J. Stat
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2020
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Griffin, J. E., Łatuszyński, K. G. & Steel, M. F. J. (2021), ‘In search of lost mixing time: adaptive Markov chain Monte Carlo schemes for Bayesian variable selection with very large p p ’, Biometrika
2021
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Tan, L. S. L. (2021), ‘Use of model reparametrization to improve variational Bayes’, J. R. Statist. Soc. B
2021
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Bai, R., Moran, G. E., Antonelli, J. L., Chen, Y. & Boland, M. R. (2022), ‘Spike-and-slab group lassos for grouped regression and sparse generalized additive models’, J. Amer. Statist. Assoc
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Fasano, A., Durante, D. & Zanella, G. (2022), ‘Scalable and accurate variational Bayes for high-dimensional binary regression models’, Biometrika
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Castillo, I., Schmidt-Hieber, J. & van der Vaart, A. (2015), ‘Bayesian linear regression with sparse priors’, Ann. Statist
2018
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Janková, J. & van de Geer, S. (2018), ‘Semiparametric efficiency bounds for high-dimensional models’, Ann. Statist
2018
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Javanmard, A. & Montanari, A. (2018), ‘Debiasing the Lasso: optimal sample size for Gaussian designs’, Ann. Statist
2018
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Wang, Y. & Blei, D. M. (2019), ‘Frequentist consistency of variational Bayes’, J. Am. Statist. Ass
2019
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Yang, D. (2019), ‘Posterior asymptotic normality for an individual coordinate in high-dimensional linear regression’, Electron. J. Stat
2019
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Alquier, P. & Ridgway, J. (2020), ‘Concentration of tempered posteriors and of their variational approximations’, Ann. Statist
2020
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R package version 1.0
Clara, G., Szabo, B. & Ray, K. (2020), sparsevb: spike and slab variational Bayes for linear and logistic regression · 2020
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2022
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Goplerud, M. (2022), ‘Fast and accurate estimation of non-nested binomial hierarchical models using variational inference’, Bayesian Anal
2022
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Komodromos, M., Aboagye, E. O., Evangelou, M., Filippi, S. & Ray, K. (2022), ‘Variational Bayes for high-dimensional proportional hazards models with applications within gene expression’, Bioinformatics
2022
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Ray, K. & Szabó, B. (2022), ‘Variational Bayes for high-dimensional linear regression with sparse priors’, J. Am. Statist. Ass
2022
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Menictas, M., Credico, G. D. & Wand, M. P. (2023), ‘Streamlined variational inference for linear mixed models with crossed random effects’, J. Comput. Graph. Statist
2023
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Wu, T., Narisetty, N. N. & Yang, Y. (2023), ‘Statistical inference via conditional Bayesian posteriors in high-dimensional linear regression’, Electron. J. Stat
2023
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You, C., Ormerod, J. T., Li, X., Pang, C. H. & Zhou, X.-H. (2023), ‘An approximated collapsed variational Bayes approach to variable selection in linear regression’, J. Comput. Graph. Statist
2023
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Adamek, R., Smeekes, S. & Wilms, I. (2024), ‘Local projection inference in high dimensions’, The Econometrics Journal
2024
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Celentano, M. & Montanari, A. (2024), ‘Correlation adjusted debiased Lasso: debiasing the Lasso with inaccurate covariate model’, J. R. Stat. Soc. Ser. B. Stat. Methodol
2024
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Goplerud, M., Papaspiliopoulos, O. & Zanella, G. (2024), ‘Partially factorized variational inference for high-dimensional mixed models’, Biometrika
2024
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Banerjee, S., Castillo, I. & Ghosal, S. (2026), ‘Bayesian inference in high-dimensional models’, Statistics Surveys
2026
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