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Papers by Peter Bühlmann
Journal of Machine Learning Research, 2014
We propose a novel and efficient algorithm for maximizing the observed log-likelihood of a multiv... more We propose a novel and efficient algorithm for maximizing the observed log-likelihood of a multivariate normal data matrix with missing values. We show that our procedure, based on iteratively regr...
Journal of the American Statistical Association
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Electronic Journal of Statistics, 2015
One challenge of large-scale data analysis is that the assumption of an identical distribution fo... more One challenge of large-scale data analysis is that the assumption of an identical distribution for all samples is often not realistic. An optimal linear regression might, for example, be markedly different for distinct groups of the data. Maximin effects have been proposed as a computationally attractive way to estimate effects that are common across all data without fitting a mixture distribution explicitly. So far just point estimators of the common maximin effects have been proposed in Meinshausen and B\"uhlmann (2014). Here we propose asymptotically valid confidence regions for these effects.
The Annals of Statistics, 2015
Selected Works in Probability and Statistics, 2012
The Annals of Statistics, 2014
Springer Series in Statistics, 2011
ABSTRACT Estimation of discrete structure such as in variable selection or graphical modeling is ... more ABSTRACT Estimation of discrete structure such as in variable selection or graphical modeling is notoriously difficult, especially for high-dimensional data. Subsampling or bootstrapping have the potential to substantially increase the stability of high-dimensional selection algorithms and to quantify their uncertainties. Stability via subsampling or bootstrapping has been introduced by Breiman (1996) in the context of prediction. Here, the focus is different: the resampling scheme can provide finite sample control for certain error rates of false discoveries and hence a transparent principle to choose a proper amount of regularization for structure estimation. We discuss methodology and theory for very general settings which include variable selection in linear or generalized linear models or graphical modeling from Chapter 13. For the special case of variable selection in linear models, the theoretical properties (developed here) for consistent selection using stable solutions based on subsampling or bootstrapping require slightly stronger assumptions and are less refined than say for the adaptive or thresholded Lasso.
Statistical Science, 2014
Statistical Science, 2002
Journal of Machine Learning Research, 2014
We propose a novel and efficient algorithm for maximizing the observed log-likelihood of a multiv... more We propose a novel and efficient algorithm for maximizing the observed log-likelihood of a multivariate normal data matrix with missing values. We show that our procedure, based on iteratively regr...
Journal of the American Statistical Association
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Electronic Journal of Statistics, 2015
One challenge of large-scale data analysis is that the assumption of an identical distribution fo... more One challenge of large-scale data analysis is that the assumption of an identical distribution for all samples is often not realistic. An optimal linear regression might, for example, be markedly different for distinct groups of the data. Maximin effects have been proposed as a computationally attractive way to estimate effects that are common across all data without fitting a mixture distribution explicitly. So far just point estimators of the common maximin effects have been proposed in Meinshausen and B\"uhlmann (2014). Here we propose asymptotically valid confidence regions for these effects.
The Annals of Statistics, 2015
Selected Works in Probability and Statistics, 2012
The Annals of Statistics, 2014
Springer Series in Statistics, 2011
ABSTRACT Estimation of discrete structure such as in variable selection or graphical modeling is ... more ABSTRACT Estimation of discrete structure such as in variable selection or graphical modeling is notoriously difficult, especially for high-dimensional data. Subsampling or bootstrapping have the potential to substantially increase the stability of high-dimensional selection algorithms and to quantify their uncertainties. Stability via subsampling or bootstrapping has been introduced by Breiman (1996) in the context of prediction. Here, the focus is different: the resampling scheme can provide finite sample control for certain error rates of false discoveries and hence a transparent principle to choose a proper amount of regularization for structure estimation. We discuss methodology and theory for very general settings which include variable selection in linear or generalized linear models or graphical modeling from Chapter 13. For the special case of variable selection in linear models, the theoretical properties (developed here) for consistent selection using stable solutions based on subsampling or bootstrapping require slightly stronger assumptions and are less refined than say for the adaptive or thresholded Lasso.
Statistical Science, 2014
Statistical Science, 2002