On the validity of the pairs bootstrap for lasso estimators

Camponovo, Lorenzo

doi:10.1093/biomet/asv039

Cited by 26 publications

(27 citation statements)

References 14 publications

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“…Thus, we only deal with homoscedastic noise, as does the modified Lasso bootstrap in Chatterjee and Lahiri (2011). For Lasso models with heteroscedastic noise, it is possible to use other bootstrap strategies such as Camponovo (2015) and Wagener and Dette (2012).…”

Section: Discussionmentioning

confidence: 99%

Probabilistic tractography using Lasso bootstrap

Prince

2017

Medical Image Analysis

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Diffusion magnetic resonance imaging (dMRI) can be used for noninvasive imaging of white matter tracts. Using fiber tracking, which propagates fiber streamlines according to fiber orientations (FOs) computed from dMRI, white matter tracts can be reconstructed for investigation of brain diseases and the brain connectome. Because of image noise, probabilistic tractography has been proposed to characterize uncertainties in FO estimation. Bootstrap provides a nonparametric approach to the estimation of FO uncertainties and residual bootstrap has been used for developing probabilistic tractography. However, recently developed models have incorporated sparsity regularization to reduce the required number of gradient directions to resolve crossing FOs, and the residual bootstrap used in previous methods is not applicable to these models. In this work, we propose a probabilistic tractography algorithm named Lasso bootstrap tractography (LBT) for the models that incorporate sparsity. Using a fixed tensor basis and a sparsity assumption, diffusion signals are modeled using a Lasso formulation. With the residuals from the Lasso model, a distribution of diffusion signals is obtained according to a modified Lasso bootstrap strategy. FOs are then estimated from the synthesized diffusion signals by an algorithm that improves FO estimation by enforcing spatial consistency of FOs. Finally, streamlining fiber tracking is performed with the computed FOs. The LBT algorithm was evaluated on simulated and real dMRI data both qualitatively and quantitatively. Results demonstrate that LBT outperforms state-of-the-art algorithms.

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Section: Discussionmentioning

confidence: 99%

Probabilistic tractography using Lasso bootstrap

Prince

2017

Medical Image Analysis

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“…settings; see, e.g., Chatterjee and Lahiri, , Minnier et al , Efron , and Camponovo . In this paper, we extend the bootstrap procedure introduced in Camponovo to more general time series models, and prove its (pointwise) consistency. In our analysis, we mainly consider settings where the dimension p of the unknown parameter of interest is fixed and the sample size n is large.…”

Section: Introductionmentioning

confidence: 86%

Oracle Properties, Bias Correction, and Bootstrap Inference for Adaptive Lasso for Time SeriesM‐Estimators

Audrino

Camponovo

2017

Journal Time Series Analysis

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We derive new theoretical results on the properties of the adaptive least absolute shrinkage and selection operator (adaptive lasso) for possibly nonlinear time series models. In particular, we investigate the question of how to conduct inference on the parameters given an adaptive lasso model. Central to this study is the test of the hypothesis that a given adaptive lasso parameter equals zero, which therefore tests for a false positive. To this end, we introduce a recentered bootstrap procedure and show, theoretically and empirically through extensive Monte Carlo simulations, that the adaptive lasso can combine efficient parameter estimation, variable selection, and inference in one step. Moreover, we analytically derive a bias correction factor that is able to significantly improve the empirical coverage of the test on the active variables. Finally, we apply the adaptive lasso and the recentered bootstrap procedure to investigate the relation between the short rate dynamics and the economy, thereby providing a statistical foundation (from a model choice perspective) for the classic Taylor rule monetary policy model.

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“…Each observation in the sample is considered as a row vector z i = ( x i 1 , …, x ip , y i ),which consists of p predictor values x ij and a single outcome value y i . A Lasso model can be fit to every bootstrap sample of N observations z i , yielding a set of Lasso coefficient estimates (Camponovo, 2014). F̂ ( β̂ j ) is defined as the distribution of β̂ j values from each of all possible bootstrap samples of size N .…”

Section: Approachmentioning

confidence: 99%

“…She found that: 1) residual and vector bootstrap SEs of Lasso coefficient estimates had similar degrees of bias in linear models; and 2) vector bootstrap CIs had superior coverage in linear and in logistic models. Camponovo (2014) used vector bootstrapping to generate simultaneous confidence regions in linear models with random predictors. He found poor coverage rates, and used an asymptotic argument to propose two modified vector bootstrapping procedures.…”

Section: Approachmentioning

confidence: 99%

“…Asymptotic analyses have found that under bootstrap resampling, Lasso coefficients for noise predictors are expected to fluctuate between positive and negative values (Chatterjee, 2011, Camponovo, 2014). This should lead noise predictors to have larger bootstrap SEs and CIs than important predictors, which suggests that these statistics are useful for identifying false positive associations.…”

Section: Introductionmentioning

confidence: 99%

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The use of vector bootstrapping to improve variable selection precision in Lasso models

Laurin¹,

Boomsma

Lubke³

2016

Statistical Applications in Genetics and Molecular Biology

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The Lasso is a shrinkage regression method that is widely used for variable selection in statistical genetics. Commonly, K-fold cross-validation is used to fit a Lasso model. This is sometimes followed by using bootstrap confidence intervals to improve precision in the resulting variable selections. Nesting cross-validation within bootstrapping could provide further improvements in precision, but this has not been investigated systematically. We performed simulation studies of Lasso variable selection precision with and without nesting cross-validation within bootstrapping. Data were simulated to represent genomic data under a polygenic model as well as under a model with effect sizes representative of typical GWAS results. We compared these approaches to each other as well as to software defaults for the Lasso. Nested cross-validation had the most precise variable selection at small effect sizes. At larger effect sizes, there was no advantage to nesting. We illustrated the nested approach with empirical data comprising SNPs and SNP-SNP interactions from the most significant SNPs in a GWAS of borderline personality symptoms. In the empirical example, we found that the default Lasso selected low-reliability SNPs and interactions which were excluded by bootstrapping.

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On the validity of the pairs bootstrap for lasso estimators

Cited by 26 publications

References 14 publications

Probabilistic tractography using Lasso bootstrap

Probabilistic tractography using Lasso bootstrap

Oracle Properties, Bias Correction, and Bootstrap Inference for Adaptive Lasso for Time SeriesM‐Estimators

The use of vector bootstrapping to improve variable selection precision in Lasso models

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