Searcharxiv⌕ Search

arXiv subjects

Lukas Meier

Publications and source records attributed to Lukas Meier.

9 recordsLinked to original sources
arXiv2025

Crystallographic control of hydrogen ingress in bcc-Iron: Insights from ab initio simulations

Hydrogen uptake into body-centered cubic (bcc) iron as a root cause for subsequent hydrogen embrittlement, is initiated at the surface. In this paper, we quantify how readily H diffuses from the surface into the bulk. We consider a set of low-index, vicinal and general Fe surfaces and treat H-permeation as a two-step process. First, density-functional calculations determine the adsorption energy of an isolated H atom at every crystallographically distinct surface site. Second, for each adsorption site we map the minimum-energy pathway that carries the atom beneath the surface and into the lattice. Across all ten orientations studied, a clear trend emerges: sites that bind hydrogen most weakly (highest adsorption energy) are the starting point of the lowest-barrier diffusion channels into the metal interior. Thus, the least-favorable adsorption pockets act as gateways for efficient subsurface penetration. These insights provide a practical design rule: suppressing or minimizing exposure of such high-energy adsorption motifs - through appropriate surface texturing or orientation control - should make bcc-iron components less susceptible to hydrogen uptake and the associated embrittlement.

cond-mat.mtrl-sci↗
arXiv2015

High-Dimensional Inference: Confidence Intervals, $p$-Values and R-Software hdi

We present a (selective) review of recent frequentist high-dimensional inference methods for constructing $p$-values and confidence intervals in linear and generalized linear models. We include a broad, comparative empirical study which complements the viewpoint from statistical methodology and theory. Furthermore, we introduce and illustrate the R-package hdi which easily allows the use of different methods and supports reproducibility.

stat.ME↗
arXiv2012

GLMMLasso: An Algorithm for High-Dimensional Generalized Linear Mixed Models Using L1-Penalization

We propose an L1-penalized algorithm for fitting high-dimensional generalized linear mixed models. Generalized linear mixed models (GLMMs) can be viewed as an extension of generalized linear models for clustered observations. This Lasso-type approach for GLMMs should be mainly used as variable screening method to reduce the number of variables below the sample size. We then suggest a refitting by maximum likelihood based on the selected variables only. This is an effective correction to overcome problems stemming from the variable screening procedure which are more severe with GLMMs. We illustrate the performance of our algorithm on simulated as well as on real data examples. Supplemental materials are available online and the algorithm is implemented in the R package glmmixedlasso.

stat.CO↗
arXiv2009

High-dimensional additive modeling

We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a computationally efficient algorithm, with provable numerical convergence properties, for optimizing the penalized likelihood. Furthermore, we provide oracle results which yield asymptotic optimality of our estimator for high dimensional but sparse additive models. Finally, an adaptive version of our sparsity-smoothness penalized approach yields large additional performance gains.

stat.ML↗
arXiv2009

P-values for high-dimensional regression

Assigning significance in high-dimensional regression is challenging. Most computationally efficient selection algorithms cannot guard against inclusion of noise variables. Asymptotically valid p-values are not available. An exception is a recent proposal by Wasserman and Roeder (2008) which splits the data into two parts. The number of variables is then reduced to a manageable size using the first split, while classical variable selection techniques can be applied to the remaining variables, using the data from the second split. This yields asymptotic error control under minimal conditions. It involves, however, a one-time random split of the data. Results are sensitive to this arbitrary choice: it amounts to a `p-value lottery' and makes it difficult to reproduce results. Here, we show that inference across multiple random splits can be aggregated, while keeping asymptotic control over the inclusion of noise variables. We show that the resulting p-values can be used for control of both family-wise error (FWER) and false discovery rate (FDR). In addition, the proposed aggregation is shown to improve power while reducing the number of falsely selected variables substantially.

stat.ME↗
arXiv2008

Least angle and $\ell_1$ penalized regression: A review

Least Angle Regression is a promising technique for variable selection applications, offering a nice alternative to stepwise regression. It provides an explanation for the similar behavior of LASSO ($\ell_1$-penalized regression) and forward stagewise regression, and provides a fast implementation of both. The idea has caught on rapidly, and sparked a great deal of research interest. In this paper, we give an overview of Least Angle Regression and the current state of related research.

stat.ME↗
arXiv2007

Smoothing $\ell_1$-penalized estimators for high-dimensional time-course data

When a series of (related) linear models has to be estimated it is often appropriate to combine the different data-sets to construct more efficient estimators. We use $\ell_1$-penalized estimators like the Lasso or the Adaptive Lasso which can simultaneously do parameter estimation and model selection. We show that for a time-course of high-dimensional linear models the convergence rates of the Lasso and of the Adaptive Lasso can be improved by combining the different time-points in a suitable way. Moreover, the Adaptive Lasso still enjoys oracle properties and consistent variable selection. The finite sample properties of the proposed methods are illustrated on simulated data and on a real problem of motif finding in DNA sequences.

math.ST↗