Lukas Meier

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.

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 that 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. This involves a one-time random split of the data, however. Results are sensitive to this arbitrary choice, which 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 maintaining 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 and false discovery rate. In addition, the proposed aggregation is shown to improve power while reducing the number of falsely selected variables substantially.

On the mechanism of extractive electrospray ionization.

Extractive electrospray ionization (EESI) is a powerful ambient ionization technique that can provide comprehensive mass spectrometric (MS) information on aerosols, complex liquids, or suspensions without any sample pretreatment. An understanding of the EESI mechanism is critical for defining its range of application, the advantages, and limitations of EESI, and for improving its repeatability, sensitivity, and selectivity. However, no systematic study of EESI mechanisms has been conducted so far. In this work, fluorescence studies in the EESI plume using rhodamine 6G and H-acid sodium salt directly demonstrate that liquid-phase interactions occur between charged ESI droplets and neutral sample droplets. Moreover, the effect of the composition of the primary ESI spray and sample spray on signals of the analyte in EESI-MS was investigated systematically. The results show that the analyte signals strongly depend on its solubility in the solvents involved, indicating that selective extraction is the dominant mechanism involved in the EESI process. This mechanistic study provides valuable insights for optimizing the performance of EESI in future applications.

Rapid fingerprinting and classification of extra virgin olive oil by microjet sampling and extractive electrospray ionization mass spectrometry

Microjet sampling in combination with extractive electrospray ionization (EESI) mass spectrometry (MS) was applied to the rapid characterization and classification of extra virgin olive oil (EVOO) without any sample pretreatment. When modifying the composition of the primary ESI spray solvent, mass spectra of an identical EVOO sample showed differences. This demonstrates the capability of this technique to extract molecules with varying polarities, hence generating rich molecular information of the EVOO. Moreover, with the aid of microjet sampling, compounds of different volatilities (e.g.E-2-hexenal, trans-trans-2,4-heptadienal, tyrosol and caffeic acid) could be sampled simultaneously. EVOO data was also compared with that of other edible oils. Principal Component Analysis (PCA) was performed to discriminate EVOO and EVOO adulterated with edible oils. Microjet sampling EESI-MS was found to be a simple, rapid (less than 2 min analysis time per sample) and powerful method to obtain MS fingerprints of EVOO without requiring any complicated sample pretreatment steps.

High-dimensional inference: confidence intervals, p-values and R-software hdi

We present a (selective) review of recent frequentist highdimensional 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 Rpackage hdi which easily allows the use of different methods and supports reproducibility.

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 (GLMMs). GLMMs can be viewed as an extension of generalized linear models for clustered observations. Our 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 that are more severe with GLMMs than for generalized linear models. We illustrate the performance of our algorithm on simulated as well as on real data examples. Supplementary materials are available online and the algorithm is implemented in the R package glmmixedlasso.

Extractive Electrospray Ionization Mass Spectrometry—Enhanced Sensitivity Using an Ion Funnel

Electrodynamic ion funnel interfaces for electrospray ionization (ESI) have shown to enhance the sensitivity of measurements by more than 2 orders of magnitude in the intermediate pressure region of the instrument (1-30 Torr). In this study, we use an ion funnel at ambient pressure to enhance the sensitivity of extractive electrospray ionization (EESI) by spraying directly into the ion funnel. EESI is a powerful ionization technique that is capable of handling complex matrixes that may contain dozens of compounds. Our results using atenolol, salbutamol, and cocaine as test compounds show that we can improve the limit of detection for these compounds by more than 3 orders of magnitude compared to standard EESI experiments.

Smoothing ℓ1-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 usel1-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 lin- ear 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. AMS 2000 subject classifications: Primary 62J07; secondary 62J99, 62H12.

Breath analysis in real time by mass spectrometry in chronic obstructive pulmonary disease.

Background: It has been suggested that exhaled breath contains relevant information on health status. Objectives: We hypothesized that a novel mass spectrometry (MS) technique to analyze breath in real time could be useful to differentiate breathprints from chronic obstructive pulmonary disease (COPD) patients and controls (smokers and nonsmokers). Methods: We studied 61 participants including 25 COPD patients [Global Initiative for Obstructive Lung Disease (GOLD) stages I-IV], 25 nonsmoking controls and 11 smoking controls. We analyzed their breath by MS in real time. Raw mass spectra were then processed and statistically analyzed. Results: A panel of discriminating mass-spectral features was identified for COPD (all stages; n = 25) versus healthy nonsmokers (n = 25), COPD (all stages; n = 25) versus healthy smokers (n = 11) and mild COPD (GOLD stages I/II; n = 13) versus severe COPD (GOLD stages III/IV; n = 12). A blind classification (i.e. leave-one-out cross validation) resulted in 96% sensitivity and 72.7% specificity (COPD vs. smoking controls), 88% sensitivity and 92% specificity (COPD vs. nonsmoking controls) and 92.3% sensitivity and 83.3% specificity (GOLD I/II vs. GOLD III/IV). Acetone and indole were identified as two of the discriminating exhaled molecules. Conclusions: We conclude that real-time MS may be a useful technique to analyze and characterize the metabolome of exhaled breath. The acquisition of breathprints in a rapid manner may be valuable to support COPD diagnosis and to gain insight into the disease.

Direct detection of chlorpropham on potato skin using desorption electrospray ionization

Most pesticides, herbicides and other plant treatment agents are applied to the crop surface. Direct mass spectrometric methods, such as desorption electrospray ionization (DESI), offer new ways to analyze plant samples directly and rapidly. A strategy for the development and optimization of a DESI method for the direct determination of chemicals on complex surfaces is described. Chlorpropham (CP) was applied to potato surfaces as an example for a crop protection agent and analyzed using a self-made DESI source. Aspects such as instrument selectivity, sensitivity and reproducibility were investigated. The MS(4) fragmentation pattern of CP was analyzed to achieve the necessary detection selectivity, and is discussed in detail. Similar fragmentation was found in the ESI and DESI mass spectra, indicating that the mechanisms of ESI and DESI are closely related. A DESI method for semi-quantification of CP on potatoes was developed. Detection limits of 6.5 µg/kg were found using MS/MS. The reproducibility, in the range of 12% (signal variation), appears to be sufficient for semi-quantitative measurements.