arXiv subjects

Nikolaus Umlauf

Publications and source records attributed to Nikolaus Umlauf.

11 recordsLinked to original sources

arXiv2025

Refuting "Debunking the GAMLSS Myth: Simplicity Reigns in Pulmonary Function Diagnostics"

We read with interest the above article by Zavorsky (2025, Respiratory Medicine, doi:10.1016/j.rmed.2024.107836) concerning reference equations for pulmonary function testing. The author compares a Generalized Additive Model for Location, Scale, and Shape (GAMLSS), which is the standard adopted by the Global Lung Function Initiative (GLI), with a segmented linear regression (SLR) model, for pulmonary function variables. The author presents an interesting comparison; however there are some fundamental issues with the approach. We welcome this opportunity for discussion of the issues that it raises. The author's contention is that (1) SLR provides "prediction accuracies on par with GAMLSS"; and (2) the GAMLSS model equations are "complicated and require supplementary spline tables", whereas the SLR is "more straightforward, parsimonious, and accessible to a broader audience". We respectfully disagree with both of these points.

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arXiv2025

Simultaneous Estimation and Model Choice for Big Discrete Time-to-Event Data with Additive Predictors

Discrete-time hazard models are widely used when event times are measured in intervals or are not precisely observed. While these models can be estimated using standard generalized linear model techniques, they rely on extensive data augmentation, making estimation computationally demanding in high-dimensional settings. In this paper, we demonstrate how the recently proposed Batchwise Backfitting algorithm, a general framework for scalable estimation and variable selection in distributional regression, can be effectively extended to discrete hazard models. Using both simulated data and a large-scale application on infant mortality in sub-Saharan Africa, we show that the algorithm delivers accurate estimates, automatically selects relevant predictors, and scales efficiently to large data sets. The findings underscore the algorithm's practical utility for analysing large-scale, complex survival data with high-dimensional covariates.

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arXiv2024

Generalized Multivariate Functional Additive Mixed Models for Location, Scale, and Shape

We propose a flexible regression framework to model the conditional distribution of multilevel generalized multivariate functional data of potentially mixed type, e.g. binary and continuous data. We make pointwise parametric distributional assumptions for each dimension of the multivariate functional data and model each distributional parameter as an additive function of covariates. The dependency between the different outcomes and, for multilevel functional data, also between different functions within a level is modelled by shared latent multivariate Gaussian processes. For a parsimonious representation of the latent processes, (generalized) multivariate functional principal components are estimated from the data and used as an empirical basis for these latent processes in the regression framework. Our modular two-step approach is very general and can easily incorporate new developments in the estimation of functional principal components for all types of (generalized) functional data. Flexible additive covariate effects for scalar or even functional covariates are available and are estimated in a Bayesian framework. We provide an easy-to-use implementation in the accompanying R package 'gmfamm' on CRAN and conduct a simulation study to confirm the validity of our regression framework and estimation strategy. The proposed multivariate functional model is applied to four dimensional traffic data in Berlin, which consists of the hourly numbers and mean speed of cars and trucks at different locations.

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arXiv2024

Stagewise Boosting Distributional Regression

Forward stagewise regression is a simple algorithm that can be used to estimate regularized models. The updating rule adds a small constant to a regression coefficient in each iteration, such that the underlying optimization problem is solved slowly with small improvements. This is similar to gradient boosting, with the essential difference that the step size is determined by the product of the gradient and a step length parameter in the latter algorithm. One often overlooked challenge in gradient boosting for distributional regression is the issue of a vanishing small gradient, which practically halts the algorithm's progress. We show that gradient boosting in this case oftentimes results in suboptimal models, especially for complex problems certain distributional parameters are never updated due to the vanishing gradient. Therefore, we propose a stagewise boosting-type algorithm for distributional regression, combining stagewise regression ideas with gradient boosting. Additionally, we extend it with a novel regularization method, correlation filtering, to provide additional stability when the problem involves a large number of covariates. Furthermore, the algorithm includes best-subset selection for parameters and can be applied to big data problems by leveraging stochastic approximations of the updating steps. Besides the advantage of processing large datasets, the stochastic nature of the approximations can lead to better results, especially for complex distributions, by reducing the risk of being trapped in a local optimum. The performance of our proposed stagewise boosting distributional regression approach is investigated in an extensive simulation study and by estimating a full probabilistic model for lightning counts with data of more than 9.1 million observations and 672 covariates.

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arXiv2023

Flexible joint models for multivariate longitudinal and time-to-event data using multivariate functional principal components

The joint modeling of multiple longitudinal biomarkers together with a time-to-event outcome is a challenging modeling task of continued scientific interest. In particular, the computational complexity of high dimensional (generalized) mixed effects models often restricts the flexibility of shared parameter joint models, even when the subject-specific marker trajectories follow highly nonlinear courses. We propose a parsimonious multivariate functional principal components representation of the shared random effects. This allows better scalability, as the dimension of the random effects does not directly increase with the number of markers, only with the chosen number of principal component basis functions used in the approximation of the random effects. The functional principal component representation additionally allows to estimate highly flexible subject-specific random trajectories without parametric assumptions. The modeled trajectories can thus be distinctly different for each biomarker. We build on the framework of flexible Bayesian additive joint models implemented in the R-package 'bamlss', which also supports estimation of nonlinear covariate effects via Bayesian P-splines. The flexible yet parsimonious functional principal components basis used in the estimation of the joint model is first estimated in a preliminary step. We validate our approach in a simulation study and illustrate its advantages by analyzing a study on primary biliary cholangitis.

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arXiv2023

Scalable Estimation for Structured Additive Distributional Regression

Recently, fitting probabilistic models have gained importance in many areas but estimation of such distributional models with very large data sets is a difficult task. In particular, the use of rather complex models can easily lead to memory-related efficiency problems that can make estimation infeasible even on high-performance computers. We therefore propose a novel backfitting algorithm, which is based on the ideas of stochastic gradient descent and can deal virtually with any amount of data on a conventional laptop. The algorithm performs automatic selection of variables and smoothing parameters, and its performance is in most cases superior or at least equivalent to other implementations for structured additive distributional regression, e.g., gradient boosting, while maintaining low computation time. Performance is evaluated using an extensive simulation study and an exceptionally challenging and unique example of lightning count prediction over Austria. A very large dataset with over 9 million observations and 80 covariates is used, so that a prediction model cannot be estimated with standard distributional regression methods but with our new approach.

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arXiv2022

Distributional Adaptive Soft Regression Trees

Random forests are an ensemble method relevant for many problems, such as regression or classification. They are popular due to their good predictive performance (compared to, e.g., decision trees) requiring only minimal tuning of hyperparameters. They are built via aggregation of multiple regression trees during training and are usually calculated recursively using hard splitting rules. Recently regression forests have been incorporated into the framework of distributional regression, a nowadays popular regression approach aiming at estimating complete conditional distributions rather than relating the mean of an output variable to input features only - as done classically. This article proposes a new type of a distributional regression tree using a multivariate soft split rule. One great advantage of the soft split is that smooth high-dimensional functions can be estimated with only one tree while the complexity of the function is controlled adaptive by information criteria. Moreover, the search for the optimal split variable is obsolete. We show by means of extensive simulation studies that the algorithm has excellent properties and outperforms various benchmark methods, especially in the presence of complex non-linear feature interactions. Finally, we illustrate the usefulness of our approach with an example on probabilistic forecasts for the Sun's activity.

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arXiv2021

Cholesky-based multivariate Gaussian regression

Distributional regression is extended to Gaussian response vectors of dimension greater than two by parameterizing the covariance matrix $Σ$ of the response distribution using the entries of its Cholesky decomposition. The more common variance-correlation parameterization limits such regressions to bivariate responses -- higher dimensions require complicated constraints among the correlations to ensure positive definite $Σ$ and a well-defined probability density function. In contrast, Cholesky-based parameterizations ensure positive definiteness for all distributional dimensions no matter what values the parameters take, enabling estimation and regularization as for other distributional regression models. In cases where components of the response vector are assumed to be conditionally independent beyond a certain lag $r$, model complexity can be further reduced by setting Cholesky parameters beyond this lag to zero a priori. Cholesky-based multivariate Gaussian regression is first illustrated and assessed on artificial data and subsequently applied to a real-world 10-dimensional weather forecasting problem. There the regression is used to obtain reliable joint probabilities of temperature across ten future times, leveraging temporal correlations over the prediction period to obtain more precise and meteorologically consistent probabilistic forecasts.

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arXiv2019

bamlss: A Lego Toolbox for Flexible Bayesian Regression (and Beyond)

Over the last decades, the challenges in applied regression and in predictive modeling have been changing considerably: (1) More flexible model specifications are needed as big(ger) data become available, facilitated by more powerful computing infrastructure. (2) Full probabilistic modeling rather than predicting just means or expectations is crucial in many applications. (3) Interest in Bayesian inference has been increasing both as an appealing framework for regularizing or penalizing model estimation as well as a natural alternative to classical frequentist inference. However, while there has been a lot of research in all three areas, also leading to associated software packages, a modular software implementation that allows to easily combine all three aspects has not yet been available. For filling this gap, the R package bamlss is introduced for Bayesian additive models for location, scale, and shape (and beyond). At the core of the package are algorithms for highly-efficient Bayesian estimation and inference that can be applied to generalized additive models (GAMs) or generalized additive models for location, scale, and shape (GAMLSS), also known as distributional regression. However, its building blocks are designed as "Lego bricks" encompassing various distributions (exponential family, Cox, joint models, ...), regression terms (linear, splines, random effects, tensor products, spatial fields, ...), and estimators (MCMC, backfitting, gradient boosting, lasso, ...). It is demonstrated how these can be easily recombined to make classical models more flexible or create new custom models for specific modeling challenges.

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arXiv2017

Nonlinear association structures in flexible Bayesian additive joint models

Joint models of longitudinal and survival data have become an important tool for modeling associations between longitudinal biomarkers and event processes. The association between marker and log-hazard is assumed to be linear in existing shared random effects models, with this assumption usually remaining unchecked. We present an extended framework of flexible additive joint models that allows the estimation of nonlinear, covariate specific associations by making use of Bayesian P-splines. Our joint models are estimated in a Bayesian framework using structured additive predictors for all model components, allowing for great flexibility in the specification of smooth nonlinear, time-varying and random effects terms for longitudinal submodel, survival submodel and their association. The ability to capture truly linear and nonlinear associations is assessed in simulations and illustrated on the widely studied biomedical data on the rare fatal liver disease primary biliary cirrhosis. All methods are implemented in the R package bamlss to facilitate the application of this flexible joint model in practice.

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arXiv2017

Flexible Bayesian additive joint models with an application to type 1 diabetes research

The joint modeling of longitudinal and time-to-event data is an important tool of growing popularity to gain insights into the association between a biomarker and an event process. We develop a general framework of flexible additive joint models that allows the specification of a variety of effects, such as smooth nonlinear, time-varying and random effects, in the longitudinal and survival parts of the models. Our extensions are motivated by the investigation of the relationship between fluctuating disease-specific markers, in this case autoantibodies, and the progression to the autoimmune disease type 1 diabetes. By making use of Bayesian P-splines we are in particular able to capture highly nonlinear subject-specific marker trajectories as well as a time-varying association between the marker and the event process allowing new insights into disease progression. The model is estimated within a Bayesian framework and implemented in the R-package bamlss.

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