151 citations · 321 across the 18 of their papers we have counts for
23 papers
Optimal approximation of smooth functions by ReLU neural networks
Thomas Nagler
We study uniform approximation of the Hölder ball by fully connected ReLU networks. Except in the one-dimensional Lipschitz case, existing constructions r…
Characterizing the Separability Gap in Prior-Data Fitted Networks
Julius Kobialka, Manuel Hülskamp, Thomas Nagler +1
Prior-data fitted networks (PFNs) are transformers pretrained on simulated datasets to approximate Bayesian posterior predictive distributions. Standard PFN theory assumes a separa…
Statistical Foundations of Prior-Data Fitted Networks
Thomas Nagler
Prior-data fitted networks (PFNs) were recently proposed as a new paradigm for machine learning. Instead of training the network to an observed training set, a fixed model is pre-t…
Approximately Bayes-Optimal Pseudo Label Selection
Julian Rodemann, Jann Goschenhofer, Emilio Dorigatti +2
Semi-supervised learning by self-training heavily relies on pseudo-label selection (PLS). The selection often depends on the initial model fit on labeled data. Early overfitting mi…
Modeling Stochastic Data Using Copulas For Application in Validation of Autonomous Driving
Katrin Lotto, Thomas Nagler, Mladjan Radic
Verification and validation of fully automated vehicles is linked to an almost intractable challenge of reflecting the real world with all its interactions in a virtual environment…
Statistical Dependence Analyses of Operational Flight Data Used for Landing Reconstruction Enhancement
Lukas Höhndorf, Thomas Nagler, Phillip Koppitz +2
The RTS smoother is widely used for state estimation and it is utilized here to increase the data quality with respect to physical coherence and to increase resolution. The purpose…
Explaining predictive models using Shapley values and non-parametric vine copulas
Kjersti Aas, Thomas Nagler, Martin Jullum +1
The original development of Shapley values for prediction explanation relied on the assumption that the features being described were independent. If the features in reality are de…
Copula-based synthetic data augmentation for machine-learning emulators
David Meyer, Thomas Nagler, Robin J. Hogan
Can we improve machine-learning (ML) emulators with synthetic data? If data are scarce or expensive to source and a physical model is available, statistically generated data may be…
Stationary vine copula models for multivariate time series
Thomas Nagler, Daniel Krüger, Aleksey Min
Multivariate time series exhibit two types of dependence: across variables and across time points. Vine copulas are graphical models for the dependence and can conveniently capture…
Modeling high-dimensional dependence among astronomical data
Roberto Vio, Thomas W. Nagler, Paola Andreani
Fixing the relationship of a set of experimental quantities is a fundamental issue in many scientific disciplines. In the 2D case, the classical approach is to compute the linear c…
Vine copula based post-processing of ensemble forecasts for temperature
Annette Möller, Ludovica Spazzini, Daniel Kraus +2
Today weather forecasting is conducted using numerical weather prediction (NWP) models, consisting of a set of differential equations describing the dynamics of the atmosphere. The…
R friendly multi-threading in C++
Thomas Nagler
Calling multi-threaded C++ code from R has its perils. Since the R interpreter is single-threaded, one must not check for user interruptions or print to the R console from multiple…
A Statistical Simulation Method for Joint Time Series of Non-stationary Hourly Wave Parameters
Wiebke S. Jäger, Thomas Nagler, Claudia Czado +1
Statistically simulated time series of wave parameters are required for many coastal and offshore engineering applications, often at the resolution of approximately one hour. Vario…
Solving estimating equations with copulas
Thomas Nagler, Thibault Vatter
Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. Mor…
Model selection in sparse high-dimensional vine copula models with application to portfolio risk
Thomas Nagler, Christian Bumann, Claudia Czado
Vine copulas allow to build flexible dependence models for an arbitrary number of variables using only bivariate building blocks. The number of parameters in a vine copula model in…
Heavy tailed spatial autocorrelation models
A. Kreuzer, T. Erhardt, T. Nagler +1
Appropriate models for spatially autocorrelated data account for the fact that observations are not independent. A popular model in this context is the simultaneous autoregressive…
D-vine quantile regression with discrete variables
Niklas Schallhorn, Daniel Kraus, Thomas Nagler +1
Quantile regression, the prediction of conditional quantiles, finds applications in various fields. Often, some or all of the variables are discrete. The authors propose two new qu…
Asymptotic analysis of the jittering kernel density estimator
Thomas Nagler
Jittering estimators are nonparametric function estimators for mixed data. They extend arbitrary estimators from the continuous setting by adding random noise to discrete variables…
A generic approach to nonparametric function estimation with mixed data
Thomas Nagler
In practice, data often contain discrete variables. But most of the popular nonparametric estimation methods have been developed in a purely continuous framework. A common trick am…
Nonparametric estimation of simplified vine copula models: comparison of methods
Thomas Nagler, Christian Schellhase, Claudia Czado
In the last decade, simplified vine copula models have been an active area of research. They build a high dimensional probability density from the product of marginals densities an…
Generalized Additive Models for Pair-Copula Constructions
Thibault Vatter, Thomas Nagler
Pair-copula constructions are flexible dependence models that use bivariate copulas as building blocks. In this paper, we use generalized additive models to extend them by allowing…
kdecopula: An R Package for the Kernel Estimation of Bivariate Copula Densities
Thomas Nagler
We describe the R package kdecopula (current version 0.9.0), which provides fast implementations of various kernel estimators for the copula density. Due to a variety of available…
Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas
Thomas Nagler, Claudia Czado
Practical applications of nonparametric density estimators in more than three dimensions suffer a great deal from the well-known curse of dimensionality: convergence slows down as…