48 citations · 192 across the 16 of their papers we have counts for
24 papers
A PAC-Bayes oracle inequality for sparse neural networks
Maximilian F. Steffen, Mathias Trabs
We study the Gibbs posterior distribution for sparse deep neural nets in a nonparametric regression setting. The posterior can be accessed via Metropolis-adjusted Langevin algorith…
Dimensionality Reduction and Wasserstein Stability for Kernel Regression
Stephan Eckstein, Armin Iske, Mathias Trabs
In a high-dimensional regression framework, we study consequences of the naive two-step procedure where first the dimension of the input variables is reduced and second, the reduce…
Calomplification -- The Power of Generative Calorimeter Models
Sebastian Bieringer, Anja Butter, Sascha Diefenbacher +7
Motivated by the high computational costs of classical simulations, machine-learned generative models can be extremely useful in particle physics and elsewhere. They become especia…
Dispersal density estimation across scales
Marc Hoffmann, Mathias Trabs
We consider a space structured population model generated by two point clouds: a homogeneous Poisson process with intensity as a model for a parent generation toge…
Nonparametric calibration for stochastic reaction-diffusion equations based on discrete observations
Florian Hildebrandt, Mathias Trabs
Nonparametric estimation for semilinear SPDEs, namely stochastic reaction-diffusion equations in one space dimension, is studied. We consider observations of the solution field on…
Parameter estimation for SPDEs based on discrete observations in time and space
Florian Hildebrandt, Mathias Trabs
Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bo…
On central limit theorems for power variations of the solution to the stochastic heat equation
Markus Bibinger, Mathias Trabs
We consider the stochastic heat equation whose solution is observed discretely in space and time. An asymptotic analysis of power variations is presented including the proof of a c…
Paracontrolled distribution approach to stochastic Volterra equations
David J. Prömel, Mathias Trabs
Based on the notion of paracontrolled distributions, we provide existence and uniqueness results for rough Volterra equations of convolution type with potentially singular kernels…
Bayesian inverse problems with unknown operators
Mathias Trabs
We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimen…
Sparse covariance matrix estimation in high-dimensional deconvolution
Denis Belomestny, Mathias Trabs, Alexandre B. Tsybakov
We study the estimation of the covariance matrix of a -dimensional normal random vector based on independent observations corrupted by additive noise. Only a general non…
Volatility estimation for stochastic PDEs using high-frequency observations
Markus Bibinger, Mathias Trabs
We study the parameter estimation for parabolic, linear, second-order, stochastic partial differential equations (SPDEs) observing a mild solution on a discrete grid in time and sp…
Profiting from correlations: Adjusted estimators for categorical data
Tobias Niebuhr, Mathias Trabs
To take sample biases and skewness in the observations into account, practitioners frequently weight their observations according to some marginal distribution. The present paper d…
Low-rank diffusion matrix estimation for high-dimensional time-changed Lévy processes
Denis Belomestny, Mathias Trabs
The estimation of the diffusion matrix of a high-dimensional, possibly time-changed Lévy process is studied, based on discrete observations of the process with a fixed distance…
Rough differential equations driven by signals in Besov spaces
David J. Prömel, Mathias Trabs
Rough differential equations are solved for signals in general Besov spaces unifying in particular the known results in Hölder and p-variation topology. To this end the paracontrol…
Spectral estimation for diffusions with random sampling times
Jakub Chorowski, Mathias Trabs
The nonparametric estimation of the volatility and the drift coefficient of a scalar diffusion is studied when the process is observed at random time points. The constructed estima…
Adaptive confidence bands for Markov chains and diffusions: Estimating the invariant measure and the drift
Jakob Söhl, Mathias Trabs
As a starting point we prove a functional central limit theorem for estimators of the invariant measure of a geometrically ergodic Harris-recurrent Markov chain in a multi-scale sp…
Quantile estimation for Lévy measures
Mathias Trabs
Generalizing the concept of quantiles to the jump measure of a Lévy process, the generalized quantiles , for , are given by the smallest values such that a jump l…
On infinitely divisible distributions with polynomially decaying characteristic functions
Mathias Trabs
We provide necessary and sufficient conditions on the characteristics of an infinitely divisible distribution under which its characteristic function decays polynomially. Under…
High-frequency Donsker theorems for Lévy measures
Richard Nickl, Markus Reiß, Jakob Söhl +1
Donsker-type functional limit theorems are proved for empirical processes arising from discretely sampled increments of a univariate Lévy process. In the asymptotic regime the samp…
Information bounds for inverse problems with application to deconvolution and Lévy models
Mathias Trabs
If a functional in an inverse problem can be estimated with parametric rate, then the minimax rate gives no information about the ill-posedness of the problem. To have a more preci…
Adaptive quantile estimation in deconvolution with unknown error distribution
Itai Dattner, Markus Reiß, Mathias Trabs
Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is b…
A uniform central limit theorem and efficiency for deconvolution estimators
Jakob Söhl, Mathias Trabs
We estimate linear functionals in the classical deconvolution problem by kernel estimators. We obtain a uniform central limit theorem with -rate on the assumption that th…
Option calibration of exponential Lévy models: Confidence intervals and empirical results
Jakob Söhl, Mathias Trabs
Observing prices of European put and call options, we calibrate exponential Lévy models nonparametrically. We discuss the efficient implementation of the spectral estimation proced…
Calibration of self-decomposable Lévy models
Mathias Trabs
We study the nonparametric calibration of exponential Lévy models with infinite jump activity. In particular our analysis applies to self-decomposable processes whose jump density…