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View article: Asymptotic confidence bands for the histogram regression estimator
Asymptotic confidence bands for the histogram regression estimator Open
In a multivariate nonparametric regression model with a Hölder continuous regression function and heteroscedastic noise asymptotic uniform confidence bands are constructed based on the histogram estimator. The radius of the confidence band…
View article: Characterization of Besov spaces with dominating mixed smoothness by differences
Characterization of Besov spaces with dominating mixed smoothness by differences Open
Besov spaces with dominating mixed smoothness, on the product of the real line and the torus as well as bounded domains, are studied. A characterization of these function spaces in terms of differences is provided. Applications to random f…
View article: Calibrating Bayesian generative machine learning for Bayesiamplification
Calibrating Bayesian generative machine learning for Bayesiamplification Open
Recently, combinations of generative and Bayesian deep learning have been introduced in particle physics for both fast detector simulation and inference tasks. These neural networks aim to quantify the uncertainty on the generated distribu…
View article: Classifier surrogates: sharing AI-based searches with the world
Classifier surrogates: sharing AI-based searches with the world Open
In recent years, neural network-based classification has been used to improve data analysis at collider experiments. While this strategy proves to be hugely successful, the underlying models are not commonly shared with the public and rely…
View article: Characterization of Besov spaces with dominating mixed smoothness by differences
Characterization of Besov spaces with dominating mixed smoothness by differences Open
Besov spaces with dominating mixed smoothness, on the product of the real line and the torus as well as bounded domains, are studied. A characterization of these function spaces in terms of differences is provided. Applications to random f…
View article: Classifier Surrogates: Sharing AI-based Searches with the World
Classifier Surrogates: Sharing AI-based Searches with the World Open
In recent years, neural network-based classification has been used to improve data analysis at collider experiments. While this strategy proves to be hugely successful, the underlying models are not commonly shared with the public and rely…
View article: AdamMCMC: Combining Metropolis Adjusted Langevin with Momentum-based Optimization
AdamMCMC: Combining Metropolis Adjusted Langevin with Momentum-based Optimization Open
Uncertainty estimation is a key issue when considering the application of deep neural network methods in science and engineering. In this work, we introduce a novel algorithm that quantifies epistemic uncertainty via Monte Carlo sampling f…
View article: The surrogate Gibbs-posterior of a corrected stochastic MALA: Towards uncertainty quantification for neural networks
The surrogate Gibbs-posterior of a corrected stochastic MALA: Towards uncertainty quantification for neural networks Open
MALA is a popular gradient-based Markov chain Monte Carlo method to access the Gibbs-posterior distribution. Stochastic MALA (sMALA) scales to large data sets, but changes the target distribution from the Gibbs-posterior to a surrogate pos…
View article: Dimensionality Reduction and Wasserstein Stability for Kernel Regression
Dimensionality Reduction and Wasserstein Stability for Kernel Regression Open
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 reduced input variables are used to predict the output variable w…
View article: Calomplification — the power of generative calorimeter models
Calomplification — the power of generative calorimeter models Open
Motivated by the high computational costs of classical simulations, machine-learned generative models can be extremely useful in particle physics and elsewhere. They become especially attractive when surrogate models can efficiently learn …
View article: A PAC-Bayes oracle inequality for sparse neural networks
A PAC-Bayes oracle inequality for sparse neural networks Open
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 algorithms. Using a mixture over uniform priors on sparse sets of n…
View article: Dispersal density estimation across scales
Dispersal density estimation across scales Open
We consider a space structured population model generated by two point clouds: a homogeneous Poisson process $M$ with intensity $n\to\infty$ as a model for a parent generation together with a Cox point process $N$ as offspring generation, …
View article: Nonparametric calibration for stochastic reaction-diffusion equations based on discrete observations
Nonparametric calibration for stochastic reaction-diffusion equations based on discrete observations Open
Nonparametric estimation for semilinear SPDEs, namely stochastic reaction-diffusion equations in one space dimension, is studied. We consider observations of the solution field on a discrete grid in time and space with infill asymptotics i…
View article: Parameter estimation for SPDEs based on discrete observations in time and space
Parameter estimation for SPDEs based on discrete observations in time and space Open
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 bounded domain. Considering an infill asymptotic regime in bo…
View article: Parameter estimation for SPDEs based on discrete observations in time\n and space
Parameter estimation for SPDEs based on discrete observations in time\n and space Open
Parameter estimation for a parabolic linear stochastic partial differential\nequation in one space dimension is studied observing the solution field on a\ndiscrete grid in a fixed bounded domain. Considering an infill asymptotic\nregime in…
View article: Sparse covariance matrix estimation in high-dimensional deconvolution
Sparse covariance matrix estimation in high-dimensional deconvolution Open
We study the estimation of the covariance matrix $Σ$ of a $p$-dimensional normal random vector based on $n$ independent observations corrupted by additive noise. Only a general nonparametric assumption is imposed on the distribution of the…
View article: Profiting from correlations: Adjusted estimators for categorical data
Profiting from correlations: Adjusted estimators for categorical data Open
To take sample biases and skewness in the observations into account, practitioners frequently weight their observations according to some marginal distribution. The present paper demonstrates that such weighting can indeed improve the esti…
View article: On central limit theorems for power variations of the solution to the\n stochastic heat equation
On central limit theorems for power variations of the solution to the\n stochastic heat equation Open
We consider the stochastic heat equation whose solution is observed\ndiscretely in space and time. An asymptotic analysis of power variations is\npresented including the proof of a central limit theorem. It generalizes the\ntheory from arX…
View article: Paracontrolled distribution approach to stochastic Volterra equations
Paracontrolled distribution approach to stochastic Volterra equations Open
Based on the notion of paracontrolled distributions, we provide existence and uniqueness results for rough Volterra equations of convolution type with potentially singular kernels and driven by the newly introduced class of convolutional r…
View article: Bayesian inverse problems with unknown operators
Bayesian inverse problems with unknown operators Open
We consider the Bayesian approach to linear inverse problems when the\nunderlying operator depends on an unknown parameter. Allowing for finite\ndimensional as well as infinite dimensional parameters, the theory covers\nseveral models with…
View article: Volatility estimation for stochastic PDEs using high-frequency\n observations
Volatility estimation for stochastic PDEs using high-frequency\n observations Open
We study the parameter estimation for parabolic, linear, second-order,\nstochastic partial differential equations (SPDEs) observing a mild solution on\na discrete grid in time and space. A high-frequency regime is considered where\nthe mes…
View article: Profiting from correlations: Adjusted estimators for discrete probability distributions
Profiting from correlations: Adjusted estimators for discrete probability distributions Open
To take sample biases and skewness in the observations into account, practitioners frequently adapt their observations to some marginal distribution using weights. Considering discrete distributions, the present paper explores the effect o…
View article: Adjusting estimators for marginal distributions in contingency tables
Adjusting estimators for marginal distributions in contingency tables Open
To take sample biases and skewness in the observations in account, practitioners frequently weight their observations. Considering discrete distributions, the present paper explores the effect of weighted data from an asymptotic point of v…
View article: Adaptive confidence bands for Markov chains and diffusions: Estimating the invariant measure and the drift
Adaptive confidence bands for Markov chains and diffusions: Estimating the invariant measure and the drift Open
\n As a starting point we prove a functional central limit theorem for estimators of the\n invariant measure of a geometrically ergodic Harris-recurrent Markov chain in a\n multi-scale space. This allows to construct confidence bands for t…