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The validity of estimation and smoothing parameter selection for the wide class of generalized additive models for location, scale and shape (GAMLSS) relies on the correct specification of a likelihood function. Deviations from such…

A statistical emulator can be used as a surrogate of complex physics-based calculations to drastically reduce the computational cost. Its successful implementation hinges on an accurate representation of the nonlinear response surface with…

Motivation: Alignment-free distance and similarity functions (AF functions, for short) are a well established alternative to two and multiple sequence alignments for many genomic, metagenomic and epigenomic tasks. Due to data-intensive…

High-dimensional functional data are becoming increasingly common in fields such as environmental monitoring and neuroimaging. This paper studies high-dimensional functional linear regression models that relate a scalar response to…

In a recent article (Proc. Natl. Acad. Sci., 110(36), 14557-14562), El Karoui et al. study the distribution of robust regression estimators in the regime in which the number of parameters p is of the same order as the number of samples n.…

In this work, we propose a novel adaptive stochastic gradient-free (ASGF) approach for solving high-dimensional nonconvex optimization problems based on function evaluations. We employ a directional Gaussian smoothing of the target function…

Inhomogeneities in real-world data, e.g., due to changes in the observation noise level or variations in the structural complexity of the source function, pose a unique set of challenges for statistical inference. Accounting for them can…

Gaussian process (GP) regression provides a strategy for accelerating saddle point searches on high-dimensional energy surfaces by reducing the number of times the energy and its derivatives with respect to atomic coordinates need to be…

This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a…

High dimensional Vector Autoregressions (VAR) have received a lot of interest recently due to novel applications in health, engineering, finance and the social sciences. Three issues arise when analyzing VAR's: (a) The high dimensional…

Gaussian processes are a widely embraced technique for regression and classification due to their good prediction accuracy, analytical tractability and built-in capabilities for uncertainty quantification. However, they suffer from the…

Anomaly detection (AD) plays a vital role across a wide range of real-world domains by identifying data instances that deviate from expected patterns, potentially signaling critical events such as system failures, fraudulent activities, or…

We consider the problem of active learning for global sensitivity analysis of expensive black-box functions. Our aim is to efficiently learn the importance of different input variables, e.g., in vehicle safety experimentation, we study the…

We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…

Anomaly detection (AD) is the machine learning task of identifying highly discrepant abnormal samples by solely relying on the consistency of the normal training samples. Under the constraints of a distribution shift, the assumption that…

All machine learning algorithms use a loss, cost, utility or reward function to encode the learning objective and oversee the learning process. This function that supervises learning is a frequently unrecognized hyperparameter that…

Value function approximation is a crucial module for policy evaluation in reinforcement learning when the state space is large or continuous. The present paper takes a generative perspective on policy evaluation via temporal-difference (TD)…

For artificial deep neural networks, we prove expression rates for analytic functions $f:\mathbb{R}^d\to\mathbb{R}$ in the norm of $L^2(\mathbb{R}^d,\gamma_d)$ where $d\in {\mathbb{N}}\cup\{ \infty \}$. Here $\gamma_d$ denotes the Gaussian…

Density functional theory (DFT) serves as the basis for computational discovery in materials science and chemistry, yet each calculation demands extensive human effort: adjusting algorithms when convergence stalls, revising plans when…

Datasets with extreme observations and/or heavy-tailed error distributions are commonly encountered and should be analyzed with careful consideration of these features from a statistical perspective. Small deviations from an assumed model,…