8 papers
Rethinking Likelihood distributions: Student's t Likelihood Boosts Bayesian Neural Network Performance
Pei-Hsuan Hsia, Lars H. Heyen, Arvid Weyrauch +4
In Bayesian neural networks (BNNs), variational inference is a widely adopted framework for modeling uncertainty in a distributional way, with the evidence lower bound (ELBO) servi…
PurSAMERE: Reliable Adversarial Purification via Sharpness-Aware Minimization of Expected Reconstruction Error
Vinh Hoang, Sebastian Krumscheid, Holger Rauhut +1
We propose a novel deterministic purification method to improve adversarial robustness by mapping a potentially adversarial sample toward a nearby sample that lies close to a mode…
Multilevel randomized quasi-Monte Carlo estimator for nested integration
Arved Bartuska, André Gustavo Carlon, Luis Espath +2
Nested integration problems arise in various scientific and engineering applications, including Bayesian experimental design, financial risk assessment, and uncertainty quantificat…
Structure-Preserving Operator Learning: Modeling the Collision Operator of Kinetic Equations
Jae Yong Lee, Steffen Schotthöfer, Tianbai Xiao +2
This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a…
Scalable method for Bayesian experimental design without integrating over posterior distribution
Vinh Hoang, Luis Espath, Sebastian Krumscheid +1
We address the computational efficiency in solving the A-optimal Bayesian design of experiments problems for which the observational map is based on partial differential equations…
Double-loop randomized quasi-Monte Carlo estimator for nested integration
Arved Bartuska, André Gustavo Carlon, Luis Espath +2
Nested integration of the form $\int f\left(\int g(\bs{y},\bs{x})\di{}\bs{x}\right)\di{}\bs{y}$, characterized by an outer integral connected to an inner integral through a nonline…
On the equivalence of different adaptive batch size selection strategies for stochastic gradient descent methods
Luis Espath, Sebastian Krumscheid, Raúl Tempone +1
In this study, we demonstrate that the norm test and inner product/orthogonality test presented in \cite{Bol18} are equivalent in terms of the convergence rates associated with Sto…
Machine learning-based conditional mean filter: a generalization of the ensemble Kalman filter for nonlinear data assimilation
Truong-Vinh Hoang, Sebastian Krumscheid, Hermann G. Matthies +1
This paper presents the machine learning-based ensemble conditional mean filter (ML-EnCMF) -- a filtering method based on the conditional mean filter (CMF) previously introduced in…