AA5 – Variational Problems in Data-Driven Applications


AA5-4 (was EF1-22)

Bayesian Optimization and Inference for Deep Networks

Project Heads

Claudia Schillings, Vladimir Spokoiny

Project Members

Project Duration

01.01.2023 − 31.12.2024

Located at



Uncertainty quantification (UQ) and reliability of deep neuronal networks is an important research question. This project aims at developing of novel numerically efficient methods for inference and UQ analysis of DNN with theoretical guarantees. Particular issues to address are high parameter dimension and nonconvexity of the objective function. We propose a new insight on the problem using the recent progress in high dimensional Laplace approximation. A further goal is to apply the proposed methods to various application problems.

External Website

Selected Publications

  • S. Athreya, O. Butkovsky, K. Lê, L. Mytnik. Well-posedness of stochastic heat equation with distributional drift and skew stochastic heat equation. Communications on Pure and Applied Mathematics, to appear, 2023+.
  • C. Bayer, D. Belomestny, O. Butkovsky, J. Schoenmakers. RKHS regularization of singular local stochastic volatility McKean-Vlasov models. Finance and Stochastics, minor revision, 2023.
  • O. Butkovsky, K. Dareiotis, M. Gerencsér. Optimal rate of convergence for approximations of SPDEs with nonregular drift. SIAM Journal on Numerical Analysis, 61(2):1103–1137, 2023.
  • O. Butkovsky, K. Dareiotis, M. Gerencsér. Strong rate of convergence of the Euler scheme for SDEs with irregular drift driven by Lévy noise. Annales de l’Institut Henri Poincare (B) Probabilites et Statistiques, to appear, 2023+.
  • O. Butkovsky, K. Lê, L. Mytnik. Stochastic equations with singular drift driven by fractional Brownian motion, 2023. arXiv:2302.11937.

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