18 papers
A weak transport approach to the Schrödinger-Bass bridge
Manuel Hasenbichler, Gudmund Pammer, Stefan Thonhauser
We study the Schrödinger-Bass problem, a one-parameter family of semimartingale optimal transport problems indexed by , whose limiting regimes interpolate between the classi…
Tighter Learning Guarantees on Digital Computers via Concentration of Measure on Finite Spaces
Anastasis Kratsios, A. Martina Neuman, Gudmund Pammer
Machine learning models with inputs in a Euclidean space , when implemented on digital computers, generalize, and their generalization gap converges to at a rate…
Implicit Regularization of Large Neural Networks via Mean-Field Formulation
Beatrice Acciaio, Jakob Heiss, Gudmund Pammer +1
We propose a mathematical framework to explain implicit regularization from early stopping during the training of overparametrized neural networks. In the mean-field limit, the par…
The Martingale Sinkhorn Algorithm
Manuel Hasenbichler, Benjamin Joseph, Gregoire Loeper +2
We develop a numerical method for the martingale analogue of the Benamou--Brenier optimal transport problem, which seeks a martingale interpolating two prescribed marginals which i…
The geometry of the adapted Bures--Wasserstein space
Beatrice Acciaio, Daniel Bartl, Anne Grass +2
The adapted Bures--Wasserstein space consists of Gaussian processes endowed with the adapted Wasserstein distance. It can be viewed as the analogue of the classical Bures--Wasserst…
Dynamic reinsurance via martingale transport
Beatrice Acciaio, Brandon Garcia Flores, Antonio Marini +1
We formulate a dynamic reinsurance problem in which the insurer seeks to control the terminal distribution of its surplus while minimizing the L2-norm of the ceded risk. Using tech…