12 citations · 35 across the 14 of their papers we have counts for
16 papers
Gromov-Wasserstein Quantization and Clustering: Structure, Rates, and Algorithms
Florian Beier, Stephan Eckstein
Clustering is a fundamental class of data analysis techniques with the most important representatives being centroid-based methods like -means. Such methods are strongly connect…
Optimal transport and Wasserstein distances for causal models
Patrick Cheridito, Stephan Eckstein
In this paper, we introduce a variant of optimal transport adapted to the causal structure given by an underlying directed graph . Different graph structures lead to different s…
Stability and Sample Complexity of Divergence Regularized Optimal Transport
Erhan Bayraktar, Stephan Eckstein, Xin Zhang
We study stability and sample complexity properties of divergence regularized optimal transport (DOT). First, we obtain quantitative stability results for optimizers of DOT measure…
Convergence Rates for Regularized Optimal Transport via Quantization
Stephan Eckstein, Marcel Nutz
We study the convergence of divergence-regularized optimal transport as the regularization parameter vanishes. Sharp rates for general divergences including relative entropy or $L^…
Dimensionality Reduction and Wasserstein Stability for Kernel Regression
Stephan Eckstein, Armin Iske, Mathias Trabs
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 reduce…
Computational methods for adapted optimal transport
Stephan Eckstein, Gudmund Pammer
Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In t…
Quantitative Stability of Regularized Optimal Transport and Convergence of Sinkhorn's Algorithm
Stephan Eckstein, Marcel Nutz
We study the stability of entropically regularized optimal transport with respect to the marginals. Lipschitz continuity of the value and Hölder continuity of the optimal coupling…
MinMax Methods for Optimal Transport and Beyond: Regularization, Approximation and Numerics
Luca De Gennaro Aquino, Stephan Eckstein
We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of…
Lipschitz neural networks are dense in the set of all Lipschitz functions
Stephan Eckstein
This note shows that, for a fixed Lipschitz constant , one layer neural networks that are -Lipschitz are dense in the set of all -Lipschitz functions with respect to t…
Limits of random walks with distributionally robust transition probabilities
Daniel Bartl, Stephan Eckstein, Michael Kupper
We consider a nonlinear random walk which, in each time step, is free to choose its own transition probability within a neighborhood (w.r.t. Wasserstein distance) of the transition…
Robust pricing and hedging of options on multiple assets and its numerics
Stephan Eckstein, Gaoyue Guo, Tongseok Lim +1
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-margin…
Martingale transport with homogeneous stock movements
Stephan Eckstein, Michael Kupper
We study a variant of the martingale optimal transport problem in a multi-period setting to derive robust price bounds of a financial derivative. On top of marginal and martingale…
Robust risk aggregation with neural networks
Stephan Eckstein, Michael Kupper, Mathias Pohl
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and tha…
Computation of optimal transport and related hedging problems via penalization and neural networks
Stephan Eckstein, Michael Kupper
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize th…
Extended Laplace Principle for Empirical Measures of a Markov Chain
Stephan Eckstein
We consider discrete time Markov chains with Polish state space. The large deviations principle for empirical measures of a Markov chain can equivalently be stated in Laplace princ…
Marginal and dependence uncertainty: bounds, optimal transport, and sharpness
Daniel Bartl, Michael Kupper, Thibaut Lux +2
Motivated by applications in model-free finance and quantitative risk management, we consider Fréchet classes of multivariate distribution functions where additional information on…