Related papers: Model Risk Measurement under Wasserstein Distance
In this work we test Wasserstein distance in conjunction with persistent homology, as a tool for discriminating large scale structures of simulated universes with different values of $\sigma_8$ cosmological parameter (present…
Generative Adversarial Networks (GANs) have been used to model the underlying probability distribution of sample based datasets. GANs are notoriuos for training difficulties and their dependence on arbitrary hyperparameters. One recent…
The convergence rate in Wasserstein distance is estimated for the empirical measures of symmetric semilinear SPDEs. Unlike in the finite-dimensional case that the convergence is of algebraic order in time, in the present situation the…
Mutual information maximization has emerged as a powerful learning objective for unsupervised representation learning obtaining state-of-the-art performance in applications such as object recognition, speech recognition, and reinforcement…
We develop an averaging approach to robust risk measurement under payoff uncertainty. Instead of taking a worst-case value over an uncertainty neighborhood, we weight nearby payoffs more heavily under a chosen metric and average the…
Reweighting adversarial data during training has been recently shown to improve adversarial robustness, where data closer to the current decision boundaries are regarded as more critical and given larger weights. However, existing methods…
Wasserstein distributionally robust optimization (WDRO) strengthens statistical learning under model uncertainty by minimizing the local worst-case risk within a prescribed ambiguity set. Although WDRO has been extensively studied in…
We study the Wasserstein metric to measure distances between molecules represented by the atom index dependent adjacency "Coulomb" matrix, used in kernel ridge regression based supervised learning. Resulting quantum machine learning models…
Understanding and measuring model risk is important to financial practitioners. However, there lacks a non-parametric approach to model risk quantification in a dynamic setting and with path-dependent losses. We propose a complete theory…
In this note, we propose an extension of the Wasserstein 1-metric ($W_1$) for matrix probability densities, matrix-valued density measures, and an unbalanced interpretation of mass transport. The key is using duality theory, in particular,…
We propose a distributionally robust logistic regression model with an unfairness penalty that prevents discrimination with respect to sensitive attributes such as gender or ethnicity. This model is equivalent to a tractable convex…
Wasserstein distance is a key metric for quantifying data divergence from a distributional perspective. However, its application in privacy-sensitive environments, where direct sharing of raw data is prohibited, presents significant…
A data-driven MPC scheme is proposed to safely control constrained stochastic linear systems using distributionally robust optimization. Distributionally robust constraints based on the Wasserstein metric are imposed to bound the state…
Model uncertainty has been one prominent issue both in the theory of risk measures and in practice such as financial risk management and regulation. Motivated by this observation, in this paper, we take a new perspective to describe the…
This paper deals with the problem of quantifying the impact of model misspecification when computing general expected values of interest. The methodology that we propose is applicable in great generality, in particular, we provide examples…
We consider distributionally robust optimization problems where the uncertainty is modeled via a structured Wasserstein ambiguity set. Specifically, the ambiguity is restricted to product measures $P^{\otimes N}$, where $P$ lies within a…
This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…
We study a static portfolio optimization problem with two risk measures: a principle risk measure in the objective function and a secondary risk measure whose value is controlled in the constraints. This problem is of interest when it is…
We consider the problem of estimating the joint distribution of $n$ independent random variables. Our approach is based on a family of candidate probabilities that we shall call a model and which is chosen to either contain the true…
Motivated by the statistical and computational challenges of computing Wasserstein distances in high-dimensional contexts, machine learning researchers have defined modified Wasserstein distances based on computing distances between…