相关论文: Exact Generalization Guarantees for (Regularized) …
The Gromov-Wasserstein (GW) distance is an effective measure of alignment between distributions supported on distinct ambient spaces. Calculating essentially the mutual departure from isometry, it has found vast usage in domain translation…
The Wasserstein distance, rooted in optimal transport (OT) theory, is a popular discrepancy measure between probability distributions with various applications to statistics and machine learning. Despite their rich structure and…
The quantization problem aims to find the best possible approximation of probability measures on ${\mathbb{R}}^d$ using finite, discrete measures. The Wasserstein distance is a typical choice to measure the quality of the approximation.…
The performance of machine learning (ML) models critically depends on the quality and representativeness of the training data. In applications with multiple heterogeneous data generating sources, standard ML methods often learn spurious…
As the complexity of modern control systems increases, it becomes challenging to derive an accurate model of the uncertainty that affects their dynamics. Wasserstein Distributionally Robust Optimization (DRO) provides a powerful framework…
The problem of adversarial examples has highlighted the need for a theory of regularisation that is general enough to apply to exotic function classes, such as universal approximators. In response, we give a very general equality result…
We propose to align distributional data from the perspective of Wasserstein means. We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the…
We investigate the problem of synthesizing distributionally robust control policies for stochastic systems under safety and reach-avoid specifications. Using a game-theoretical framework, we consider the setting where the probability…
This paper demonstrates the robustness of Lipschitz-regularized $\alpha$-divergences as objective functionals in generative modeling, showing they enable stable learning across a wide range of target distributions with minimal assumptions.…
The success of autoregressive models largely depends on the effectiveness of vector quantization, a technique that discretizes continuous features by mapping them to the nearest code vectors within a learnable codebook. Two critical issues…
The paper proposes a new approach to model risk measurement based on the Wasserstein distance between two probability measures. It formulates the theoretical motivation resulting from the interpretation of fictitious adversary of robust…
Though remarkable progress has been achieved in various vision tasks, deep neural networks still suffer obvious performance degradation when tested in out-of-distribution scenarios. We argue that the feature statistics (mean and standard…
This paper concerns the convergence of empirical measures in high dimensions. We propose a new class of probability metrics and show that under such metrics, the convergence is free of the curse of dimensionality (CoD). Such a feature is…
This paper is focused on the study of entropic regularization in optimal transport as a smoothing method for Wasserstein estimators, through the prism of the classical tradeoff between approximation and estimation errors in statistics.…
Distributionally robust optimization (DRO) has attracted attention in machine learning due to its connections to regularization, generalization, and robustness. Existing work has considered uncertainty sets based on phi-divergences and…
For statistical models on circles, we investigate performance of estimators defined as the projections of the empirical distribution with respect to the Wasserstein distance. We develop algorithms for computing the Wasserstein projection…
Data consisting of time-indexed distributions of cross-sectional or intraday returns have been extensively studied in finance, and provide one example in which the data atoms consist of serially dependent probability distributions.…
Recently, the Wasserstein loss function has been proven to be effective when applied to deterministic full-waveform inversion (FWI) problems. We consider the application of this loss function in Bayesian FWI so that the uncertainty can be…
This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent…
Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…