相关论文: Wasserstein Geodesic Generator for Conditional Dis…

Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…

Generative Adversarial Networks (GANs) have been successful in producing outstanding results in areas as diverse as image, video, and text generation. Building on these successes, a large number of empirical studies have validated the…

Learning conditional distributions is challenging because the desired outcome is not a single distribution but multiple distributions that correspond to multiple instances of the covariates. We introduce a novel neural entropic optimal…

When learning graph neural networks (GNNs) in node-level prediction tasks, most existing loss functions are applied for each node independently, even if node embeddings and their labels are non-i.i.d. because of their graph structures. To…

Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…

We study first-order optimality conditions for constrained optimization in the Wasserstein space, whereby one seeks to minimize a real-valued function over the space of probability measures endowed with the Wasserstein distance. Our…

It was recently shown that under smoothness conditions, the squared Wasserstein distance between two distributions could be efficiently computed with appealing statistical error upper bounds. However, rather than the distance itself, the…

In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional…

In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional…

We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates…

Within a broad class of generative adversarial networks, we show that discriminator optimization process increases a lower bound of the dual cost function for the Wasserstein distance between the target distribution $p$ and the generator…

We consider statistical methods which invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning…

Illumination estimation remains a pivotal challenge in image processing, particularly for robotics, where robust environmental perception is essential under varying lighting conditions. Traditional approaches, such as RGB histograms and…

In this work we prove the existence and uniqueness of the optimal transport map for $L^p$-Wasserstein distance with $p>1$, and particularly present an explicit expression of the optimal transport map for the case $p=2$. As an application,…

Wasserstein gradient flows (WGFs) describe the evolution of probability distributions in Wasserstein space as steepest descent dynamics for a free energy functional. Computing the full path from an arbitrary initial distribution to…

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

Classical optimal transport problem seeks a transportation map that preserves the total mass betwenn two probability distributions, requiring their mass to be the same. This may be too restrictive in certain applications such as color or…

This paper advances the theory and practice of Domain Generalization (DG) in machine learning. We consider the typical DG setting where the hypothesis is composed of a representation mapping followed by a labeling function. Within this…

Optimal transport between classical probability distributions has been proven useful in areas such as machine learning and random combinatorial optimization. Quantum optimal transport, and the quantum Wasserstein distance as the minimal…

Optimal Transport (OT) metrics allow for defining discrepancies between two probability measures. Wasserstein distance is for longer the celebrated OT-distance frequently-used in the literature, which seeks probability distributions to be…