相关论文: Amortized Projection Optimization for Sliced Wasse…

We propose a simple algorithm to train stochastic neural networks to draw samples from given target distributions for probabilistic inference. Our method is based on iteratively adjusting the neural network parameters so that the output…

In many real-world applications of Machine Learning it is of paramount importance not only to provide accurate predictions, but also to ensure certain levels of robustness. Adversarial Training is a training procedure aiming at providing…

Deep metric learning employs deep neural networks to embed instances into a metric space such that distances between instances of the same class are small and distances between instances from different classes are large. In most existing…

The sliced Wasserstein distance as well as its variants have been widely considered in comparing probability measures defined on $\mathbb R^d$. Here we derive the notion of sliced Wasserstein distance for measures on an infinite dimensional…

We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…

The core principle of Variational Inference (VI) is to convert the statistical inference problem of computing complex posterior probability densities into a tractable optimization problem. This property enables VI to be faster than several…

The sliced Wasserstein barycenter (SWB) is a widely acknowledged method for efficiently generalizing the averaging operation within probability measure spaces. However, achieving marginal fairness SWB, ensuring approximately equal distances…

Compressive covariance estimation has arisen as a class of techniques whose aim is to obtain second-order statistics of stochastic processes from compressive measurements. Recently, these methods have been used in various image processing…

Sliced Optimal Transport (SOT) is a rapidly developing branch of optimal transport (OT) that exploits the tractability of one-dimensional OT problems. By combining tools from OT, integral geometry, and computational statistics, SOT enables…

Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…

Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…

This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected…

We study distributionally robust online learning, where a risk-averse learner updates decisions sequentially to guard against worst-case distributions drawn from a Wasserstein ambiguity set centered at past observations. While this paradigm…

Optimal selection of optimization algorithms is crucial for training deep learning models. The Adam optimizer has gained significant attention due to its efficiency and wide applicability. However, to enhance the adaptability of optimizers…

We propose a novel amortized optimization method for predicting optimal transport (OT) plans across multiple pairs of measures by leveraging Kantorovich potentials derived from sliced OT. We introduce two amortization strategies:…

Optimization over the space of probability measures endowed with the Wasserstein-2 geometry is central to modern machine learning and mean-field modeling. However, traditional methods relying on full Wasserstein gradients often suffer from…

We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent variable models of the data distribution based on the primal and the dual formulations of the optimal transport (OT) problem. We utilize the primal…

Efficient trajectory optimization is essential for avoiding collisions in unstructured environments, but it remains challenging to have both speed and quality in the solutions. One reason is that second-order optimality requires calculating…

We study estimation problems in safety-critical applications with streaming data. Since estimation problems can be posed as optimization problems in the probability space, we devise a stochastic projected Wasserstein gradient flow that…

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…