相关论文: Streaming Sliced Optimal Transport

Optimal Transport (OT) offers a powerful framework for finding correspondences between distributions and addressing matching and alignment problems in various areas of computer vision, including shape analysis, image generation, and…

Motivated by the growing popularity of variants of the Wasserstein distance in statistics and machine learning, we study statistical inference for the Sliced Wasserstein distance--an easily computable variant of the Wasserstein distance.…

Thompson sampling (TS) is a class of algorithms for sequential decision-making, which requires maintaining a posterior distribution over a model. However, calculating exact posterior distributions is intractable for all but the simplest…

While statistical modeling of distributional data has gained increased attention, the case of multivariate distributions has been somewhat neglected despite its relevance in various applications. This is because the Wasserstein distance,…

Generative adversarial nets (GANs) and variational auto-encoders have significantly improved our distribution modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to…

Flow matching has recently emerged as a flexible and efficient framework for generative modelling by learning deterministic transport dynamics between probability measures. In this work, we extend flow matching to the space of probability…

Covariate shift arises when covariate distributions differ between source and target populations while the conditional distribution of the response remains invariant, and it underlies problems in missing data and causal inference. We…

Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the Streaming Tensor Train Approximation (STTA), a new class of algorithms for approximating a given tensor…

Score-based generative models are shown to achieve remarkable empirical performances in various applications such as image generation and audio synthesis. However, a theoretical understanding of score-based diffusion models is still…

While there are software systems that simplify trajectory streams on the fly, few curve simplification algorithms with quality guarantees fit the streaming requirements. We present streaming algorithms for two such problems under the…

We introduce Deep Set Linearized Optimal Transport, an algorithm designed for the efficient simultaneous embedding of point clouds into an $L^2-$space. This embedding preserves specific low-dimensional structures within the Wasserstein…

Learning an effective representation of 3D point clouds requires a good metric to measure the discrepancy between two 3D point sets, which is non-trivial due to their irregularity. Most of the previous works resort to using the Chamfer…

Gaussian mixture models (GMMs) are widely used in machine learning for tasks such as clustering, classification, image reconstruction, and generative modeling. A key challenge in working with GMMs is defining a computationally efficient and…

We present the Fourier Sliced-Wasserstein (FSW) embedding - a novel method to embed multisets and measures over $\mathbb{R}^d$ into Euclidean space. Our proposed embedding approximately preserves the sliced Wasserstein distance on…

An increasing number of machine learning tasks deal with learning representations from set-structured data. Solutions to these problems involve the composition of permutation-equivariant modules (e.g., self-attention, or individual…

Resource-efficiently computing representations of probability distributions and the distances between them while only having access to the samples is a fundamental and useful problem across mathematical sciences. In this paper, we propose a…

We propose a multi-class point optimization formulation based on continuous Wasserstein barycenters. Our formulation is designed to handle hundreds to thousands of optimization objectives and comes with a practical optimization scheme. We…

In recent years, the machine learning community has increasingly embraced the optimal transport (OT) framework for modeling distributional relationships. In this work, we introduce a sample-based neural solver for computing the Wasserstein…

Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is the most popular algorithm for estimating the GMM parameters. However, EM…

The Sliced-Wasserstein (SW) distance between probability measures is defined as the average of the Wasserstein distances resulting for the associated one-dimensional projections. As a consequence, the SW distance can be written as an…