Related papers: Streaming Sliced Optimal Transport
We propose a new statistical model, the spiked transport model, which formalizes the assumption that two probability distributions differ only on a low-dimensional subspace. We study the minimax rate of estimation for the Wasserstein…
Optimal transport with quadratic cost provides a geometric framework for steering an ensemble, modeled by a probability law, with minimal effort. Yet ambient-space formulations become unwieldy in high dimensions, and sensing or actuation in…
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…
We describe a method for signal parameter estimation using the signed cumulative distribution transform (SCDT), a recently introduced signal representation tool based on optimal transport theory. The method builds upon signal estimation…
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…
Obtaining solutions to Optimal Transportation (OT) problems is typically intractable when the marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d.…
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 propose a fast algorithm for the calculation of the Wasserstein-1 distance, which is a particular type of optimal transport distance with homogeneous of degree one transport cost. Our algorithm is built on multilevel primal-dual…
The Optimal Transport (a.k.a. Wasserstein) distance is an increasingly popular similarity measure for rich data domains, such as images or text documents. This raises the necessity for fast nearest neighbor search algorithms according to…
The smooth 1-Wasserstein distance (SWD) $W_1^\sigma$ was recently proposed as a means to mitigate the curse of dimensionality in empirical approximation while preserving the Wasserstein structure. Indeed, SWD exhibits parametric convergence…
We present the Fourier Sliced-Wasserstein (FSW) embedding - a novel method to embed multisets and measures over R^d into Euclidean space. Our proposed embedding approximately preserves the sliced Wasserstein distance on distributions,…
Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In…
Comparing probability measures modulo unknown rigid transformations is a central challenge in geometric data analysis. Classical optimal transport (OT) distances, including Wasserstein and sliced Wasserstein, are sensitive to rotations and…
Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…
This paper presents a proposal of a faster Wasserstein $k$-means algorithm for histogram data by reducing Wasserstein distance computations and exploiting sparse simplex projection. We shrink data samples, centroids, and the ground cost…
Stream stochastic gradient descent (SGD) is a simple and efficient method for solving online optimization problems in operations research (OR), where data is generated by parameter-dependent Markov chains. Unlike traditional approaches…
Optimal transport (OT) is a powerful framework to compare probability measures, a fundamental task in many statistical and machine learning problems. Substantial advances have been made in designing OT variants which are either…
Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…
Minimum expected distance estimation (MEDE) algorithms have been widely used for probabilistic models with intractable likelihood functions and they have become increasingly popular due to their use in implicit generative modeling (e.g.…
The Straight-Through (ST) estimator is a widely used technique for back-propagating gradients through discrete random variables. However, this effective method lacks theoretical justification. In this paper, we show that ST can be…