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We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…
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,…
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…
We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure $\mu$ of a diffusion process and the measure $\nu$ of an approximating Markov chain. Our result is…
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.…
Variational Inference approximates an unnormalized distribution via the minimization of Kullback-Leibler (KL) divergence. Although this divergence is efficient for computation and has been widely used in applications, it suffers from some…
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…
Wasserstein distances are widely used in modern data analysis but pose significant computational and statistical challenges in high dimensions. The sliced Wasserstein distance alleviates these challenges by leveraging one-dimensional…
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…
Approximate Bayesian Computation (ABC) is a popular method for approximate inference in generative models with intractable but easy-to-sample likelihood. It constructs an approximate posterior distribution by finding parameters for which…
Generalized sliced Wasserstein distance is a variant of sliced Wasserstein distance that exploits the power of non-linear projection through a given defining function to better capture the complex structures of the probability…
The sliced Wasserstein (SW) distance has been widely recognized as a statistically effective and computationally efficient metric between two probability measures. A key component of the SW distance is the slicing distribution. There are…
The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…
In the field of modern high-energy physics research, there is a growing emphasis on utilizing deep learning techniques to optimize event simulation, thereby expanding the statistical sample size for more accurate physical analysis.…
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…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…
The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an…
We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…