Related papers: Geometrical Insights for Implicit Generative Model…
Understanding the space of probability measures on a metric space equipped with a Wasserstein distance is one of the fundamental questions in mathematical analysis. The Wasserstein metric has received a lot of attention in the machine…
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…
Generative models with both discrete and continuous latent variables are highly motivated by the structure of many real-world data sets. They present, however, subtleties in training often manifesting in the discrete latent being under…
Statistical models often include thousands of parameters. However, large models decrease the investigator's ability to interpret and communicate the estimated parameters. Reducing the dimensionality of the parameter space in the estimation…
Generative Adversarial Networks are a popular method for learning distributions from data by modeling the target distribution as a function of a known distribution. The function, often referred to as the generator, is optimized to minimize…
In recent years there has been increased interest in understanding the interplay between deep generative models (DGMs) and the manifold hypothesis. Research in this area focuses on understanding the reasons why commonly-used DGMs succeed or…
Minimum distance estimation (MDE) gained recent attention as a formulation of (implicit) generative modeling. It considers minimizing, over model parameters, a statistical distance between the empirical data distribution and the model. This…
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…
The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…
Generative Adversial Networks (GANs) have made a major impact in computer vision and machine learning as generative models. Wasserstein GANs (WGANs) brought Optimal Transport (OT) theory into GANs, by minimizing the $1$-Wasserstein distance…
Implicit models, which allow for the generation of samples but not for point-wise evaluation of probabilities, are omnipresent in real-world problems tackled by machine learning and a hot topic of current research. Some examples include…
Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each…
The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…
Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…
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…
The analysis of parametric and non-parametric uncertainties of very large dynamical systems requires the construction of a stochastic model of said system. Linear approaches relying on random matrix theory and principal componant analysis…
This paper explains the math behind a generative adversarial network (GAN) model and why it is hard to be trained. Wasserstein GAN is intended to improve GANs' training by adopting a smooth metric for measuring the distance between two…
Computing optimal transport maps between high-dimensional and continuous distributions is a challenging problem in optimal transport (OT). Generative adversarial networks (GANs) are powerful generative models which have been successfully…
Generative adversarial networks (GANs) provide an algorithmic framework for constructing generative models with several appealing properties: they do not require a likelihood function to be specified, only a generating procedure; they…
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…