Related papers: Neural Wasserstein Two-Sample Tests

Testing heteroscedasticity of the errors is a major challenge in high-dimensional regressions where the number of covariates is large compared to the sample size. Traditional procedures such as the White and the Breusch-Pagan tests…

The proliferation of large data sets and Bayesian inference techniques motivates demand for better data sparsification. Coresets provide a principled way of summarizing a large dataset via a smaller one that is guaranteed to match the…

Let $M$ be a connected compact Riemannian manifold possibly with a boundary, let $V\in C^2(M)$ such that $\mu(\d x):=\e^{V(x)}\d x$ is a probability measure, where $\d x$ is the volume measure, and let $L=\Delta+\nabla V$. The exact…

We use Stein's method to bound the Wasserstein distance of order $2$ between a measure $\nu$ and the Gaussian measure using a stochastic process $(X_t)_{t \geq 0}$ such that $X_t$ is drawn from $\nu$ for any $t > 0$. If the stochastic…

We introduce a distributionally robust minimium mean square error estimation model with a Wasserstein ambiguity set to recover an unknown signal from a noisy observation. The proposed model can be viewed as a zero-sum game between a…

Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and…

In order to adapt the Wasserstein distance to the large sample multivariate non-parametric two-sample problem, making its application computationally feasible, permutation tests based on the Sinkhorn divergence between probability vectors…

Despite of its importance for safe machine learning, uncertainty quantification for neural networks is far from being solved. State-of-the-art approaches to estimate neural uncertainties are often hybrid, combining parametric models with…

We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…

In this paper we propose tight upper and lower bounds for the Wasserstein distance between any two {{univariate continuous distributions}} with probability densities $p_1$ and $p_2$ having nested supports. These explicit bounds are…

We study the machine learning task for models with operators mapping between the Wasserstein space of probability measures and a space of functions, like e.g. in mean-field games/control problems. Two classes of neural networks, based on…

Construction of ambiguity set in robust optimization relies on the choice of divergences between probability distributions. In distribution learning, choosing appropriate probability distributions based on observed data is critical for…

This paper is focused on the statistical analysis of probability measures $\nu_{1},\ldots,\nu_{n}$ on $\mathbb{R}$ that can be viewed as independent realizations of an underlying stochastic process. We consider the situation of practical…

The unequal representation of different groups in a sample population can lead to discrimination of minority groups when machine learning models make automated decisions. To address these issues, fairness-aware machine learning jointly…

Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…

Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating…

The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which…

The Wasserstein distance has been an attractive tool in many fields. But due to its high computational complexity and the phenomenon of the curse of dimensionality in empirical estimation, various extensions of the Wasserstein distance have…

Nowadays stochastic computer simulations with both numeral and distribution inputs are widely used to mimic complex systems which contain a great deal of uncertainty. This paper studies the design and analysis issues of such computer…

We propose optimal Bayesian two-sample tests for testing equality of high-dimensional mean vectors and covariance matrices between two populations. In many applications including genomics and medical imaging, it is natural to assume that…