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Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…

When approximating an intractable density via variational inference (VI) the variational family is typically chosen as a simple parametric family that very likely does not contain the target. This raises the question: Under which conditions…

A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation (ABC) has become a popular approach to overcome this issue, in which one simulates…

Most Kalman filters for non-linear systems, such as the unscented Kalman filter, are based on Gaussian approximations. We use Poincar\'e inequalities to bound the Wasserstein distance between the true joint distribution of the prediction…

We develop the Bayesian Wasserstein repulsive Gaussian mixture model that promotes well-separated clusters. Unlike existing repulsive mixture approaches that focus on separating the component means, our method encourages separation between…

Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…

Generative Adversarial Nets (GANs) are very successful at modeling distributions from given samples, even in the high-dimensional case. However, their formulation is also known to be hard to optimize and often not stable. While this is…

This paper targets the task with discrete and periodic class labels ($e.g.,$ pose/orientation estimation) in the context of deep learning. The commonly used cross-entropy or regression loss is not well matched to this problem as they ignore…

We propose algorithms for sampling from posterior path measures $P(C([0, T], \mathbb{R}^d))$ under a general prior process. This leverages ideas from (1) controlled equilibrium dynamics, which gradually transport between two path measures,…

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…

In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…

We provide a general bound on the Wasserstein distance between two arbitrary distributions of sequences of Bernoulli random variables. The bound is in terms of a mixing quantity for the Glauber dynamics of one of the sequences, and a simple…

We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distances. For Wasserstein bounds, our main tool…

This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and…

Let $\pi\in \Pi(\mu,\nu)$ be a coupling between two probability measures $\mu$ and $\nu$ on a Polish space. In this article we propose and study a class of nonparametric measures of association between $\mu$ and $\nu$, which we call…

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…

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…

Generative-adversarial networks (GANs) have been used to produce data closely resembling example data in a compressed, latent space that is close to sufficient for reconstruction in the original vector space. The Wasserstein metric has been…

The convergence rate in Wasserstein distance is estimated for the empirical measures of symmetric semilinear SPDEs. Unlike in the finite-dimensional case that the convergence is of algebraic order in time, in the present situation the…

Learning to predict multi-label outputs is challenging, but in many problems there is a natural metric on the outputs that can be used to improve predictions. In this paper we develop a loss function for multi-label learning, based on the…