Related papers: Minimum Wasserstein Distance Estimator under Finit…
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 propose a new formulation and learning strategy for computing the Wasserstein geodesic between two probability distributions in high dimensions. By applying the method of Lagrange multipliers to the dynamic formulation of the optimal…
The maximum mean discrepancy and Wasserstein distance are popular distance measures between distributions and play important roles in many machine learning problems such as metric learning, generative modeling, domain adaption, and…
Mixture density networks are neural networks that produce Gaussian mixtures to represent continuous multimodal conditional densities. Standard training procedures involve maximum likelihood estimation using the negative log-likelihood (NLL)…
Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…
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)…
We present \emph{Local Moment Matching (LMM)}, a unified methodology for symmetric functional estimation and distribution estimation under Wasserstein distance. We construct an efficiently computable estimator that achieves the minimax…
This paper deals with Elliptical Wishart distributions - which generalize the Wishart distribution - in the context of signal processing and machine learning. Two algorithms to compute the maximum likelihood estimator (MLE) are proposed: a…
Scenario reduction techniques are widely applied for solving sophisticated dynamic and stochastic programs, especially in energy and power systems, but also used in probabilistic forecasting, clustering and estimating generative adversarial…
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…
Maximum likelihood estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution that best explain the observed data. In the context of text generation, MLE is often used to train generative language…
We define a modified Wasserstein distance for distribution clustering which inherits many of the properties of the Wasserstein distance but which can be estimated easily and computed quickly. The modified distance is the sum of two terms.…
A key challenge of modern machine learning systems is to achieve Out-of-Distribution (OOD) generalization -- generalizing to target data whose distribution differs from that of source data. Despite its significant importance, the…
Accurate estimation of evolutionary distances between taxa is important for many phylogenetic reconstruction methods. In the case of bacteria, distances can be estimated using a range of different evolutionary models, from single nucleotide…
We introduce a principled way of computing the Wasserstein distance between two distributions in a federated manner. Namely, we show how to estimate the Wasserstein distance between two samples stored and kept on different devices/clients…
Optimal transport has recently proved to be a useful tool in various machine learning applications needing comparisons of probability measures. Among these, applications of distributionally robust optimization naturally involve Wasserstein…
Robust inferential methods based on divergences measures have shown an appealing trade-off between efficiency and robustness in many different statistical models. In this paper, minimum density power divergence estimators (MDPDEs) for the…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…
We consider learning in an adversarial environment, where an $\varepsilon$-fraction of samples from a distribution $P$ are arbitrarily modified (global corruptions) and the remaining perturbations have average magnitude bounded by $\rho$…