Related papers: Differentially Private Wasserstein Barycenters
Differential privacy is a restriction on data processing algorithms that provides strong confidentiality guarantees for individual records in the data. However, research on proper statistical inference, that is, research on properly…
In this work we consider regularized Wasserstein barycenters (average in Wasserstein distance) in Fourier basis. We prove that random Fourier parameters of the barycenter converge to some Gaussian random vector by distribution. The…
In this paper, based on the Fr{\'e}chet mean, we define a notion of barycenter corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein barycenters of random distributions defined on a geodesic space (E,…
Many applications of machine learning, for example in health care, would benefit from methods that can guarantee privacy of data subjects. Differential privacy (DP) has become established as a standard for protecting learning results. The…
In this paper we propose to perform model ensembling in a multiclass or a multilabel learning setting using Wasserstein (W.) barycenters. Optimal transport metrics, such as the Wasserstein distance, allow incorporating semantic side…
Wasserstein distances provide a powerful framework for comparing data distributions. They can be used to analyze processes over time or to detect inhomogeneities within data. However, simply calculating the Wasserstein distance or analyzing…
In this paper, we establish sharp upper and lower bounds on the convergence rate of the empirical measures of point processes under the Wasserstein distance. To this end, we first introduce a new metric on the space of counting measures…
We study a setting where a data holder wishes to share data with a receiver, without revealing certain summary statistics of the data distribution (e.g., mean, standard deviation). It achieves this by passing the data through a…
Safeguarding privacy in sensitive training data is paramount, particularly in the context of generative modeling. This can be achieved through either differentially private stochastic gradient descent or a differentially private metric for…
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…
Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…
Many modern databases include personal and sensitive correlated data, such as private information on users connected together in a social network, and measurements of physical activity of single subjects across time. However, differential…
Collecting and aggregating information from several probability measures or histograms is a fundamental task in machine learning. One of the popular solution methods for this task is to compute the barycenter of the probability measures…
Parameter estimation in statistics and system identification relies on data that may contain sensitive information. To protect this sensitive information, the notion of \emph{differential privacy} (DP) has been proposed, which enforces…
Differential Privacy (DP) is the current gold-standard for ensuring privacy for statistical queries. Estimation problems under DP constraints appearing in the literature have largely focused on providing equal privacy to all users. We…
Wasserstein dictionary learning is an unsupervised approach to learning a collection of probability distributions that generate observed distributions as Wasserstein barycentric combinations. Existing methods for Wasserstein dictionary…
Algorithms such as Differentially Private SGD enable training machine learning models with formal privacy guarantees. However, there is a discrepancy between the protection that such algorithms guarantee in theory and the protection they…
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…
In the literature of data privacy, differential privacy is the most popular model. An algorithm is differentially private if its outputs with and without any individual's data are indistinguishable. In this paper, we focus on data generated…
We study the existence and uniqueness of the barycenter of a signed distribution of probability measures on a Hilbert space. The barycenter is found, as usual, as a minimum of a functional. In the case where the positive part of the signed…