Related papers: Differentially Private Wasserstein Barycenters
We consider machine learning, particularly regression, using locally-differentially private datasets. The Wasserstein distance is used to define an ambiguity set centered at the empirical distribution of the dataset corrupted by local…
Differential privacy (DP) is a mathematical privacy notion increasingly deployed across government and industry. With DP, privacy protections are probabilistic: they are bounded by the privacy budget parameter, $\epsilon$. Prior work in…
We study person-level differentially private (DP) mean estimation in the case where each person holds multiple samples. DP here requires the usual notion of distributional stability when $\textit{all}$ of a person's datapoints can be…
Equilibrium multi-population matching (matching for teams) is a problem from mathematical economics which is related to multi-marginal optimal transport. A special but important case is the Wasserstein barycenter problem, which has…
A data-driven MPC scheme is proposed to safely control constrained stochastic linear systems using distributionally robust optimization. Distributionally robust constraints based on the Wasserstein metric are imposed to bound the state…
Wasserstein barycenters and variance-like criteria based on the Wasserstein distance are used in many problems to analyze the homogeneity of collections of distributions and structural relationships between the observations. We propose the…
Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…
Differential privacy (DP) provides robust privacy guarantees for statistical inference, but this can lead to unreliable results and biases in downstream applications. While several noise-aware approaches have been proposed which integrate…
Distributed systems require fusing heterogeneous local probability distributions into a global summary over sparse and unreliable communication networks. Traditional consensus algorithms, which average distributions in Euclidean space,…
Divide-and-conquer based methods for Bayesian inference provide a general approach for tractable posterior inference when the sample size is large. These methods divide the data into smaller subsets, sample from the posterior distribution…
Differential privacy is the state-of-the-art definition for privacy, guaranteeing that any analysis performed on a sensitive dataset leaks no information about the individuals whose data are contained therein. In this thesis, we develop…
Differential privacy guarantees allow the results of a statistical analysis involving sensitive data to be released without compromising the privacy of any individual taking part. Achieving such guarantees generally requires the injection…
Differential privacy is the leading mathematical framework for privacy protection, providing a probabilistic guarantee that safeguards individuals' private information when publishing statistics from a dataset. This guarantee is achieved by…
In this work we introduce the concept of Bures-Wasserstein barycenter $Q_*$, that is essentially a Fr\'echet mean of some distribution $\mathbb{P}$ supported on a subspace of positive semi-definite Hermitian operators $\mathbb{H}_{+}(d)$.…
We propose a new \cu{class-optimal} algorithm for the distributed computation of Wasserstein Barycenters over networks. Assuming that each node in a graph has a probability distribution, we prove that every node can reach the barycenter of…
Inspired by recent advances in distributed algorithms for approximating Wasserstein barycenters, we propose a novel distributed algorithm for this problem. The main novelty is that we consider time-varying computational networks, which are…
In the standard use case of Algorithmic Fairness, the goal is to eliminate the relationship between a sensitive variable and a corresponding score. Throughout recent years, the scientific community has developed a host of definitions and…
Many machine learning applications are based on data collected from people, such as their tastes and behaviour as well as biological traits and genetic data. Regardless of how important the application might be, one has to make sure…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
This paper studies the statistical estimation of exact Wasserstein barycenters. Existing non-asymptotic results for empirical barycenters exhibit a severe curse of dimensionality. Motivated by the semi-dual formulation of the barycenter…