Related papers: Differentially Private Sampling from Distributions…
The asymptotic behaviour of empirical measures has plenty of studies. However, the research on conditional empirical measures is limited. Being the development of Wang \cite{eW1}, under the quadratic Wasserstein distance, we investigate the…
Gaussian Mixture Models (GMMs) are widely used statistical models for representing multi-modal data distributions, with numerous applications in data mining, pattern recognition, data simulation, and machine learning. However, recent…
Given an empirical distribution $f(x)$ of sensitive data $x$, we consider the task of minimizing $F(y) = D_{\text{KL}} (f(x)\Vert y)$ over a probability simplex, while protecting the privacy of $x$. We observe that, if we take the…
Motivated by applications of large embedding models, we study differentially private (DP) optimization problems under sparsity of individual gradients. We start with new near-optimal bounds for the classic mean estimation problem but with…
Differential privacy (DP) is the prevailing technique for protecting user data in machine learning models. However, deficits to this framework include a lack of clarity for selecting the privacy budget $\epsilon$ and a lack of…
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…
While modern machine learning models rely on increasingly large training datasets, data is often limited in privacy-sensitive domains. Generative models trained with differential privacy (DP) on sensitive data can sidestep this challenge,…
Off-policy evaluation and learning are concerned with assessing a given policy and learning an optimal policy from offline data without direct interaction with the environment. Often, the environment in which the data are collected differs…
In this work, we give a new technique for analyzing individualized privacy accounting via the following simple observation: if an algorithm is one-sided add-DP, then its subsampled variant satisfies two-sided DP. From this, we obtain…
Distributionally robust control (DRC) aims to effectively manage distributional ambiguity in stochastic systems. While most existing works address inaccurate distributional information in fully observable settings, we consider a partially…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…
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…
This paper introduces a comprehensive framework to adjust a discrete test statistic for improving its hypothesis testing procedure. The adjustment minimizes the Wasserstein distance to a null-approximating continuous distribution, tackling…
We study the fundamental problem of frequency estimation under both privacy and communication constraints, where the data is distributed among $k$ parties. We consider two application scenarios: (1) one-shot, where the data is static and…
Generative modeling aims to produce new random examples from an unknown target distribution, given access to a finite collection of examples. Among the leading approaches, denoising diffusion probabilistic models (DDPMs) construct such…
Data engineering often requires accuracy (utility) constraints on results, posing significant challenges in designing differentially private (DP) mechanisms, particularly under stringent privacy parameter $\epsilon$. In this paper, we…
A privacy-utility tradeoff is developed for an arbitrary set of finite-alphabet source distributions. Privacy is quantified using differential privacy (DP), and utility is quantified using expected Hamming distortion maximized over the set…
Differential Privacy (DP) provides an elegant mathematical framework for defining a provable disclosure risk in the presence of arbitrary adversaries; it guarantees that whether an individual is in a database or not, the results of a DP…
We investigate a stochastic program with expected value constraints, addressing the problem in a general context through Distributionally Robust Optimization (DRO) approach using Wasserstein distances, where the ambiguity set depends on the…
The streaming model of computation is a popular approach for working with large-scale data. In this setting, there is a stream of items and the goal is to compute the desired quantities (usually data statistics) while making a single pass…