相关论文: Differentially private Riemannian optimization

In this paper, we initiate a systematic investigation of differentially private algorithms for convex empirical risk minimization. Various instantiations of this problem have been studied before. We provide new algorithms and matching lower…

This paper studies the privacy-preserving distributed optimization problem under limited communication, where each agent aims to keep its cost function private while minimizing the sum of all agents' cost functions. To this end, we propose…

We provide computationally efficient, differentially private algorithms for the classical regression settings of Least Squares Fitting, Binary Regression and Linear Regression with unbounded covariates. Prior to our work, privacy…

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…

Distributed machine learning is an approach allowing different parties to learn a model over all data sets without disclosing their own data. In this paper, we propose a weighted distributed differential privacy (WD-DP) empirical risk…

Differential privacy mechanisms such as the Gaussian or Laplace mechanism have been widely used in data analytics for preserving individual privacy. However, they are mostly designed for continuous outputs and are unsuitable for scenarios…

This paper proposes a novel general framework of Riemannian conjugate gradient methods, that is, conjugate gradient methods on Riemannian manifolds. The conjugate gradient methods are important first-order optimization algorithms both in…

Differential privacy is achieved by the introduction of Laplacian noise in the response to a query, establishing a precise trade-off between the level of differential privacy and the accuracy of the database response (via the amount of…

We develop theoretically guaranteed stochastic methods for outlier-robust PCA. Outlier-robust PCA seeks an underlying low-dimensional linear subspace from a dataset that is corrupted with outliers. We are able to show that our methods,…

Differential privacy is a formal mathematical {stand-ard} for quantifying the degree of that individual privacy in a statistical database is preserved. To guarantee differential privacy, a typical method is adding random noise to the…

We study gradient descent under linearly correlated noise. Our work is motivated by recent practical methods for optimization with differential privacy (DP), such as DP-FTRL, which achieve strong performance in settings where privacy…

We study distributed estimation and learning problems in a networked environment where agents exchange information to estimate unknown statistical properties of random variables from their privately observed samples. The agents can…

Data privacy is an important concern in learning, when datasets contain sensitive information about individuals. This paper considers consensus-based distributed optimization under data privacy constraints. Consensus-based optimization…

We study the problem of subsampling in differential privacy (DP), a question that is the centerpiece behind many successful differentially private machine learning algorithms. Specifically, we provide a tight upper bound on the R\'enyi…

We revisit the input perturbations framework for differential privacy where noise is added to the input $A\in \mathcal{S}$ and the result is then projected back to the space of admissible datasets $\mathcal{S}$. Through this framework, we…

Low-rank optimization problems with sparse simplex constraints involve variables that must satisfy nonnegativity, sparsity, and sum-to-1 conditions, making their optimization particularly challenging due to the interplay between low-rank…

In this work we address the practical challenges of training machine learning models on privacy-sensitive datasets by introducing a modular approach that minimizes changes to training algorithms, provides a variety of configuration…

We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method, is for solving Riemannian constrained optimization problems. We establish…

Various tasks in scientific computing can be modeled as an optimization problem on the indefinite Stiefel manifold. We address this using the Riemannian approach, which basically consists of equipping the feasible set with a Riemannian…

We propose a novel theoretical and methodological framework for Gaussian process regression subject to privacy constraints. The proposed method can be used when a data owner is unwilling to share a high-fidelity supervised learning model…