相关论文: Differentially private Riemannian optimization

Gaussian processes (GPs) are non-parametric Bayesian models that are widely used for diverse prediction tasks. Previous work in adding strong privacy protection to GPs via differential privacy (DP) has been limited to protecting only the…

Traditionally, the random noise is equally injected when training with different data instances in the field of differential privacy (DP). In this paper, we first give sharper excess risk bounds of DP stochastic gradient descent (SGD)…

The approximation introduced by finite-precision representation of continuous data can induce arbitrarily large information leaks even when the computation using exact semantics is secure. Such leakage can thus undermine design efforts…

Deep learning models leak significant amounts of information about their training datasets. Previous work has investigated training models with differential privacy (DP) guarantees through adding DP noise to the gradients. However, such…

We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two…

We consider the problem of reinforcing federated learning with formal privacy guarantees. We propose to employ Bayesian differential privacy, a relaxation of differential privacy for similarly distributed data, to provide sharper privacy…

Network routing problems are common across many engineering applications. Computing optimal routing policies requires knowledge about network demand, i.e., the origin and destination (OD) of all requests in the network. However, privacy…

We analyze convergence of gradient-descent methods on Riemannian manifolds. In particular, we study randomization of Riemannian gradient algorithms for minimizing smooth cost functions (of Morse-Bott type). We prove that randomized gradient…

Bayesian methods lie at the heart of modern data science and provide a powerful scaffolding for estimation in data-constrained settings and principled quantification and propagation of uncertainty. Yet in many real-world use cases where…

We propose a novel Bayesian inference framework for distributed differentially private linear regression. We consider a distributed setting where multiple parties hold parts of the data and share certain summary statistics of their portions…

Differentially private stochastic gradient descent privatizes model training by injecting noise into each iteration, where the noise magnitude increases with the number of model parameters. Recent works suggest that we can reduce the noise…

Training generative models with differential privacy (DP) typically involves injecting noise into gradient updates or adapting the discriminator's training procedure. As a result, such approaches often struggle with hyper-parameter tuning…

In this paper, we consider optimization problems over closed embedded submanifolds of $\mathbb{R}^n$, which are defined by the constraints $c(x) = 0$. We propose a class of constraint dissolving approaches for these Riemannian optimization…

Learning a privacy-preserving model from sensitive data which are distributed across multiple devices is an increasingly important problem. The problem is often formulated in the federated learning context, with the aim of learning a single…

With changes in privacy laws, there is often a hard requirement for client data to remain on the device rather than being sent to the server. Therefore, most processing happens on the device, and only an altered element is sent to the…

Conjugate gradient (CG) methods are widely acknowledged as efficient for minimizing continuously differentiable functions in Euclidean spaces. In recent years, various CG methods have been extended to Riemannian manifold optimization, but…

In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…

Many modern statistical analysis and machine learning applications require training models on sensitive user data. Under a formal definition of privacy protection, differentially private algorithms inject calibrated noise into the…

Generalized linear models (GLMs) such as logistic regression are among the most widely used arms in data analyst's repertoire and often used on sensitive datasets. A large body of prior works that investigate GLMs under differential privacy…

We propose an inexact optimization algorithm on Riemannian manifolds, motivated by quadratic discrimination tasks in high-dimensional, low-sample-size (HDLSS) imaging settings. In such applications, gradient evaluations are often biased due…