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Related papers: On Differentially Private Linear Algebra

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A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…

High Energy Physics - Theory · Physics 2009-10-22 A. Turbiner

In recent years a large literature on deep learning based methods for the numerical solution partial differential equations has emerged; results for integro-differential equations on the other hand are scarce. In this paper we study deep…

Numerical Analysis · Mathematics 2021-09-27 Rüdiger Frey , Verena Köck

Differentially private (DP) tabular data synthesis generates artificial data that preserves the statistical properties of private data while safeguarding individual privacy. The emergence of diverse algorithms in recent years has introduced…

Cryptography and Security · Computer Science 2025-11-19 Kai Chen , Xiaochen Li , Chen Gong , Ryan McKenna , Tianhao Wang

Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…

Machine Learning · Computer Science 2023-10-31 Derick Nganyu Tanyu , Jianfeng Ning , Tom Freudenberg , Nick Heilenkötter , Andreas Rademacher , Uwe Iben , Peter Maass

We use an embedding of the symmetric $d$th power of any algebraic curve $C$ of genus $g$ into a Grassmannian space to give algorithms for working with divisors on $C$, using only linear algebra in vector spaces of dimension $O(g)$, and…

Number Theory · Mathematics 2007-05-23 Kamal Khuri-Makdisi

Machine learning models are increasingly used in high-stakes decision-making systems. In such applications, a major concern is that these models sometimes discriminate against certain demographic groups such as individuals with certain…

Machine Learning · Computer Science 2023-06-06 Andrew Lowy , Devansh Gupta , Meisam Razaviyayn

We revisit the problem of linear regression under a differential privacy constraint. By consolidating existing pieces in the literature, we clarify the correct dependence of the feature, label and coefficient domains in the optimization…

Machine Learning · Statistics 2018-07-10 Yu-Xiang Wang

Motivated by problems arising in digital advertising, we introduce the task of training differentially private (DP) machine learning models with semi-sensitive features. In this setting, a subset of the features is known to the attacker…

We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…

Machine Learning · Computer Science 2020-11-16 Maysum Panju , Kourosh Parand , Ali Ghodsi

In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…

Symbolic Computation · Computer Science 2009-01-14 Jean-Guillaume Dumas , Pascal Giorgi , Clément Pernet

We introduce an $(\epsilon, \delta)$-jointly differentially private algorithm for packing problems. Our algorithm not only achieves the optimal trade-off between the privacy parameter $\epsilon$ and the minimum supply requirement (up to…

Data Structures and Algorithms · Computer Science 2019-05-03 Zhiyi Huang , Xue Zhu

Differential privacy (DP) ensures that training a machine learning model does not leak private data. In practice, we may have access to auxiliary public data that is free of privacy concerns. In this work, we assume access to a given amount…

Machine Learning · Computer Science 2024-09-11 Andrew Lowy , Zeman Li , Tianjian Huang , Meisam Razaviyayn

This paper studies the problem of differentially private empirical risk minimization (DP-ERM) for binary linear classification. We obtain an efficient $(\varepsilon,\delta)$-DP algorithm with an empirical zero-one risk bound of…

Machine Learning · Computer Science 2025-06-02 Erchi Wang , Yuqing Zhu , Yu-Xiang Wang

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…

Machine Learning · Computer Science 2021-06-04 Quanming Yao , Hangsi Yang , En-Liang Hu , James Kwok

Differential Privacy (DP) is an important privacy-enhancing technology for private machine learning systems. It allows to measure and bound the risk associated with an individual participation in a computation. However, it was recently…

Machine Learning · Computer Science 2022-09-09 Cuong Tran , My H. Dinh , Ferdinando Fioretto

Differential privacy enables organizations to collect accurate aggregates over sensitive data with strong, rigorous guarantees on individuals' privacy. Previous work has found that under differential privacy, computing multiple correlated…

Databases · Computer Science 2016-05-18 Ganzhao Yuan , Yin Yang , Zhenjie Zhang , Zhifeng Hao

We study the problem of differentially private (DP) mechanisms for representing sets of size $k$ from a large universe. Our first construction creates $(\epsilon,\delta)$-DP representations with error probability of $1/(e^\epsilon + 1)$…

Cryptography and Security · Computer Science 2025-07-23 Sarvar Patel , Giuseppe Persiano , Joon Young Seo , Kevin Yeo

This paper presents a differentially private algorithm for linear regression learning in a decentralized fashion. Under this algorithm, privacy budget is theoretically derived, in addition to that the solution error is shown to be bounded…

Cryptography and Security · Computer Science 2020-04-17 Yang Liu , Xiong Zhang , Shuqi Qin , Xiaoping Lei

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

Data Structures and Algorithms · Computer Science 2020-03-19 Agniva Chowdhury , Palma London , Haim Avron , Petros Drineas

Motivated by the increasing deployment of reinforcement learning in the real world, involving a large consumption of personal data, we introduce a differentially private (DP) policy gradient algorithm. We show that, in this setting, the…

Machine Learning · Computer Science 2025-02-03 Alexandre Rio , Merwan Barlier , Igor Colin