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In this work, we study the trade-off between differential privacy and adversarial robustness under L2-perturbations in the context of learning halfspaces. We prove nearly tight bounds on the sample complexity of robust private learning of…

Machine Learning · Computer Science 2021-03-29 Badih Ghazi , Ravi Kumar , Pasin Manurangsi , Thao Nguyen

Parities have become a standard benchmark for evaluating learning algorithms. Recent works show that regular neural networks trained by gradient descent can efficiently learn degree $k$ parities on uniform inputs for constant $k$, but fail…

Machine Learning · Computer Science 2025-03-06 Emmanuel Abbe , Elisabetta Cornacchia , Jan Hązła , Donald Kougang-Yombi

We provide a differentially private algorithm for hypothesis selection. Given samples from an unknown probability distribution $P$ and a set of $m$ probability distributions $\mathcal{H}$, the goal is to output, in a…

Data Structures and Algorithms · Computer Science 2021-01-05 Mark Bun , Gautam Kamath , Thomas Steinke , Zhiwei Steven Wu

ldp deployments are vulnerable to inference attacks as an adversary can link the noisy responses to their identity and subsequently, auxiliary information using the order of the data. An alternative model, shuffle DP, prevents this by…

Machine Learning · Computer Science 2021-10-18 Casey Meehan , Amrita Roy Chowdhury , Kamalika Chaudhuri , Somesh Jha

We consider learning under the constraint of local differential privacy (LDP). For many learning problems known efficient algorithms in this model require many rounds of communication between the server and the clients holding the data…

Machine Learning · Computer Science 2019-10-29 Amit Daniely , Vitaly Feldman

The discrete logarithm problem is a fundamental challenge in number theory with significant implications for cryptographic protocols. In this paper, we investigate the limitations of gradient-based methods for learning the parity bit of the…

Machine Learning · Computer Science 2023-10-04 Rustem Takhanov , Maxat Tezekbayev , Artur Pak , Arman Bolatov , Zhibek Kadyrsizova , Zhenisbek Assylbekov

The shuffle model of Differential Privacy (DP) is an enhanced privacy protocol which introduces an intermediate trusted server between local users and a central data curator. It significantly amplifies the central DP guarantee by…

Cryptography and Security · Computer Science 2024-07-26 Yixuan Liu , Yuhan Liu , Li Xiong , Yujie Gu , Hong Chen

We show a new lower bound on the sample complexity of $(\varepsilon, \delta)$-differentially private algorithms that accurately answer statistical queries on high-dimensional databases. The novelty of our bound is that it depends optimally…

Data Structures and Algorithms · Computer Science 2015-01-27 Thomas Steinke , Jonathan Ullman

We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…

Machine Learning · Computer Science 2023-07-18 Ilias Diakonikolas , Jelena Diakonikolas , Daniel M. Kane , Puqian Wang , Nikos Zarifis

We construct a universally Bayes consistent learning rule that satisfies differential privacy (DP). We first handle the setting of binary classification and then extend our rule to the more general setting of density estimation (with…

Machine Learning · Computer Science 2022-12-09 Olivier Bousquet , Haim Kaplan , Aryeh Kontorovich , Yishay Mansour , Shay Moran , Menachem Sadigurschi , Uri Stemmer

Multi-distribution learning generalizes the classic PAC learning to handle data coming from multiple distributions. Given a set of $k$ data distributions and a hypothesis class of VC dimension $d$, the goal is to learn a hypothesis that…

Machine Learning · Computer Science 2024-01-30 Binghui Peng

We study the fundamental problems of identity testing (goodness of fit), and closeness testing (two sample test) of distributions over $k$ elements, under differential privacy. While the problems have a long history in statistics, finite…

Machine Learning · Computer Science 2017-11-01 Jayadev Acharya , Ziteng Sun , Huanyu Zhang

We consider the sample complexity of learning with adversarial robustness. Most prior theoretical results for this problem have considered a setting where different classes in the data are close together or overlapping. Motivated by some…

Machine Learning · Computer Science 2023-01-19 Robi Bhattacharjee , Somesh Jha , Kamalika Chaudhuri

The shuffle model of differential privacy provides promising privacy-utility balances in decentralized, privacy-preserving data analysis. However, the current analyses of privacy amplification via shuffling lack both tightness and…

Cryptography and Security · Computer Science 2024-07-30 Shaowei Wang , Yun Peng , Jin Li , Zikai Wen , Zhipeng Li , Shiyu Yu , Di Wang , Wei Yang

In this paper, we introduce the imperfect shuffle differential privacy model, where messages sent from users are shuffled in an almost uniform manner before being observed by a curator for private aggregation. We then consider the private…

Cryptography and Security · Computer Science 2023-08-29 Badih Ghazi , Ravi Kumar , Pasin Manurangsi , Jelani Nelson , Samson Zhou

We prove that any algorithm for learning parities requires either a memory of quadratic size or an exponential number of samples. This proves a recent conjecture of Steinhardt, Valiant and Wager and shows that for some learning problems a…

Machine Learning · Computer Science 2016-02-17 Ran Raz

We show new lower bounds on the sample complexity of $(\varepsilon, \delta)$-differentially private algorithms that accurately answer large sets of counting queries. A counting query on a database $D \in (\{0,1\}^d)^n$ has the form "What…

Cryptography and Security · Computer Science 2018-10-25 Mark Bun , Jonathan Ullman , Salil Vadhan

We study the sample complexity of learning a uniform approximation of an $n$-dimensional cumulative distribution function (CDF) within an error $\epsilon > 0$, when observations are restricted to a minimal one-bit feedback. This serves as a…

Machine Learning · Computer Science 2026-05-12 Matteo Castiglioni , Anna Lunghi , Alberto Marchesi

We present new differentially private algorithms for learning a large-margin halfspace. In contrast to previous algorithms, which are based on either differentially private simulations of the statistical query model or on private convex…

Machine Learning · Computer Science 2020-02-25 Huy L. Nguyen , Jonathan Ullman , Lydia Zakynthinou

We study the problem of learning mixtures of Gaussians with approximate differential privacy. We prove that roughly $kd^2 + k^{1.5} d^{1.75} + k^2 d$ samples suffice to learn a mixture of $k$ arbitrary $d$-dimensional Gaussians up to low…

Machine Learning · Computer Science 2024-11-05 Hassan Ashtiani , Mahbod Majid , Shyam Narayanan