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We consider differentially private approximate singular vector computation. Known worst-case lower bounds show that the error of any differentially private algorithm must scale polynomially with the dimension of the singular vector. We are…

Data Structures and Algorithms · Computer Science 2012-11-06 Moritz Hardt , Aaron Roth

We study the sample complexity of private synthetic data generation over an unbounded sized class of statistical queries, and show that any class that is privately proper PAC learnable admits a private synthetic data generator (perhaps…

Machine Learning · Computer Science 2020-12-08 Olivier Bousquet , Roi Livni , Shay Moran

We study the problem of learning robust classifiers where the classifier will receive a perturbed input. Unlike robust PAC learning studied in prior work, here the clean data and its label are also adversarially chosen. We formulate this…

Machine Learning · Computer Science 2026-03-02 Sajad Ashkezari

We give an example of a class of distributions that is learnable up to constant error in total variation distance with a finite number of samples, but not learnable under $(\varepsilon, \delta)$-differential privacy with the same target…

Data Structures and Algorithms · Computer Science 2026-05-20 Mark Bun , Gautam Kamath , Argyris Mouzakis , Vikrant Singhal

We consider the following fundamental question on $\epsilon$-differential privacy. Consider an arbitrary $\epsilon$-differentially private algorithm defined on a subset of the input space. Is it possible to extend it to an…

Statistics Theory · Mathematics 2018-11-01 Christian Borgs , Jennifer Chayes , Adam Smith , Ilias Zadik

We initiate a study of computable online (c-online) learning, which we analyze under varying requirements for "optimality" in terms of the mistake bound. Our main contribution is to give a necessary and sufficient condition for optimal…

Machine Learning · Computer Science 2023-02-10 Niki Hasrati , Shai Ben-David

We study multiclass classification in the agnostic adversarial online learning setting. As our main result, we prove that any multiclass concept class is agnostically learnable if and only if its Littlestone dimension is finite. This solves…

Machine Learning · Computer Science 2023-07-10 Steve Hanneke , Shay Moran , Vinod Raman , Unique Subedi , Ambuj Tewari

We study the question of learning an adversarially robust predictor. We show that any hypothesis class $\mathcal{H}$ with finite VC dimension is robustly PAC learnable with an improper learning rule. The requirement of being improper is…

Machine Learning · Computer Science 2019-07-04 Omar Montasser , Steve Hanneke , Nathan Srebro

Given a real-valued hypothesis class $\mathcal{H}$, we investigate under what conditions there is a differentially private algorithm which learns an optimal hypothesis from $\mathcal{H}$ given i.i.d. data. Inspired by recent results for the…

Machine Learning · Computer Science 2021-11-29 Noah Golowich

This paper studies classification with an abstention option in the online setting. In this setting, examples arrive sequentially, the learner is given a hypothesis class $\mathcal H$, and the goal of the learner is to either predict a label…

Machine Learning · Computer Science 2016-09-29 Chicheng Zhang , Kamalika Chaudhuri

A classical result in learning theory shows the equivalence of PAC learnability of binary hypothesis classes and the finiteness of VC dimension. Extending this to the multiclass setting was an open problem, which was settled in a recent…

Machine Learning · Statistics 2023-03-28 Moses Charikar , Chirag Pabbaraju

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

In 2008, Kasiviswanathan et al. defined private learning as a combination of PAC learning and differential privacy. Informally, a private learner is applied to a collection of labeled individual information and outputs a hypothesis while…

Cryptography and Security · Computer Science 2014-02-12 Amos Beimel , Kobbi Nissim , Uri Stemmer

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

We study the problem of {\em properly} learning large margin halfspaces in the agnostic PAC model. In more detail, we study the complexity of properly learning $d$-dimensional halfspaces on the unit ball within misclassification error…

Machine Learning · Computer Science 2019-08-30 Ilias Diakonikolas , Daniel M. Kane , Pasin Manurangsi

Previous work on user-level differential privacy (DP) [Ghazi et al. NeurIPS 2021, Bun et al. STOC 2023] obtained generic algorithms that work for various learning tasks. However, their focus was on the example-rich regime, where the users…

Data Structures and Algorithms · Computer Science 2023-09-25 Badih Ghazi , Pritish Kamath , Ravi Kumar , Pasin Manurangsi , Raghu Meka , Chiyuan Zhang

This paper focuses on the relation between computational learning theory and resource-bounded dimension. We intend to establish close connections between the learnability/nonlearnability of a concept class and its corresponding size in…

Computational Complexity · Computer Science 2015-03-17 Ricard Gavalda , Maria Lopez-Valdes , Elvira Mayordomo , N. V. Vinodchandran

We develop theory for using heuristics to solve computationally hard problems in differential privacy. Heuristic approaches have enjoyed tremendous success in machine learning, for which performance can be empirically evaluated. However,…

Machine Learning · Computer Science 2018-11-20 Seth Neel , Aaron Roth , Zhiwei Steven Wu

A private learner is an algorithm that given a sample of labeled individual examples outputs a generalizing hypothesis while preserving the privacy of each individual. In 2008, Kasiviswanathan et al. (FOCS 2008) gave a generic construction…

Machine Learning · Computer Science 2015-07-03 Amos Beimel , Kobbi Nissim , Uri Stemmer

Ensuring differential privacy of models learned from sensitive user data is an important goal that has been studied extensively in recent years. It is now known that for some basic learning problems, especially those involving…

Machine Learning · Computer Science 2018-05-10 Cynthia Dwork , Vitaly Feldman