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no code implementations • 10 Apr 2022 • Gal Yona, Shay Moran, Gal Elidan, Amir Globerson

We show that there is a natural class where this approach is sub-optimal, and that there is a more comparison-efficient active learning scheme.

no code implementations • 3 Mar 2022 • Nataly Brukhim, Daniel Carmon, Irit Dinur, Shay Moran, Amir Yehudayoff

This work resolves this problem: we characterize multiclass PAC learnability through the DS dimension, a combinatorial dimension defined by Daniely and Shalev-Shwartz (2014).

no code implementations • 10 Feb 2022 • Olivier Bousquet, Amit Daniely, Haim Kaplan, Yishay Mansour, Shay Moran, Uri Stemmer

Our transformation readily implies monotone learners in a variety of contexts: for example it extends Pestov's result to classification tasks with an arbitrary number of labels.

no code implementations • NeurIPS 2021 • Nataly Brukhim, Elad Hazan, Shay Moran, Indraneel Mukherjee, Robert E. Schapire

Here, we focus on an especially natural formulation in which the weak hypotheses are assumed to belong to an ''easy-to-learn'' base class, and the weak learner is an agnostic PAC learner for that class with respect to the standard classification loss.

no code implementations • 19 Nov 2021 • Kunal Dutta, Arijit Ghosh, Shay Moran

We study the connections between three seemingly different combinatorial structures - "uniform" brackets in statistics and probability theory, "containers" in online and distributed learning theory, and "combinatorial Macbeath regions", or Mnets in discrete and computational geometry.

no code implementations • NeurIPS 2021 • Mahdi Haghifam, Gintare Karolina Dziugaite, Shay Moran, Daniel M. Roy

We further show that an inherent limitation of proper learning of VC classes contradicts the existence of a proper learner with constant CMI, and it implies a negative resolution to an open problem of Steinke and Zakynthinou (2020).

no code implementations • 17 Aug 2021 • Olivier Bousquet, Mark Braverman, Klim Efremenko, Gillat Kol, Shay Moran

We derive an optimal $2$-approximation learning strategy for the Hypothesis Selection problem, outputting $q$ such that $\mathsf{TV}(p, q) \leq2 \cdot opt + \eps$, with a (nearly) optimal sample complexity of~$\tilde O(\log n/\epsilon^2)$.

no code implementations • 12 Aug 2021 • Maryanthe Malliaris, Shay Moran

We use algorithmic methods from online learning to revisit a key idea from the interaction of model theory and combinatorics, the existence of large "indivisible" sets, called "$\epsilon$-excellent," in $k$-edge stable graphs (equivalently, Littlestone classes).

no code implementations • 18 Jul 2021 • Noga Alon, Steve Hanneke, Ron Holzman, Shay Moran

In fact we exhibit easy-to-learn partial concept classes which provably cannot be captured by the traditional PAC theory.

no code implementations • 2 Feb 2021 • Steve Hanneke, Roi Livni, Shay Moran

More precisely, given any concept class C and any hypothesis class H, we provide nearly tight bounds (up to a log factor) on the optimal mistake bounds for online learning C using predictors from H. Our bound yields an exponential improvement over the previously best known bound by Chase and Freitag (2020).

no code implementations • 22 Jan 2021 • Noga Alon, Omri Ben-Eliezer, Yuval Dagan, Shay Moran, Moni Naor, Eylon Yogev

Laws of large numbers guarantee that given a large enough sample from some population, the measure of any fixed sub-population is well-estimated by its frequency in the sample.

no code implementations • NeurIPS 2020 • Olivier Bousquet, Roi Livni, Shay Moran

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 non-efficient).

no code implementations • 9 Nov 2020 • Olivier Bousquet, Steve Hanneke, Shay Moran, Ramon van Handel, Amir Yehudayoff

How quickly can a given class of concepts be learned from examples?

no code implementations • 5 Nov 2020 • Mahdi Haghifam, Gintare Karolina Dziugaite, Shay Moran, Daniel M. Roy

We provide a negative resolution to a conjecture of Steinke and Zakynthinou (2020a), by showing that their bound on the conditional mutual information (CMI) of proper learners of Vapnik--Chervonenkis (VC) classes cannot be improved from $d \log n +2$ to $O(d)$, where $n$ is the number of i. i. d.

no code implementations • NeurIPS 2020 • Raef Bassily, Shay Moran, Anupama Nandi

Inspired by the above example, we consider a model in which the population $\mathcal{D}$ is a mixture of two sub-populations: a private sub-population $\mathcal{D}_{\sf priv}$ of private and sensitive data, and a public sub-population $\mathcal{D}_{\sf pub}$ of data with no privacy concerns.

no code implementations • NeurIPS 2020 • Roi Livni, Shay Moran

PAC-Bayes is a useful framework for deriving generalization bounds which was introduced by McAllester ('98).

no code implementations • 24 May 2020 • Olivier Bousquet, Steve Hanneke, Shay Moran, Nikita Zhivotovskiy

It has been recently shown by Hanneke (2016) that the optimal sample complexity of PAC learning for any VC class C is achieved by a particular improper learning algorithm, which outputs a specific majority-vote of hypotheses in C. This leaves the question of when this bound can be achieved by proper learning algorithms, which are restricted to always output a hypothesis from C. In this paper we aim to characterize the classes for which the optimal sample complexity can be achieved by a proper learning algorithm.

no code implementations • ICML 2020 • Raef Bassily, Albert Cheu, Shay Moran, Aleksandar Nikolov, Jonathan Ullman, Zhiwei Steven Wu

In comparison, with only private samples, this problem cannot be solved even for simple query classes with VC-dimension one, and without any private samples, a larger public sample of size $d/\alpha^2$ is needed.

no code implementations • 10 Mar 2020 • Noga Alon, Amos Beimel, Shay Moran, Uri Stemmer

Let~$\cH$ be a class of boolean functions and consider a {\it composed class} $\cH'$ that is derived from~$\cH$ using some arbitrary aggregation rule (for example, $\cH'$ may be the class of all 3-wise majority-votes of functions in $\cH$).

no code implementations • NeurIPS 2020 • Nataly Brukhim, Xinyi Chen, Elad Hazan, Shay Moran

Boosting is a widely used machine learning approach based on the idea of aggregating weak learning rules.

no code implementations • 1 Mar 2020 • Mark Bun, Roi Livni, Shay Moran

We prove that every concept class with finite Littlestone dimension can be learned by an (approximate) differentially-private algorithm.

1 code implementation • 31 Jan 2020 • Noga Alon, Alon Gonen, Elad Hazan, Shay Moran

(ii) Expressivity: Which tasks can be learned by boosting weak hypotheses from a bounded VC class?

no code implementations • NeurIPS 2019 • Noga Alon, Raef Bassily, Shay Moran

We consider learning problems where the training set consists of two types of examples: private and public.

no code implementations • 8 Sep 2019 • Mark Braverman, Gillat Kol, Shay Moran, Raghuvansh R. Saxena

For Convex Set Disjointness (and the equivalent task of distributed LP feasibility) we derive upper and lower bounds of $\tilde O(d^2\log n)$ and~$\Omega(d\log n)$.

1 code implementation • NeurIPS 2019 • Akshay Balsubramani, Sanjoy Dasgupta, Yoav Freund, Shay Moran

We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter.

no code implementations • NeurIPS 2019 • Alon Gonen, Elad Hazan, Shay Moran

We study the relationship between the notions of differentially private learning and online learning in games.

no code implementations • 27 Feb 2019 • Amos Beimel, Shay Moran, Kobbi Nissim, Uri Stemmer

The building block for this learner is a differentially private algorithm for locating an approximate center point of $m>\mathrm{poly}(d, 2^{\log^*|X|})$ points -- a high dimensional generalization of the median function.

no code implementations • NeurIPS 2019 • Alon Cohen, Avinatan Hassidim, Haim Kaplan, Yishay Mansour, Shay Moran

(ii) In the second variant it is assumed that before the process starts, the algorithm has an access to a training set of $n$ items drawn independently from the same unknown distribution (e. g.\ data of candidates from previous recruitment seasons).

no code implementations • 10 Feb 2019 • Olivier Bousquet, Daniel Kane, Shay Moran

We complement and extend this result by showing that: (i) the factor 3 can not be improved if one restricts the algorithm to output a density from $\mathcal{Q}$, and (ii) if one allows the algorithm to output arbitrary densities (e. g.\ a mixture of densities from $\mathcal{Q}$), then the approximation factor can be reduced to 2, which is optimal.

no code implementations • 9 Feb 2019 • Olivier Bousquet, Roi Livni, Shay Moran

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 non-efficient).

no code implementations • 5 Dec 2018 • Jérémie Chalopin, Victor Chepoi, Shay Moran, Manfred K. Warmuth

On the positive side we present a new construction of an unlabeled sample compression scheme for maximum classes.

no code implementations • 14 Jun 2018 • Shay Moran, Ido Nachum, Itai Panasoff, Amir Yehudayoff

We study and provide exposition to several phenomena that are related to the perceptron's compression.

no code implementations • 14 Jun 2018 • Zeev Dvir, Shay Moran

We show that any family of subsets $A\subseteq 2^{[n]}$ satisfies $\lvert A\rvert \leq O\bigl(n^{\lceil{d}/{2}\rceil}\bigr)$, where $d$ is the VC dimension of $\{S\triangle T \,\vert\, S, T\in A\}$, and $\triangle$ is the symmetric difference operator.

no code implementations • 4 Jun 2018 • Noga Alon, Roi Livni, Maryanthe Malliaris, Shay Moran

We show that every approximately differentially private learning algorithm (possibly improper) for a class $H$ with Littlestone dimension~$d$ requires $\Omega\bigl(\log^*(d)\bigr)$ examples.

no code implementations • 16 Nov 2017 • Daniel M. Kane, Roi Livni, Shay Moran, Amir Yehudayoff

To naturally fit into the framework of learning theory, the players can send each other examples (as well as bits) where each example/bit costs one unit of communication.

no code implementations • 14 Nov 2017 • Shai Ben-David, Pavel Hrubes, Shay Moran, Amir Shpilka, Amir Yehudayoff

We consider the following statistical estimation problem: given a family F of real valued functions over some domain X and an i. i. d.

no code implementations • 14 Oct 2017 • Raef Bassily, Shay Moran, Ido Nachum, Jonathan Shafer, Amir Yehudayoff

We discuss an approach that allows us to prove upper bounds on the amount of information that algorithms reveal about their inputs, and also provide a lower bound by showing a simple concept class for which every (possibly randomized) empirical risk minimizer must reveal a lot of information.

no code implementations • NeurIPS 2017 • Noga Alon, Moshe Babaioff, Yannai A. Gonczarowski, Yishay Mansour, Shay Moran, Amir Yehudayoff

In this work we derive a variant of the classic Glivenko-Cantelli Theorem, which asserts uniform convergence of the empirical Cumulative Distribution Function (CDF) to the CDF of the underlying distribution.

no code implementations • 4 May 2017 • Daniel M. Kane, Shachar Lovett, Shay Moran

We construct near optimal linear decision trees for a variety of decision problems in combinatorics and discrete geometry.

no code implementations • 11 Apr 2017 • Daniel M. Kane, Shachar Lovett, Shay Moran, Jiapeng Zhang

We identify a combinatorial dimension, called the \emph{inference dimension}, that captures the query complexity when each additional query is determined by $O(1)$ examples (such as comparison queries, each of which is determined by the two compared examples).

no code implementations • NeurIPS 2016 • Ofir David, Shay Moran, Amir Yehudayoff

This work continues the study of the relationship between sample compression schemes and statistical learning, which has been mostly investigated within the framework of binary classification.

no code implementations • 5 Nov 2016 • Yuval Dagan, Yuval Filmus, Ariel Gabizon, Shay Moran

An optimal strategy for the "20 questions" game is given by a Huffman code for $\pi$: Bob's questions reveal the codeword for $x$ bit by bit.

no code implementations • 12 Oct 2016 • Ofir David, Shay Moran, Amir Yehudayoff

(iv) A dichotomy for sample compression in multiclass categorization problems: If a non-trivial compression exists then a compression of logarithmic size exists.

no code implementations • 30 May 2015 • Shay Moran, Manfred K. Warmuth

We consider a generalization of maximum classes called extremal classes.

no code implementations • 24 Mar 2015 • Shay Moran, Amir Yehudayoff

Sample compression schemes were defined by Littlestone and Warmuth (1986) as an abstraction of the structure underlying many learning algorithms.

no code implementations • 22 Feb 2015 • Shay Moran, Amir Shpilka, Avi Wigderson, Amir Yehudayoff

We further construct sample compression schemes of size $k$ for $C$, with additional information of $k \log(k)$ bits.

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