7 Search Results for "Cohen, Edith"

Document
DOI: 10.4230/LIPIcs.ITCS.2023.8
A Framework for Adversarial Streaming via Differential Privacy and Difference Estimators

Authors: Idan Attias, Edith Cohen, Moshe Shechner, and Uri Stemmer

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
Classical streaming algorithms operate under the (not always reasonable) assumption that the input stream is fixed in advance. Recently, there is a growing interest in designing robust streaming algorithms that provide provable guarantees even when the input stream is chosen adaptively as the execution progresses. We propose a new framework for robust streaming that combines techniques from two recently suggested frameworks by Hassidim et al. [NeurIPS 2020] and by Woodruff and Zhou [FOCS 2021]. These recently suggested frameworks rely on very different ideas, each with its own strengths and weaknesses. We combine these two frameworks into a single hybrid framework that obtains the "best of both worlds", thereby solving a question left open by Woodruff and Zhou.
Cite as

Idan Attias, Edith Cohen, Moshe Shechner, and Uri Stemmer. A Framework for Adversarial Streaming via Differential Privacy and Difference Estimators. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{attias_et_al:LIPIcs.ITCS.2023.8,
  author =	{Attias, Idan and Cohen, Edith and Shechner, Moshe and Stemmer, Uri},
  title =	{{A Framework for Adversarial Streaming via Differential Privacy and Difference Estimators}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.8},
  URN =		{urn:nbn:de:0030-drops-175115},
  doi =		{10.4230/LIPIcs.ITCS.2023.8},
  annote =	{Keywords: Streaming, adversarial robustness, differential privacy}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.39
Generalized Private Selection and Testing with High Confidence

Authors: Edith Cohen, Xin Lyu, Jelani Nelson, Tamás Sarlós, and Uri Stemmer

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
Composition theorems are general and powerful tools that facilitate privacy accounting across multiple data accesses from per-access privacy bounds. However they often result in weaker bounds compared with end-to-end analysis. Two popular tools that mitigate that are the exponential mechanism (or report noisy max) and the sparse vector technique, generalized in a recent private selection framework by Liu and Talwar (STOC 2019). In this work, we propose a flexible framework of private selection and testing that generalizes the one proposed by Liu and Talwar, supporting a wide range of applications. We apply our framework to solve several fundamental tasks, including query releasing, top-k selection, and stable selection, with improved confidence-accuracy tradeoffs. Additionally, for online settings, we apply our private testing to design a mechanism for adaptive query releasing, which improves the sample complexity dependence on the confidence parameter for the celebrated private multiplicative weights algorithm of Hardt and Rothblum (FOCS 2010).
Cite as

Edith Cohen, Xin Lyu, Jelani Nelson, Tamás Sarlós, and Uri Stemmer. Generalized Private Selection and Testing with High Confidence. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 39:1-39:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cohen_et_al:LIPIcs.ITCS.2023.39,
  author =	{Cohen, Edith and Lyu, Xin and Nelson, Jelani and Sarl\'{o}s, Tam\'{a}s and Stemmer, Uri},
  title =	{{Generalized Private Selection and Testing with High Confidence}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{39:1--39:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.39},
  URN =		{urn:nbn:de:0030-drops-175426},
  doi =		{10.4230/LIPIcs.ITCS.2023.39},
  annote =	{Keywords: differential privacy, sparse vector technique, adaptive data analysis}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2022.23
Almost Shortest Paths with Near-Additive Error in Weighted Graphs

Authors: Michael Elkin, Yuval Gitlitz, and Ofer Neiman

Published in: LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)

Abstract
Let G = (V,E,w) be a weighted undirected graph with n vertices and m edges, and fix a set of s sources S ⊆ V. We study the problem of computing almost shortest paths (ASP) for all pairs in S × V in both classical centralized and parallel (PRAM) models of computation. Consider the regime of multiplicative approximation of 1+ε, for an arbitrarily small constant ε > 0 (henceforth (1+ε)-ASP for S × V). In this regime existing centralized algorithms require Ω(min{|E|s,n^ω}) time, where ω < 2.372 is the matrix multiplication exponent. Existing PRAM algorithms with polylogarithmic depth (aka time) require work Ω(min{|E|s,n^ω}). In a bold attempt to achieve centralized time close to the lower bound of m + n s, Cohen [Edith Cohen, 2000] devised an algorithm which, in addition to the multiplicative stretch of 1+ε, allows also additive error of β ⋅ W_{max}, where W_{max} is the maximum edge weight in G (assuming that the minimum edge weight is 1), and β = (log n)^{O((log 1/ρ)/ρ)} is polylogarithmic in n. It also depends on the (possibly) arbitrarily small parameter ρ > 0 that determines the running time O((m + ns)n^ρ) of the algorithm. The tradeoff of [Edith Cohen, 2000] was improved in [M. Elkin, 2001], whose algorithm has similar approximation guarantee and running time, but its β is (1/ρ)^{O((log 1/ρ)/ρ)}. However, the latter algorithm produces distance estimates rather than actual approximate shortest paths. Also, the additive terms in [Edith Cohen, 2000; M. Elkin, 2001] depend linearly on a possibly quite large global maximum edge weight W_{max}. In the current paper we significantly improve this state of affairs. Our centralized algorithm has running time O((m+ ns)n^ρ), and its PRAM counterpart has polylogarithmic depth and work O((m + ns)n^ρ), for an arbitrarily small constant ρ > 0. For a pair (s,v) ∈ S× V, it provides a path of length d̂(s,v) that satisfies d̂(s,v) ≤ (1+ε)d_G(s,v) + β ⋅ W(s,v), where W(s,v) is the weight of the heaviest edge on some shortest s-v path. Hence our additive term depends linearly on a local maximum edge weight, as opposed to the global maximum edge weight in [Edith Cohen, 2000; M. Elkin, 2001]. Finally, our β = (1/ρ)^{O(1/ρ)}, i.e., it is significantly smaller than in [Edith Cohen, 2000; M. Elkin, 2001]. We also extend a centralized algorithm of Dor et al. [D. Dor et al., 2000]. For a parameter κ = 1,2,…, this algorithm provides for unweighted graphs a purely additive approximation of 2(κ -1) for all pairs shortest paths (APASP) in time Õ(n^{2+1/κ}). Within the same running time, our algorithm for weighted graphs provides a purely additive error of 2(κ - 1) W(u,v), for every vertex pair (u,v) ∈ binom(V,2), with W(u,v) defined as above. On the way to these results we devise a suite of novel constructions of spanners, emulators and hopsets.
Cite as

Michael Elkin, Yuval Gitlitz, and Ofer Neiman. Almost Shortest Paths with Near-Additive Error in Weighted Graphs. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{elkin_et_al:LIPIcs.SWAT.2022.23,
  author =	{Elkin, Michael and Gitlitz, Yuval and Neiman, Ofer},
  title =	{{Almost Shortest Paths with Near-Additive Error in Weighted Graphs}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{23:1--23:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-236-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{227},
  editor =	{Czumaj, Artur and Xin, Qin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.23},
  URN =		{urn:nbn:de:0030-drops-161833},
  doi =		{10.4230/LIPIcs.SWAT.2022.23},
  annote =	{Keywords: spanners, hopset, shortest paths, PRAM, distance oracles}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.104
Non-Mergeable Sketching for Cardinality Estimation

Authors: Seth Pettie, Dingyu Wang, and Longhui Yin

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
Cardinality estimation is perhaps the simplest non-trivial statistical problem that can be solved via sketching. Industrially-deployed sketches like HyperLogLog, MinHash, and PCSA are mergeable, which means that large data sets can be sketched in a distributed environment, and then merged into a single sketch of the whole data set. In the last decade a variety of sketches have been developed that are non-mergeable, but attractive for other reasons. They are simpler, their cardinality estimates are strictly unbiased, and they have substantially lower variance. We evaluate sketching schemes on a reasonably level playing field, in terms of their memory-variance product (MVP). E.g., a sketch that occupies 5m bits and whose relative variance is 2/m (standard error √{2/m}) has an MVP of 10. Our contributions are as follows. - Cohen [Edith Cohen, 2015] and Ting [Daniel Ting, 2014] independently discovered what we call the {Martingale transform} for converting a mergeable sketch into a non-mergeable sketch. We present a simpler way to analyze the limiting MVP of Martingale-type sketches. - Pettie and Wang proved that the Fishmonger sketch [Seth Pettie and Dingyu Wang, 2021] has the best MVP, H₀/I₀ ≈ 1.98, among a class of mergeable sketches called "linearizable" sketches. (H₀ and I₀ are precisely defined constants.) We prove that the Martingale transform is optimal in the non-mergeable world, and that Martingale Fishmonger in particular is optimal among linearizable sketches, with an MVP of H₀/2 ≈ 1.63. E.g., this is circumstantial evidence that to achieve 1% standard error, we cannot do better than a 2 kilobyte sketch. - Martingale Fishmonger is neither simple nor practical. We develop a new mergeable sketch called Curtain that strikes a nice balance between simplicity and efficiency, and prove that Martingale Curtain has limiting MVP≈ 2.31. It can be updated with O(1) memory accesses and it has lower empirical variance than Martingale LogLog, a practical non-mergeable version of HyperLogLog.
Cite as

Seth Pettie, Dingyu Wang, and Longhui Yin. Non-Mergeable Sketching for Cardinality Estimation. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 104:1-104:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{pettie_et_al:LIPIcs.ICALP.2021.104,
  author =	{Pettie, Seth and Wang, Dingyu and Yin, Longhui},
  title =	{{Non-Mergeable Sketching for Cardinality Estimation}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{104:1--104:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.104},
  URN =		{urn:nbn:de:0030-drops-141731},
  doi =		{10.4230/LIPIcs.ICALP.2021.104},
  annote =	{Keywords: Cardinality Estimation, Sketching}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2020.28
Locality Sensitive Hashing for Set-Queries, Motivated by Group Recommendations

Authors: Haim Kaplan and Jay Tenenbaum

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

Abstract
Locality Sensitive Hashing (LSH) is an effective method to index a set of points such that we can efficiently find the nearest neighbors of a query point. We extend this method to our novel Set-query LSH (SLSH), such that it can find the nearest neighbors of a set of points, given as a query. Let s(x,y) be the similarity between two points x and y. We define a similarity between a set Q and a point x by aggregating the similarities s(p,x) for all p∈ Q. For example, we can take s(p,x) to be the angular similarity between p and x (i.e., 1-(∠(x,p)/π)), and aggregate by arithmetic or geometric averaging, or taking the lowest similarity. We develop locality sensitive hash families and data structures for a large set of such arithmetic and geometric averaging similarities, and analyze their collision probabilities. We also establish an analogous framework and hash families for distance functions. Specifically, we give a structure for the euclidean distance aggregated by either averaging or taking the maximum. We leverage SLSH to solve a geometric extension of the approximate near neighbors problem. In this version, we consider a metric for which the unit ball is an ellipsoid and its orientation is specified with the query. An important application that motivates our work is group recommendation systems. Such a system embeds movies and users in the same feature space, and the task of recommending a movie for a group to watch together, translates to a set-query Q using an appropriate similarity.
Cite as

Haim Kaplan and Jay Tenenbaum. Locality Sensitive Hashing for Set-Queries, Motivated by Group Recommendations. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kaplan_et_al:LIPIcs.SWAT.2020.28,
  author =	{Kaplan, Haim and Tenenbaum, Jay},
  title =	{{Locality Sensitive Hashing for Set-Queries, Motivated by Group Recommendations}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{28:1--28:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.28},
  URN =		{urn:nbn:de:0030-drops-122756},
  doi =		{10.4230/LIPIcs.SWAT.2020.28},
  annote =	{Keywords: Locality sensitive hashing, nearest neighbors, similarity search, group recommendations, distance functions, similarity functions, ellipsoid}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.29
Sample Complexity Bounds for Influence Maximization

Authors: Gal Sadeh, Edith Cohen, and Haim Kaplan

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
Influence maximization (IM) is the problem of finding for a given s ≥ 1 a set S of |S|=s nodes in a network with maximum influence. With stochastic diffusion models, the influence of a set S of seed nodes is defined as the expectation of its reachability over simulations, where each simulation specifies a deterministic reachability function. Two well-studied special cases are the Independent Cascade (IC) and the Linear Threshold (LT) models of Kempe, Kleinberg, and Tardos [Kempe et al., 2003]. The influence function in stochastic diffusion is unbiasedly estimated by averaging reachability values over i.i.d. simulations. We study the IM sample complexity: the number of simulations needed to determine a (1-ε)-approximate maximizer with confidence 1-δ. Our main result is a surprising upper bound of O(s τ ε^{-2} ln (n/δ)) for a broad class of models that includes IC and LT models and their mixtures, where n is the number of nodes and τ is the number of diffusion steps. Generally τ ≪ n, so this significantly improves over the generic upper bound of O(s n ε^{-2} ln (n/δ)). Our sample complexity bounds are derived from novel upper bounds on the variance of the reachability that allow for small relative error for influential sets and additive error when influence is small. Moreover, we provide a data-adaptive method that can detect and utilize fewer simulations on models where it suffices. Finally, we provide an efficient greedy design that computes an (1-1/e-ε)-approximate maximizer from simulations and applies to any submodular stochastic diffusion model that satisfies the variance bounds.
Cite as

Gal Sadeh, Edith Cohen, and Haim Kaplan. Sample Complexity Bounds for Influence Maximization. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 29:1-29:36, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{sadeh_et_al:LIPIcs.ITCS.2020.29,
  author =	{Sadeh, Gal and Cohen, Edith and Kaplan, Haim},
  title =	{{Sample Complexity Bounds for Influence Maximization}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{29:1--29:36},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.29},
  URN =		{urn:nbn:de:0030-drops-117140},
  doi =		{10.4230/LIPIcs.ITCS.2020.29},
  annote =	{Keywords: Sample complexity, Influence maximization, Submodular maximization}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.659
Average Distance Queries through Weighted Samples in Graphs and Metric Spaces: High Scalability with Tight Statistical Guarantees

Authors: Shiri Chechik, Edith Cohen, and Haim Kaplan

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)

Abstract
The average distance from a node to all other nodes in a graph, or from a query point in a metric space to a set of points, is a fundamental quantity in data analysis. The inverse of the average distance, known as the (classic) closeness centrality of a node, is a popular importance measure in the study of social networks. We develop novel structural insights on the sparsifiability of the distance relation via weighted sampling. Based on that, we present highly practical algorithms with strong statistical guarantees for fundamental problems. We show that the average distance (and hence the centrality) for all nodes in a graph can be estimated using O(epsilon^{-2}) single-source distance computations. For a set V of n points in a metric space, we show that after preprocessing which uses O(n) distance computations we can compute a weighted sample S subset of V of size O(epsilon^{-2}) such that the average distance from any query point v to V can be estimated from the distances from v to S. Finally, we show that for a set of points V in a metric space, we can estimate the average pairwise distance using O(n+epsilon^{-2}) distance computations. The estimate is based on a weighted sample of O(epsilon^{-2}) pairs of points, which is computed using O(n) distance computations. Our estimates are unbiased with normalized mean square error (NRMSE) of at most epsilon. Increasing the sample size by a O(log(n)) factor ensures that the probability that the relative error exceeds epsilon is polynomially small.
Cite as

Shiri Chechik, Edith Cohen, and Haim Kaplan. Average Distance Queries through Weighted Samples in Graphs and Metric Spaces: High Scalability with Tight Statistical Guarantees. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 659-679, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{chechik_et_al:LIPIcs.APPROX-RANDOM.2015.659,
  author =	{Chechik, Shiri and Cohen, Edith and Kaplan, Haim},
  title =	{{Average Distance Queries through Weighted Samples in Graphs and Metric Spaces: High Scalability with Tight Statistical Guarantees}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{659--679},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.659},
  URN =		{urn:nbn:de:0030-drops-53291},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.659},
  annote =	{Keywords: Closeness Centrality; Average Distance; Metric Space; Weighted Sampling}
}
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