30 Search Results for "Roth, Aaron"

Volume

LIPIcs, Volume 156

1st Symposium on Foundations of Responsible Computing (FORC 2020)

FORC 2020, June 1-3, 2020, Harvard University, Cambridge, MA, USA (Virtual Conference)

Editors: Aaron Roth

Document
DOI: 10.4230/LIPIcs.ESA.2024.60
New Algorithms and Lower Bounds for Streaming Tournaments

Authors: Prantar Ghosh and Sahil Kuchlous

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We study fundamental directed graph (digraph) problems in the streaming model. An initial investigation by Chakrabarti, Ghosh, McGregor, and Vorotnikova [SODA'20] on streaming digraphs showed that while most of these problems are provably hard in general, some of them become tractable when restricted to the well-studied class of tournament graphs where every pair of nodes shares exactly one directed edge. Thus, we focus on tournaments and improve the state of the art for multiple problems in terms of both upper and lower bounds. Our primary upper bound is a deterministic single-pass semi-streaming algorithm (using Õ(n) space for n-node graphs, where Õ(.) hides polylog(n) factors) for decomposing a tournament into strongly connected components (SCC). It improves upon the previously best-known algorithm by Baweja, Jia, and Woodruff [ITCS'22] in terms of both space and passes: for p ⩾ 1, they used (p+1) passes and Õ(n^{1+1/p}) space. We further extend our algorithm to digraphs that are close to tournaments and establish tight bounds demonstrating that the problem’s complexity grows smoothly with the "distance" from tournaments. Applying our SCC-decomposition framework, we obtain improved - and in some cases, optimal - tournament algorithms for s,t-reachability, strong connectivity, Hamiltonian paths and cycles, and feedback arc set. On the other hand, we prove lower bounds exhibiting that some well-studied problems - such as (exact) feedback arc set and s,t-distance - remain hard (require Ω(n²) space) on tournaments. Moreover, we generalize the former problem’s lower bound to establish space-approximation tradeoffs: any single-pass (1± ε)-approximation algorithm requires Ω(n/√{ε}) space. Finally, we settle the streaming complexities of two basic digraph problems studied by prior work: acyclicity testing of tournaments and sink finding in DAGs. As a whole, our collection of results contributes significantly to the growing literature on streaming digraphs.
Cite as

Prantar Ghosh and Sahil Kuchlous. New Algorithms and Lower Bounds for Streaming Tournaments. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 60:1-60:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ghosh_et_al:LIPIcs.ESA.2024.60,
  author =	{Ghosh, Prantar and Kuchlous, Sahil},
  title =	{{New Algorithms and Lower Bounds for Streaming Tournaments}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{60:1--60:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.60},
  URN =		{urn:nbn:de:0030-drops-211318},
  doi =		{10.4230/LIPIcs.ESA.2024.60},
  annote =	{Keywords: tournaments, streaming algorithms, graph algorithms, communication complexity, strongly connected components, reachability, feedback arc set}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.40
Private Counting of Distinct Elements in the Turnstile Model and Extensions

Authors: Monika Henzinger, A. R. Sricharan, and Teresa Anna Steiner

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
Privately counting distinct elements in a stream is a fundamental data analysis problem with many applications in machine learning. In the turnstile model, Jain et al. [NeurIPS2023] initiated the study of this problem parameterized by the maximum flippancy of any element, i.e., the number of times that the count of an element changes from 0 to above 0 or vice versa. They give an item-level (ε,δ)-differentially private algorithm whose additive error is tight with respect to that parameterization. In this work, we show that a very simple algorithm based on the sparse vector technique achieves a tight additive error for item-level (ε,δ)-differential privacy and item-level ε-differential privacy with regards to a different parameterization, namely the sum of all flippancies. Our second result is a bound which shows that for a large class of algorithms, including all existing differentially private algorithms for this problem, the lower bound from item-level differential privacy extends to event-level differential privacy. This partially answers an open question by Jain et al. [NeurIPS2023].
Cite as

Monika Henzinger, A. R. Sricharan, and Teresa Anna Steiner. Private Counting of Distinct Elements in the Turnstile Model and Extensions. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 40:1-40:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{henzinger_et_al:LIPIcs.APPROX/RANDOM.2024.40,
  author =	{Henzinger, Monika and Sricharan, A. R. and Steiner, Teresa Anna},
  title =	{{Private Counting of Distinct Elements in the Turnstile Model and Extensions}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{40:1--40:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.40},
  URN =		{urn:nbn:de:0030-drops-210335},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.40},
  annote =	{Keywords: differential privacy, turnstile model, counting distinct elements}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.53
When Do Low-Rate Concatenated Codes Approach The Gilbert-Varshamov Bound?

Authors: Dean Doron, Jonathan Mosheiff, and Mary Wootters

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
The Gilbert-Varshamov (GV) bound is a classical existential result in coding theory. It implies that a random linear binary code of rate ε² has relative distance at least 1/2 - O(ε) with high probability. However, it is a major challenge to construct explicit codes with similar parameters. One hope to derandomize the Gilbert-Varshamov construction is with code concatenation: We begin with a (hopefully explicit) outer code 𝒞_out over a large alphabet, and concatenate that with a small binary random linear code 𝒞_in. It is known that when we use independent small codes for each coordinate, then the result lies on the GV bound with high probability, but this still uses a lot of randomness. In this paper, we consider the question of whether code concatenation with a single random linear inner code 𝒞_in can lie on the GV bound; and if so what conditions on 𝒞_out are sufficient for this. We show that first, there do exist linear outer codes 𝒞_out that are "good" for concatenation in this sense (in fact, most linear codes codes are good). We also provide two sufficient conditions for 𝒞_out, so that if 𝒞_out satisfies these, 𝒞_out∘𝒞_in will likely lie on the GV bound. We hope that these conditions may inspire future work towards constructing explicit codes 𝒞_out.
Cite as

Dean Doron, Jonathan Mosheiff, and Mary Wootters. When Do Low-Rate Concatenated Codes Approach The Gilbert-Varshamov Bound?. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 53:1-53:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{doron_et_al:LIPIcs.APPROX/RANDOM.2024.53,
  author =	{Doron, Dean and Mosheiff, Jonathan and Wootters, Mary},
  title =	{{When Do Low-Rate Concatenated Codes Approach The Gilbert-Varshamov Bound?}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{53:1--53:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.53},
  URN =		{urn:nbn:de:0030-drops-210467},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.53},
  annote =	{Keywords: Error-correcting codes, Concatenated codes, Derandomization, Gilbert-Varshamov bound}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.73
Additive Noise Mechanisms for Making Randomized Approximation Algorithms Differentially Private

Authors: Jakub Tětek

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
The exponential increase in the amount of available data makes taking advantage of them without violating users' privacy one of the fundamental problems of computer science. This question has been investigated thoroughly under the framework of differential privacy. However, most of the literature has not focused on settings where the amount of data is so large that we are not even able to compute the exact answer in the non-private setting (such as in the streaming setting, sublinear-time setting, etc.). This can often make the use of differential privacy unfeasible in practice. In this paper, we show a general approach for making Monte-Carlo randomized approximation algorithms differentially private. We only need to assume the error R of the approximation algorithm is sufficiently concentrated around 0 (e.g. 𝔼[|R|] is bounded) and that the function being approximated has a small global sensitivity Δ. Specifically, if we have a randomized approximation algorithm with sufficiently concentrated error which has time/space/query complexity T(n,ρ) with ρ being an accuracy parameter, we can generally speaking get an algorithm with the same accuracy and complexity T(n,Θ(ε ρ)) that is ε-differentially private. Our technical results are as follows. First, we show that if the error is subexponential, then the Laplace mechanism with error magnitude proportional to the sum of the global sensitivity Δ and the subexponential diameter of the error of the algorithm makes the algorithm differentially private. This is true even if the worst-case global sensitivity of the algorithm is large or infinite. We then introduce a new additive noise mechanism, which we call the zero-symmetric Pareto mechanism. We show that using this mechanism, we can make an algorithm differentially private even if we only assume a bound on the first absolute moment of the error 𝔼[|R|]. Finally, we use our results to give either the first known or improved sublinear-complexity differentially private algorithms for various problems. This includes results for frequency moments, estimating the average degree of a graph in subliinear time, rank queries, or estimating the size of the maximum matching. Our results raise many new questions and we state multiple open problems.
Cite as

Jakub Tětek. Additive Noise Mechanisms for Making Randomized Approximation Algorithms Differentially Private. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 73:1-73:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{tetek:LIPIcs.APPROX/RANDOM.2024.73,
  author =	{T\v{e}tek, Jakub},
  title =	{{Additive Noise Mechanisms for Making Randomized Approximation Algorithms Differentially Private}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{73:1--73:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.73},
  URN =		{urn:nbn:de:0030-drops-210660},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.73},
  annote =	{Keywords: Differential privacy, Randomized approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.SAT.2024.13
Entailing Generalization Boosts Enumeration

Authors: Dror Fried, Alexander Nadel, Roberto Sebastiani, and Yogev Shalmon

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract
Given a combinational circuit Γ with a single output o, AllSAT-CT is the problem of enumerating all solutions of Γ. Recently, we introduced several state-of-the-art AllSAT-CT algorithms based on satisfying generalization, which generalizes a given total Boolean solution to a smaller ternary solution that still satisfies the circuit. We implemented them in our open-source tool HALL. In this work we draw upon recent theoretical works suggesting that utilizing generalization algorithms, which can produce solutions that entail the circuit without satisfying it, may enhance enumeration. After considering the theory and adapting it to our needs, we enrich HALL’s AllSAT-CT algorithms by incorporating several newly implemented generalization schemes and additional SAT solvers. By conducting extensive experiments we show that entailing generalization substantially boosts HALL’s performance and quality (where quality corresponds to the number of reported generalized solutions per instance), with the best results achieved by combining satisfying and entailing generalization.
Cite as

Dror Fried, Alexander Nadel, Roberto Sebastiani, and Yogev Shalmon. Entailing Generalization Boosts Enumeration. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fried_et_al:LIPIcs.SAT.2024.13,
  author =	{Fried, Dror and Nadel, Alexander and Sebastiani, Roberto and Shalmon, Yogev},
  title =	{{Entailing Generalization Boosts Enumeration}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{13:1--13:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.13},
  URN =		{urn:nbn:de:0030-drops-205351},
  doi =		{10.4230/LIPIcs.SAT.2024.13},
  annote =	{Keywords: Generalization, Minimization, Prime Implicant, AllSAT, SAT, Circuits}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2024.12
A Linear Type System for L^p-Metric Sensitivity Analysis

Authors: Victor Sannier and Patrick Baillot

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
When working in optimisation or privacy protection, one may need to estimate the sensitivity of computer programs, i.e., the maximum multiplicative increase in the distance between two inputs and the corresponding two outputs. In particular, differential privacy is a rigorous and widely used notion of privacy that is closely related to sensitivity. Several type systems for sensitivity and differential privacy based on linear logic have been proposed in the literature, starting with the functional language Fuzz. However, they are either limited to certain metrics (L¹ and L^∞), and thus to the associated privacy mechanisms, or they rely on a complex notion of type contexts that does not interact well with operational semantics. We therefore propose a graded linear type system - inspired by Bunched Fuzz [{w}under et al., 2023] - called Plurimetric Fuzz that handles L^p vector metrics (for 1 ≤ p ≤ +∞), uses standard type contexts, gives reasonable bounds on sensitivity, and has good metatheoretical properties. We also provide a denotational semantics in terms of metric complete partial orders, and translation mappings from and to Fuzz.
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Victor Sannier and Patrick Baillot. A Linear Type System for L^p-Metric Sensitivity Analysis. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{sannier_et_al:LIPIcs.FSCD.2024.12,
  author =	{Sannier, Victor and Baillot, Patrick},
  title =	{{A Linear Type System for L^p-Metric Sensitivity Analysis}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{12:1--12:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.12},
  URN =		{urn:nbn:de:0030-drops-203412},
  doi =		{10.4230/LIPIcs.FSCD.2024.12},
  annote =	{Keywords: type system, linear logic, sensitivity, vector metrics, differential privacy, lambda-calculus, functional programming, denotational semantics}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.27
The Discrepancy of Shortest Paths

Authors: Greg Bodwin, Chengyuan Deng, Jie Gao, Gary Hoppenworth, Jalaj Upadhyay, and Chen Wang

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
The hereditary discrepancy of a set system is a quantitative measure of the pseudorandom properties of the system. Roughly speaking, hereditary discrepancy measures how well one can 2-color the elements of the system so that each set contains approximately the same number of elements of each color. Hereditary discrepancy has numerous applications in computational geometry, communication complexity and derandomization. More recently, the hereditary discrepancy of the set system of shortest paths has found applications in differential privacy [Chen et al. SODA 23]. The contribution of this paper is to improve the upper and lower bounds on the hereditary discrepancy of set systems of unique shortest paths in graphs. In particular, we show that any system of unique shortest paths in an undirected weighted graph has hereditary discrepancy O(n^{1/4}), and we construct lower bound examples demonstrating that this bound is tight up to polylog n factors. Our lower bounds hold even for planar graphs and bipartite graphs, and improve a previous lower bound of Ω(n^{1/6}) obtained by applying the trace bound of Chazelle and Lvov [SoCG'00] to a classical point-line system of Erdős. As applications, we improve the lower bound on the additive error for differentially-private all pairs shortest distances from Ω(n^{1/6}) [Chen et al. SODA 23] to Ω̃(n^{1/4}), and we improve the lower bound on additive error for the differentially-private all sets range queries problem to Ω̃(n^{1/4}), which is tight up to polylog n factors [Deng et al. WADS 23].
Cite as

Greg Bodwin, Chengyuan Deng, Jie Gao, Gary Hoppenworth, Jalaj Upadhyay, and Chen Wang. The Discrepancy of Shortest Paths. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 27:1-27:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bodwin_et_al:LIPIcs.ICALP.2024.27,
  author =	{Bodwin, Greg and Deng, Chengyuan and Gao, Jie and Hoppenworth, Gary and Upadhyay, Jalaj and Wang, Chen},
  title =	{{The Discrepancy of Shortest Paths}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{27:1--27:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.27},
  URN =		{urn:nbn:de:0030-drops-201705},
  doi =		{10.4230/LIPIcs.ICALP.2024.27},
  annote =	{Keywords: Discrepancy, hereditary discrepancy, shortest paths, differential privacy}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.97
Cut Sparsification and Succinct Representation of Submodular Hypergraphs

Authors: Yotam Kenneth and Robert Krauthgamer

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
In cut sparsification, all cuts of a hypergraph H = (V,E,w) are approximated within 1±ε factor by a small hypergraph H'. This widely applied method was generalized recently to a setting where the cost of cutting each hyperedge e is provided by a splitting function g_e: 2^e → ℝ_+. This generalization is called a submodular hypergraph when the functions {g_e}_{e ∈ E} are submodular, and it arises in machine learning, combinatorial optimization, and algorithmic game theory. Previous work studied the setting where H' is a reweighted sub-hypergraph of H, and measured the size of H' by the number of hyperedges in it. In this setting, we present two results: (i) all submodular hypergraphs admit sparsifiers of size polynomial in n = |V| and ε^{-1}; (ii) we propose a new parameter, called spread, and use it to obtain smaller sparsifiers in some cases. We also show that for a natural family of splitting functions, relaxing the requirement that H' be a reweighted sub-hypergraph of H yields a substantially smaller encoding of the cuts of H (almost a factor n in the number of bits). This is in contrast to graphs, where the most succinct representation is attained by reweighted subgraphs. A new tool in our construction of succinct representation is the notion of deformation, where a splitting function g_e is decomposed into a sum of functions of small description, and we provide upper and lower bounds for deformation of common splitting functions.
Cite as

Yotam Kenneth and Robert Krauthgamer. Cut Sparsification and Succinct Representation of Submodular Hypergraphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 97:1-97:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kenneth_et_al:LIPIcs.ICALP.2024.97,
  author =	{Kenneth, Yotam and Krauthgamer, Robert},
  title =	{{Cut Sparsification and Succinct Representation of Submodular Hypergraphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{97:1--97:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.97},
  URN =		{urn:nbn:de:0030-drops-202406},
  doi =		{10.4230/LIPIcs.ICALP.2024.97},
  annote =	{Keywords: Cut Sparsification, Submodular Hypergraphs, Succinct Representation}
}
Document
DOI: 10.4230/LIPIcs.FORC.2024.4
Balanced Filtering via Disclosure-Controlled Proxies

Authors: Siqi Deng, Emily Diana, Michael Kearns, and Aaron Roth

Published in: LIPIcs, Volume 295, 5th Symposium on Foundations of Responsible Computing (FORC 2024)

Abstract
We study the problem of collecting a cohort or set that is balanced with respect to sensitive groups when group membership is unavailable or prohibited from use at deployment time. Specifically, our deployment-time collection mechanism does not reveal significantly more about the group membership of any individual sample than can be ascertained from base rates alone. To do this, we study a learner that can use a small set of labeled data to train a proxy function that can later be used for this filtering or selection task. We then associate the range of the proxy function with sampling probabilities; given a new example, we classify it using our proxy function and then select it with probability corresponding to its proxy classification. Importantly, we require that the proxy classification does not reveal significantly more information about the sensitive group membership of any individual example compared to population base rates alone (i.e., the level of disclosure should be controlled) and show that we can find such a proxy in a sample- and oracle-efficient manner. Finally, we experimentally evaluate our algorithm and analyze its generalization properties.
Cite as

Siqi Deng, Emily Diana, Michael Kearns, and Aaron Roth. Balanced Filtering via Disclosure-Controlled Proxies. In 5th Symposium on Foundations of Responsible Computing (FORC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 295, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{deng_et_al:LIPIcs.FORC.2024.4,
  author =	{Deng, Siqi and Diana, Emily and Kearns, Michael and Roth, Aaron},
  title =	{{Balanced Filtering via Disclosure-Controlled Proxies}},
  booktitle =	{5th Symposium on Foundations of Responsible Computing (FORC 2024)},
  pages =	{4:1--4:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-319-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{295},
  editor =	{Rothblum, Guy N.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2024.4},
  URN =		{urn:nbn:de:0030-drops-200872},
  doi =		{10.4230/LIPIcs.FORC.2024.4},
  annote =	{Keywords: Algorithms, Sampling, Ethical/Societal Implications}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.41
HappyMap : A Generalized Multicalibration Method

Authors: Zhun Deng, Cynthia Dwork, and Linjun Zhang

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

Abstract
Multicalibration is a powerful and evolving concept originating in the field of algorithmic fairness. For a predictor f that estimates the outcome y given covariates x, and for a function class C, multi-calibration requires that the predictor f(x) and outcome y are indistinguishable under the class of auditors in C. Fairness is captured by incorporating demographic subgroups into the class of functions C. Recent work has shown that, by enriching the class C to incorporate appropriate propensity re-weighting functions, multi-calibration also yields target-independent learning, wherein a model trained on a source domain performs well on unseen, future, target domains {(approximately) captured by the re-weightings.} Formally, multicalibration with respect to C bounds |𝔼_{(x,y)∼D}[c(f(x),x)⋅(f(x)-y)]| for all c ∈ C. In this work, we view the term (f(x)-y) as just one specific mapping, and explore the power of an enriched class of mappings. We propose s-Happy Multicalibration, a generalization of multi-calibration, which yields a wide range of new applications, including a new fairness notion for uncertainty quantification, a novel technique for conformal prediction under covariate shift, and a different approach to analyzing missing data, while also yielding a unified understanding of several existing seemingly disparate algorithmic fairness notions and target-independent learning approaches. We give a single HappyMap meta-algorithm that captures all these results, together with a sufficiency condition for its success.
Cite as

Zhun Deng, Cynthia Dwork, and Linjun Zhang. HappyMap : A Generalized Multicalibration Method. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 41:1-41:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{deng_et_al:LIPIcs.ITCS.2023.41,
  author =	{Deng, Zhun and Dwork, Cynthia and Zhang, Linjun},
  title =	{{HappyMap : A Generalized Multicalibration Method}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{41:1--41:23},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.41},
  URN =		{urn:nbn:de:0030-drops-175449},
  doi =		{10.4230/LIPIcs.ITCS.2023.41},
  annote =	{Keywords: algorithmic fairness, target-independent learning, transfer learning}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.82
Online Multivalid Learning: Means, Moments, and Prediction Intervals

Authors: Varun Gupta, Christopher Jung, Georgy Noarov, Mallesh M. Pai, and Aaron Roth

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
We present a general, efficient technique for providing contextual predictions that are "multivalid" in various senses, against an online sequence of adversarially chosen examples (x,y). This means that the resulting estimates correctly predict various statistics of the labels y not just marginally - as averaged over the sequence of examples - but also conditionally on x ∈ G for any G belonging to an arbitrary intersecting collection of groups 𝒢. We provide three instantiations of this framework. The first is mean prediction, which corresponds to an online algorithm satisfying the notion of multicalibration from [Hébert-Johnson et al., 2018]. The second is variance and higher moment prediction, which corresponds to an online algorithm satisfying the notion of mean-conditioned moment multicalibration from [Jung et al., 2021]. Finally, we define a new notion of prediction interval multivalidity, and give an algorithm for finding prediction intervals which satisfy it. Because our algorithms handle adversarially chosen examples, they can equally well be used to predict statistics of the residuals of arbitrary point prediction methods, giving rise to very general techniques for quantifying the uncertainty of predictions of black box algorithms, even in an online adversarial setting. When instantiated for prediction intervals, this solves a similar problem as conformal prediction, but in an adversarial environment and with multivalidity guarantees stronger than simple marginal coverage guarantees.
Cite as

Varun Gupta, Christopher Jung, Georgy Noarov, Mallesh M. Pai, and Aaron Roth. Online Multivalid Learning: Means, Moments, and Prediction Intervals. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 82:1-82:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gupta_et_al:LIPIcs.ITCS.2022.82,
  author =	{Gupta, Varun and Jung, Christopher and Noarov, Georgy and Pai, Mallesh M. and Roth, Aaron},
  title =	{{Online Multivalid Learning: Means, Moments, and Prediction Intervals}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{82:1--82:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.82},
  URN =		{urn:nbn:de:0030-drops-156785},
  doi =		{10.4230/LIPIcs.ITCS.2022.82},
  annote =	{Keywords: Uncertainty Estimation, Calibration, Online Learning}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ESA.2021.2
A User Friendly Power Tool for Deriving Online Learning Algorithms (Invited Talk)

Authors: Aaron Roth

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
In this talk, we overview a simple and user friendly framework developed in [Noarov et al., 2021] that can be used to derive online learning algorithms in a number of settings. In the core framework, at every round, an adaptive adversary introduces a new game, consisting of an action space for the learner, an action space for the adversary, and a vector valued objective function that is concave-convex in every coordinate. The learner and the adversary then play in this game. The learner’s goal is to play so as to minimize the maximum coordinate of the cumulative vector-valued loss. The resulting one-shot game is not concave-convex, and so the minimax theorem does not apply. Nevertheless we give a simple algorithm that can compete with the setting in which the adversary must announce their action first, with optimally diminishing regret. We demonstrate the power of our simple framework by using it to derive optimal bounds and algorithms across a variety of domains. This includes no regret learning: we can recover optimal algorithms and bounds for minimizing exernal regret, internal regret, adaptive regret, multigroup regret, subsequence regret, and permutation regret in the sleeping experts setting. It also includes (multi)calibration [Hébert-Johnson et al., 2018] and related notions: we are able to recover recently derived algorithms and bounds for online adversarial multicalibration [Gupta et al., 2021], mean conditioned moment multicalibration [Jung et al., 2021], and prediction interval multivalidity [Gupta et al., 2021]. Finally we use it to derive a new variant of Blackwell’s Approachability Theorem, which we term "Fast Polytope Approachability".
Cite as

Aaron Roth. A User Friendly Power Tool for Deriving Online Learning Algorithms (Invited Talk). In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{roth:LIPIcs.ESA.2021.2,
  author =	{Roth, Aaron},
  title =	{{A User Friendly Power Tool for Deriving Online Learning Algorithms}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.2},
  URN =		{urn:nbn:de:0030-drops-145835},
  doi =		{10.4230/LIPIcs.ESA.2021.2},
  annote =	{Keywords: Online Learning, Multicalibration, Multivalidity, Blackwell Approachability}
}
Document
DOI: 10.4230/LIPIcs.FORC.2021.2
An Algorithmic Framework for Fairness Elicitation

Authors: Christopher Jung, Michael Kearns, Seth Neel, Aaron Roth, Logan Stapleton, and Zhiwei Steven Wu

Published in: LIPIcs, Volume 192, 2nd Symposium on Foundations of Responsible Computing (FORC 2021)

Abstract
We consider settings in which the right notion of fairness is not captured by simple mathematical definitions (such as equality of error rates across groups), but might be more complex and nuanced and thus require elicitation from individual or collective stakeholders. We introduce a framework in which pairs of individuals can be identified as requiring (approximately) equal treatment under a learned model, or requiring ordered treatment such as "applicant Alice should be at least as likely to receive a loan as applicant Bob". We provide a provably convergent and oracle efficient algorithm for learning the most accurate model subject to the elicited fairness constraints, and prove generalization bounds for both accuracy and fairness. This algorithm can also combine the elicited constraints with traditional statistical fairness notions, thus "correcting" or modifying the latter by the former. We report preliminary findings of a behavioral study of our framework using human-subject fairness constraints elicited on the COMPAS criminal recidivism dataset.
Cite as

Christopher Jung, Michael Kearns, Seth Neel, Aaron Roth, Logan Stapleton, and Zhiwei Steven Wu. An Algorithmic Framework for Fairness Elicitation. In 2nd Symposium on Foundations of Responsible Computing (FORC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 192, pp. 2:1-2:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{jung_et_al:LIPIcs.FORC.2021.2,
  author =	{Jung, Christopher and Kearns, Michael and Neel, Seth and Roth, Aaron and Stapleton, Logan and Wu, Zhiwei Steven},
  title =	{{An Algorithmic Framework for Fairness Elicitation}},
  booktitle =	{2nd Symposium on Foundations of Responsible Computing (FORC 2021)},
  pages =	{2:1--2:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-187-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{192},
  editor =	{Ligett, Katrina and Gupta, Swati},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2021.2},
  URN =		{urn:nbn:de:0030-drops-138701},
  doi =		{10.4230/LIPIcs.FORC.2021.2},
  annote =	{Keywords: Fairness, Fairness Elicitation}
}
Document
DOI: 10.4230/LIPIcs.FORC.2021.6
Lexicographically Fair Learning: Algorithms and Generalization

Authors: Emily Diana, Wesley Gill, Ira Globus-Harris, Michael Kearns, Aaron Roth, and Saeed Sharifi-Malvajerdi

Published in: LIPIcs, Volume 192, 2nd Symposium on Foundations of Responsible Computing (FORC 2021)

Abstract
We extend the notion of minimax fairness in supervised learning problems to its natural conclusion: lexicographic minimax fairness (or lexifairness for short). Informally, given a collection of demographic groups of interest, minimax fairness asks that the error of the group with the highest error be minimized. Lexifairness goes further and asks that amongst all minimax fair solutions, the error of the group with the second highest error should be minimized, and amongst all of those solutions, the error of the group with the third highest error should be minimized, and so on. Despite its naturalness, correctly defining lexifairness is considerably more subtle than minimax fairness, because of inherent sensitivity to approximation error. We give a notion of approximate lexifairness that avoids this issue, and then derive oracle-efficient algorithms for finding approximately lexifair solutions in a very general setting. When the underlying empirical risk minimization problem absent fairness constraints is convex (as it is, for example, with linear and logistic regression), our algorithms are provably efficient even in the worst case. Finally, we show generalization bounds - approximate lexifairness on the training sample implies approximate lexifairness on the true distribution with high probability. Our ability to prove generalization bounds depends on our choosing definitions that avoid the instability of naive definitions.
Cite as

Emily Diana, Wesley Gill, Ira Globus-Harris, Michael Kearns, Aaron Roth, and Saeed Sharifi-Malvajerdi. Lexicographically Fair Learning: Algorithms and Generalization. In 2nd Symposium on Foundations of Responsible Computing (FORC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 192, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{diana_et_al:LIPIcs.FORC.2021.6,
  author =	{Diana, Emily and Gill, Wesley and Globus-Harris, Ira and Kearns, Michael and Roth, Aaron and Sharifi-Malvajerdi, Saeed},
  title =	{{Lexicographically Fair Learning: Algorithms and Generalization}},
  booktitle =	{2nd Symposium on Foundations of Responsible Computing (FORC 2021)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-187-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{192},
  editor =	{Ligett, Katrina and Gupta, Swati},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2021.6},
  URN =		{urn:nbn:de:0030-drops-138748},
  doi =		{10.4230/LIPIcs.FORC.2021.6},
  annote =	{Keywords: Fair Learning, Lexicographic Fairness, Online Learning, Game Theory}
}
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