6 Search Results for "Juba, Brendan"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.112
Lower Bounds Beyond DNF of Parities

Authors: Artur Riazanov, Anastasia Sofronova, and Dmitry Sokolov

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We consider a subclass of AC⁰[2] circuits that simultaneously captures DNF∘Xor and depth-3 AC⁰ circuits. For this class we show a technique for proving lower bounds inspired by the top-down approach. We give lower bounds for the middle slice function, inner product function, and affine dispersers.
Cite as

Artur Riazanov, Anastasia Sofronova, and Dmitry Sokolov. Lower Bounds Beyond DNF of Parities. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 112:1-112:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{riazanov_et_al:LIPIcs.ITCS.2026.112,
  author =	{Riazanov, Artur and Sofronova, Anastasia and Sokolov, Dmitry},
  title =	{{Lower Bounds Beyond DNF of Parities}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{112:1--112:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.112},
  URN =		{urn:nbn:de:0030-drops-253996},
  doi =		{10.4230/LIPIcs.ITCS.2026.112},
  annote =	{Keywords: boolean circuits, top-down, unpredictability}
}
Document
DOI: 10.4230/LIPIcs.SAT.2025.20
Scalable Precise Computation of Shannon Entropy

Authors: Yong Lai, Haolong Tong, Zhenghang Xu, and Minghao Yin

Published in: LIPIcs, Volume 341, 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)

Abstract
Quantitative information flow analyses (QIF) are a class of techniques for measuring the amount of confidential information leaked by a program to its public outputs. Shannon entropy is an important method to quantify the amount of leakage in QIF. This paper focuses on the programs modeled in Boolean constraints and optimizes the two stages of the Shannon entropy computation to implement a scalable precise tool PSE. In the first stage, we design a knowledge compilation language called ADD[∧] that combines Algebraic Decision Diagrams and conjunctive decomposition. ADD[∧] avoids enumerating possible outputs of a program and supports tractable entropy computation. In the second stage, we optimize the model counting queries that are used to compute the probabilities of outputs. We compare PSE with the state-of-the-art probabilistic approximately correct tool EntropyEstimation, which was shown to significantly outperform the previous precise tools. The experimental results demonstrate that PSE solved 56 more benchmarks compared to EntropyEstimation in a total of 459. For 98% of the benchmarks that both PSE and EntropyEstimation solved, PSE is at least 10× as efficient as EntropyEstimation.
Cite as

Yong Lai, Haolong Tong, Zhenghang Xu, and Minghao Yin. Scalable Precise Computation of Shannon Entropy. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lai_et_al:LIPIcs.SAT.2025.20,
  author =	{Lai, Yong and Tong, Haolong and Xu, Zhenghang and Yin, Minghao},
  title =	{{Scalable Precise Computation of Shannon Entropy}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{20:1--20:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-381-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{341},
  editor =	{Berg, Jeremias and Nordstr\"{o}m, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.20},
  URN =		{urn:nbn:de:0030-drops-237540},
  doi =		{10.4230/LIPIcs.SAT.2025.20},
  annote =	{Keywords: Knowledge Compilation, Algebraic Decision Diagrams, Quantitative Information Flow, Shannon Entropy}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.3
Private Estimation When Data and Privacy Demands Are Correlated

Authors: Syomantak Chaudhuri and Thomas A. Courtade

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
Differential Privacy (DP) is the current gold-standard for ensuring privacy for statistical queries. Estimation problems under DP constraints appearing in the literature have largely focused on providing equal privacy to all users. We consider the problems of empirical mean estimation for univariate data and frequency estimation for categorical data, both subject to heterogeneous privacy constraints. Each user, contributing a sample to the dataset, is allowed to have a different privacy demand. The dataset itself is assumed to be worst-case and we study both problems under two different formulations - first, where privacy demands and data may be correlated, and second, where correlations are weakened by random permutation of the dataset. We establish theoretical performance guarantees for our proposed algorithms, under both PAC error and mean-squared error. These performance guarantees translate to minimax optimality in several instances, and experiments confirm superior performance of our algorithms over other baseline techniques.
Cite as

Syomantak Chaudhuri and Thomas A. Courtade. Private Estimation When Data and Privacy Demands Are Correlated. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chaudhuri_et_al:LIPIcs.FORC.2025.3,
  author =	{Chaudhuri, Syomantak and Courtade, Thomas A.},
  title =	{{Private Estimation When Data and Privacy Demands Are Correlated}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{3:1--3:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.3},
  URN =		{urn:nbn:de:0030-drops-231305},
  doi =		{10.4230/LIPIcs.FORC.2025.3},
  annote =	{Keywords: Differential Privacy, Personalized Privacy, Heterogeneous Privacy, Correlations in Privacy}
}
Document
DOI: 10.4230/LIPIcs.FORC.2024.5
Distribution-Specific Auditing for Subgroup Fairness

Authors: Daniel Hsu, Jizhou Huang, and Brendan Juba

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

Abstract
We study the problem of auditing classifiers for statistical subgroup fairness. Kearns et al. [Kearns et al., 2018] showed that the problem of auditing combinatorial subgroups fairness is as hard as agnostic learning. Essentially all work on remedying statistical measures of discrimination against subgroups assumes access to an oracle for this problem, despite the fact that no efficient algorithms are known for it. If we assume the data distribution is Gaussian, or even merely log-concave, then a recent line of work has discovered efficient agnostic learning algorithms for halfspaces. Unfortunately, the reduction of Kearns et al. was formulated in terms of weak, "distribution-free" learning, and thus did not establish a connection for families such as log-concave distributions. In this work, we give positive and negative results on auditing for Gaussian distributions: On the positive side, we present an alternative approach to leverage these advances in agnostic learning and thereby obtain the first polynomial-time approximation scheme (PTAS) for auditing nontrivial combinatorial subgroup fairness: we show how to audit statistical notions of fairness over homogeneous halfspace subgroups when the features are Gaussian. On the negative side, we find that under cryptographic assumptions, no polynomial-time algorithm can guarantee any nontrivial auditing, even under Gaussian feature distributions, for general halfspace subgroups.
Cite as

Daniel Hsu, Jizhou Huang, and Brendan Juba. Distribution-Specific Auditing for Subgroup Fairness. In 5th Symposium on Foundations of Responsible Computing (FORC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 295, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hsu_et_al:LIPIcs.FORC.2024.5,
  author =	{Hsu, Daniel and Huang, Jizhou and Juba, Brendan},
  title =	{{Distribution-Specific Auditing for Subgroup Fairness}},
  booktitle =	{5th Symposium on Foundations of Responsible Computing (FORC 2024)},
  pages =	{5:1--5:20},
  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.2024.5},
  URN =		{urn:nbn:de:0030-drops-200882},
  doi =		{10.4230/LIPIcs.FORC.2024.5},
  annote =	{Keywords: Fairness auditing, agnostic learning, intractability}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2017.45
Conditional Sparse Linear Regression

Authors: Brendan Juba

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract
Machine learning and statistics typically focus on building models that capture the vast majority of the data, possibly ignoring a small subset of data as "noise" or "outliers." By contrast, here we consider the problem of jointly identifying a significant (but perhaps small) segment of a population in which there is a highly sparse linear regression fit, together with the coefficients for the linear fit. We contend that such tasks are of interest both because the models themselves may be able to achieve better predictions in such special cases, but also because they may aid our understanding of the data. We give algorithms for such problems under the sup norm, when this unknown segment of the population is described by a k-DNF condition and the regression fit is s-sparse for constant k and s. For the variants of this problem when the regression fit is not so sparse or using expected error, we also give a preliminary algorithm and highlight the question as a challenge for future work.
Cite as

Brendan Juba. Conditional Sparse Linear Regression. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 45:1-45:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{juba:LIPIcs.ITCS.2017.45,
  author =	{Juba, Brendan},
  title =	{{Conditional Sparse Linear Regression}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{45:1--45:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.45},
  URN =		{urn:nbn:de:0030-drops-81518},
  doi =		{10.4230/LIPIcs.ITCS.2017.45},
  annote =	{Keywords: linear regression, conditional regression, conditional distribution search}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.35
AC^0 o MOD_2 Lower Bounds for the Boolean Inner Product

Authors: Mahdi Cheraghchi, Elena Grigorescu, Brendan Juba, Karl Wimmer, and Ning Xie

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
AC^0 o MOD_2 circuits are AC^0 circuits augmented with a layer of parity gates just above the input layer. We study AC^0 o MOD2 circuit lower bounds for computing the Boolean Inner Product functions. Recent works by Servedio and Viola (ECCC TR12-144) and Akavia et al. (ITCS 2014) have highlighted this problem as a frontier problem in circuit complexity that arose both as a first step towards solving natural special cases of the matrix rigidity problem and as a candidate for constructing pseudorandom generators of minimal complexity. We give the first superlinear lower bound for the Boolean Inner Product function against AC^0 o MOD2 of depth four or greater. Specifically, we prove a superlinear lower bound for circuits of arbitrary constant depth, and an ~Omega(n^2) lower bound for the special case of depth-4 AC^0 o MOD_2. Our proof of the depth-4 lower bound employs a new "moment-matching" inequality for bounded, nonnegative integer-valued random variables that may be of independent interest: we prove an optimal bound on the maximum difference between two discrete distributions’ values at 0, given that their first d moments match.
Cite as

Mahdi Cheraghchi, Elena Grigorescu, Brendan Juba, Karl Wimmer, and Ning Xie. AC^0 o MOD_2 Lower Bounds for the Boolean Inner Product. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 35:1-35:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{cheraghchi_et_al:LIPIcs.ICALP.2016.35,
  author =	{Cheraghchi, Mahdi and Grigorescu, Elena and Juba, Brendan and Wimmer, Karl and Xie, Ning},
  title =	{{AC^0 o MOD\underline2 Lower Bounds for the Boolean Inner Product}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{35:1--35:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.35},
  URN =		{urn:nbn:de:0030-drops-63150},
  doi =		{10.4230/LIPIcs.ICALP.2016.35},
  annote =	{Keywords: Boolean analysis, circuit complexity, lower bounds}
}
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