3 Search Results for "Sur, Pragya"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.102
Fourier Analysis of Iterative Algorithms

Authors: Chris Jones and Lucas Pesenti

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We study a general class of nonlinear iterative algorithms which includes power iteration, belief propagation and approximate message passing, and many forms of gradient descent. When the input is a random matrix with i.i.d. entries, we use Boolean Fourier analysis to analyze these algorithms as low-degree polynomials in the entries of the input matrix. Each symmetrized Fourier character represents all monomials with a certain shape as specified by a small graph, which we call a Fourier diagram. We prove fundamental asymptotic properties of the Fourier diagrams: over the randomness of the input, all diagrams with cycles are negligible; the tree-shaped diagrams form a basis of asymptotically independent Gaussian vectors; and, when restricted to the trees, iterative algorithms exactly follow an idealized Gaussian dynamic. We use this to prove a state evolution formula, giving a "complete" asymptotic description of the algorithm’s trajectory. The restriction to tree-shaped monomials mirrors the assumption of the cavity method, a 40-year-old non-rigorous technique in statistical physics which has served as one of the most important techniques in the field. We demonstrate how to implement cavity method derivations by 1) restricting the iteration to its tree approximation, and 2) observing that heuristic cavity method-type arguments hold rigorously on the simplified iteration. Our proofs use combinatorial arguments similar to the trace method from random matrix theory. Finally, we push the diagram analysis to a number of iterations that scales with the dimension n of the input matrix, proving that the tree approximation still holds for a simple variant of power iteration all the way up to n^{Ω(1)} iterations.
Cite as

Chris Jones and Lucas Pesenti. Fourier Analysis of Iterative Algorithms. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 102:1-102:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jones_et_al:LIPIcs.ICALP.2025.102,
  author =	{Jones, Chris and Pesenti, Lucas},
  title =	{{Fourier Analysis of Iterative Algorithms}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{102:1--102:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.102},
  URN =		{urn:nbn:de:0030-drops-234791},
  doi =		{10.4230/LIPIcs.ICALP.2025.102},
  annote =	{Keywords: Iterative Algorithms, Message-passing Algorithms, Random Matrix Theory}
}
Document
DOI: 10.4230/LIPIcs.FORC.2022.6
Improved Generalization Guarantees in Restricted Data Models

Authors: Elbert Du and Cynthia Dwork

Published in: LIPIcs, Volume 218, 3rd Symposium on Foundations of Responsible Computing (FORC 2022)

Abstract
Differential privacy is known to protect against threats to validity incurred due to adaptive, or exploratory, data analysis - even when the analyst adversarially searches for a statistical estimate that diverges from the true value of the quantity of interest on the underlying population. The cost of this protection is the accuracy loss incurred by differential privacy. In this work, inspired by standard models in the genomics literature, we consider data models in which individuals are represented by a sequence of attributes with the property that where distant attributes are only weakly correlated. We show that, under this assumption, it is possible to "re-use" privacy budget on different portions of the data, significantly improving accuracy without increasing the risk of overfitting.
Cite as

Elbert Du and Cynthia Dwork. Improved Generalization Guarantees in Restricted Data Models. In 3rd Symposium on Foundations of Responsible Computing (FORC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 218, pp. 6:1-6:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{du_et_al:LIPIcs.FORC.2022.6,
  author =	{Du, Elbert and Dwork, Cynthia},
  title =	{{Improved Generalization Guarantees in Restricted Data Models}},
  booktitle =	{3rd Symposium on Foundations of Responsible Computing (FORC 2022)},
  pages =	{6:1--6:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-226-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{218},
  editor =	{Celis, L. Elisa},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2022.6},
  URN =		{urn:nbn:de:0030-drops-165299},
  doi =		{10.4230/LIPIcs.FORC.2022.6},
  annote =	{Keywords: Differential Privacy, Adaptive Data Analysis, Transfer Theorem}
}
Document
DOI: 10.4230/LIPIcs.FORC.2020.8
Abstracting Fairness: Oracles, Metrics, and Interpretability

Authors: Cynthia Dwork, Christina Ilvento, Guy N. Rothblum, and Pragya Sur

Published in: LIPIcs, Volume 156, 1st Symposium on Foundations of Responsible Computing (FORC 2020)

Abstract
It is well understood that classification algorithms, for example, for deciding on loan applications, cannot be evaluated for fairness without taking context into account. We examine what can be learned from a fairness oracle equipped with an underlying understanding of "true" fairness. The oracle takes as input a (context, classifier) pair satisfying an arbitrary fairness definition, and accepts or rejects the pair according to whether the classifier satisfies the underlying fairness truth. Our principal conceptual result is an extraction procedure that learns the underlying truth; moreover, the procedure can learn an approximation to this truth given access to a weak form of the oracle. Since every "truly fair" classifier induces a coarse metric, in which those receiving the same decision are at distance zero from one another and those receiving different decisions are at distance one, this extraction process provides the basis for ensuring a rough form of metric fairness, also known as individual fairness. Our principal technical result is a higher fidelity extractor under a mild technical constraint on the weak oracle’s conception of fairness. Our framework permits the scenario in which many classifiers, with differing outcomes, may all be considered fair. Our results have implications for interpretablity - a highly desired but poorly defined property of classification systems that endeavors to permit a human arbiter to reject classifiers deemed to be "unfair" or illegitimately derived.
Cite as

Cynthia Dwork, Christina Ilvento, Guy N. Rothblum, and Pragya Sur. Abstracting Fairness: Oracles, Metrics, and Interpretability. In 1st Symposium on Foundations of Responsible Computing (FORC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 156, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{dwork_et_al:LIPIcs.FORC.2020.8,
  author =	{Dwork, Cynthia and Ilvento, Christina and Rothblum, Guy N. and Sur, Pragya},
  title =	{{Abstracting Fairness: Oracles, Metrics, and Interpretability}},
  booktitle =	{1st Symposium on Foundations of Responsible Computing (FORC 2020)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-142-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{156},
  editor =	{Roth, Aaron},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2020.8},
  URN =		{urn:nbn:de:0030-drops-120247},
  doi =		{10.4230/LIPIcs.FORC.2020.8},
  annote =	{Keywords: Algorithmic fairness, fairness definitions, causality-based fairness, interpretability, individual fairness, metric fairness}
}
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