3 Search Results for "Kearns, Michael"

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.6
Facility Location in the Sublinear Geometric Model

Authors: Morteza Monemizadeh

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
In the sublinear geometric model, we are provided with an oracle access to a point set P of n points in a bounded discrete space [Δ]², where Δ = n^O(1) is a polynomially bounded number in n. That is, we do not have direct access to the points, but we can make certain types of queries and there is an oracle that responds to our queries. The type of queries that we assume we can make in this paper, are range counting queries where ranges are axis-aligned rectangles (that are basic primitives in database [Srikanta Tirthapura and David P. Woodruff, 2012; Bentley, 1975; Mark de Berg et al., 2008], computational geometry [Pankaj K. Agarwal, 2004; Pankaj K. Agarwal et al., 1996; Boris Aronov et al., 2010; Boris Aronov et al., 2009], and machine learning [Menachem Sadigurschi and Uri Stemmer, 2021; Long and Tan, 1998; Michael J. Kearns and Umesh V. Vazirani, 1995; Michael J. Kearns and Umesh V. Vazirani, 1994]). The oracle then answers these queries by returning the number of points that are in queried ranges. Let {Alg} be an algorithm that (exactly or approximately) solves a problem 𝒫 in the sublinear geometric model. The query complexity of Alg is measured in terms of the number of queries that Alg makes to solve 𝒫. In this paper, we study the complexity of the (uniform) Euclidean facility location problem in the sublinear geometric model. We develop a randomized sublinear algorithm that with high probability, (1+ε)-approximates the cost of the Euclidean facility location problem of the point set P in the sublinear geometric model using Õ(√n) range counting queries. We complement this result by showing that approximating the cost of the Euclidean facility location problem within o(log(n))-factor in the sublinear geometric model using the sampling strategy that we propose for our sublinear algorithm needs Ω̃(n^{1/4}) RangeCount queries. We leave it as an open problem whether such a polynomial lower bound on the number of RangeCount queries exists for any randomized sublinear algorithm that approximates the cost of the facility location problem within a constant factor.
Cite as

Morteza Monemizadeh. Facility Location in the Sublinear Geometric Model. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 6:1-6:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{monemizadeh:LIPIcs.APPROX/RANDOM.2023.6,
  author =	{Monemizadeh, Morteza},
  title =	{{Facility Location in the Sublinear Geometric Model}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{6:1--6:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  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.2023.6},
  URN =		{urn:nbn:de:0030-drops-188315},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.6},
  annote =	{Keywords: Facility Location, Sublinear Geometric Model, Range Counting Queries}
}
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-dev.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-dev.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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