4 Search Results for "Lee, Mu-Woong"

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.64
Optimal Convergence Rate of Hamiltonian Monte Carlo for Strongly Logconcave Distributions

Authors: Zongchen Chen and Santosh S. Vempala

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
We study Hamiltonian Monte Carlo (HMC) for sampling from a strongly logconcave density proportional to e^{-f} where f:R^d -> R is mu-strongly convex and L-smooth (the condition number is kappa = L/mu). We show that the relaxation time (inverse of the spectral gap) of ideal HMC is O(kappa), improving on the previous best bound of O(kappa^{1.5}); we complement this with an example where the relaxation time is Omega(kappa). When implemented using a nearly optimal ODE solver, HMC returns an epsilon-approximate point in 2-Wasserstein distance using O~((kappa d)^{0.5} epsilon^{-1}) gradient evaluations per step and O~((kappa d)^{1.5}epsilon^{-1}) total time.
Cite as

Zongchen Chen and Santosh S. Vempala. Optimal Convergence Rate of Hamiltonian Monte Carlo for Strongly Logconcave Distributions. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 64:1-64:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chen_et_al:LIPIcs.APPROX-RANDOM.2019.64,
  author =	{Chen, Zongchen and Vempala, Santosh S.},
  title =	{{Optimal Convergence Rate of Hamiltonian Monte Carlo for Strongly Logconcave Distributions}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{64:1--64:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  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.2019.64},
  URN =		{urn:nbn:de:0030-drops-112790},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.64},
  annote =	{Keywords: logconcave distribution, sampling, Hamiltonian Monte Carlo, spectral gap, strong convexity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.26
Approximate Minimum-Weight Matching with Outliers Under Translation

Authors: Pankaj K. Agarwal, Haim Kaplan, Geva Kipper, Wolfgang Mulzer, Günter Rote, Micha Sharir, and Allen Xiao

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Our goal is to compare two planar point sets by finding subsets of a given size such that a minimum-weight matching between them has the smallest weight. This can be done by a translation of one set that minimizes the weight of the matching. We give efficient algorithms (a) for finding approximately optimal matchings, when the cost of a matching is the L_p-norm of the tuple of the Euclidean distances between the pairs of matched points, for any p in [1,infty], and (b) for constructing small-size approximate minimization (or matching) diagrams: partitions of the translation space into regions, together with an approximate optimal matching for each region.
Cite as

Pankaj K. Agarwal, Haim Kaplan, Geva Kipper, Wolfgang Mulzer, Günter Rote, Micha Sharir, and Allen Xiao. Approximate Minimum-Weight Matching with Outliers Under Translation. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 26:1-26:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{agarwal_et_al:LIPIcs.ISAAC.2018.26,
  author =	{Agarwal, Pankaj K. and Kaplan, Haim and Kipper, Geva and Mulzer, Wolfgang and Rote, G\"{u}nter and Sharir, Micha and Xiao, Allen},
  title =	{{Approximate Minimum-Weight Matching with Outliers Under Translation}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{26:1--26:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.26},
  URN =		{urn:nbn:de:0030-drops-99747},
  doi =		{10.4230/LIPIcs.ISAAC.2018.26},
  annote =	{Keywords: Minimum-weight partial matching, Pattern matching, Approximation}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.50
Stabbing Pairwise Intersecting Disks by Five Points

Authors: Sariel Har-Peled, Haim Kaplan, Wolfgang Mulzer, Liam Roditty, Paul Seiferth, Micha Sharir, and Max Willert

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Suppose we are given a set D of n pairwise intersecting disks in the plane. A planar point set P stabs D if and only if each disk in D contains at least one point from P. We present a deterministic algorithm that takes O(n) time to find five points that stab D. Furthermore, we give a simple example of 13 pairwise intersecting disks that cannot be stabbed by three points. This provides a simple - albeit slightly weaker - algorithmic version of a classical result by Danzer that such a set D can always be stabbed by four points.
Cite as

Sariel Har-Peled, Haim Kaplan, Wolfgang Mulzer, Liam Roditty, Paul Seiferth, Micha Sharir, and Max Willert. Stabbing Pairwise Intersecting Disks by Five Points. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 50:1-50:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{harpeled_et_al:LIPIcs.ISAAC.2018.50,
  author =	{Har-Peled, Sariel and Kaplan, Haim and Mulzer, Wolfgang and Roditty, Liam and Seiferth, Paul and Sharir, Micha and Willert, Max},
  title =	{{Stabbing Pairwise Intersecting Disks by Five Points}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{50:1--50:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.50},
  URN =		{urn:nbn:de:0030-drops-99989},
  doi =		{10.4230/LIPIcs.ISAAC.2018.50},
  annote =	{Keywords: Disk graph, piercing set, LP-type problem}
}
Document
DOI: 10.4230/DagSemProc.08421.9
A Uncertainty Perspective on Qualitative Preference

Authors: Seung-won Hwang and Mu-Woong Lee

Published in: Dagstuhl Seminar Proceedings, Volume 8421, Uncertainty Management in Information Systems (2009)

Abstract
Collaborative filtering has been successfully applied for predicting a person's preference on an item, by aggregating community preference on the item. Typically, collaborative filtering systems are based on based on quantitative preference modeling, which requires users to express their preferences in absolute numerical ratings. However, quantitative user ratings are known to be biased and inconsistent and also significantly more burdensome to the user than the alternative qualitative preference modeling, requiring only to specify relative preferences between the item pair. More specifically, we identify three main components of collaborative filtering-- preference representation, aggregation, and similarity computation, and view each component from a qualitative perspective. From this perspective, we build a framework, which collects only qualitative feedbacks from users. Our rating-oblivious framework was empirically validated to have comparable prediction accuracies to an (impractical) upper bound accuracy obtained by collaborative filtering system using ratings.
Cite as

Seung-won Hwang and Mu-Woong Lee. A Uncertainty Perspective on Qualitative Preference. In Uncertainty Management in Information Systems. Dagstuhl Seminar Proceedings, Volume 8421, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{hwang_et_al:DagSemProc.08421.9,
  author =	{Hwang, Seung-won and Lee, Mu-Woong},
  title =	{{A Uncertainty Perspective on Qualitative Preference}},
  booktitle =	{Uncertainty Management in Information Systems},
  pages =	{1--9},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{8421},
  editor =	{Christoph Koch and Birgitta K\"{o}nig-Ries and Volker Markl and Maurice van Keulen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08421.9},
  URN =		{urn:nbn:de:0030-drops-19323},
  doi =		{10.4230/DagSemProc.08421.9},
  annote =	{Keywords: Collaborative filtering, qualitative preference, uncertainty}
}
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