6 Search Results for "Xu, Hu"


Document
Stability Yields Sublinear Time Algorithms for Geometric Optimization in Machine Learning

Authors: Hu Ding

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


Abstract
In this paper, we study several important geometric optimization problems arising in machine learning. First, we revisit the Minimum Enclosing Ball (MEB) problem in Euclidean space ℝ^d. The problem has been extensively studied before, but real-world machine learning tasks often need to handle large-scale datasets so that we cannot even afford linear time algorithms. Motivated by the recent developments on beyond worst-case analysis, we introduce the notion of stability for MEB, which is natural and easy to understand. Roughly speaking, an instance of MEB is stable, if the radius of the resulting ball cannot be significantly reduced by removing a small fraction of the input points. Under the stability assumption, we present two sampling algorithms for computing radius-approximate MEB with sample complexities independent of the number of input points n. In particular, the second algorithm has the sample complexity even independent of the dimensionality d. We also consider the general case without the stability assumption. We present a hybrid algorithm that can output either a radius-approximate MEB or a covering-approximate MEB, which improves the running time and the number of passes for the previous sublinear MEB algorithms. Further, we extend our proposed notion of stability and design sublinear time algorithms for other geometric optimization problems including MEB with outliers, polytope distance, one-class and two-class linear SVMs (without or with outliers). Our proposed algorithms also work fine for kernels.

Cite as

Hu Ding. Stability Yields Sublinear Time Algorithms for Geometric Optimization in Machine Learning. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 38:1-38:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{ding:LIPIcs.ESA.2021.38,
  author =	{Ding, Hu},
  title =	{{Stability Yields Sublinear Time Algorithms for Geometric Optimization in Machine Learning}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{38:1--38:19},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.38},
  URN =		{urn:nbn:de:0030-drops-146194},
  doi =		{10.4230/LIPIcs.ESA.2021.38},
  annote =	{Keywords: stability, sublinear time, geometric optimization, machine learning}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Analytical Differential Calculus with Integration

Authors: Han Xu and Zhenjiang Hu

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)


Abstract
Differential lambda-calculus was first introduced by Thomas Ehrhard and Laurent Regnier in 2003. Despite more than 15 years of history, little work has been done on a differential calculus with integration. In this paper, we shall propose a differential calculus with integration from a programming point of view. We show its good correspondence with mathematics, which is manifested by how we construct these reduction rules and how we preserve important mathematical theorems in our calculus. Moreover, we highlight applications of the calculus in incremental computation, automatic differentiation, and computation approximation.

Cite as

Han Xu and Zhenjiang Hu. Analytical Differential Calculus with Integration. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 143:1-143:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{xu_et_al:LIPIcs.ICALP.2021.143,
  author =	{Xu, Han and Hu, Zhenjiang},
  title =	{{Analytical Differential Calculus with Integration}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{143:1--143:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.143},
  URN =		{urn:nbn:de:0030-drops-142127},
  doi =		{10.4230/LIPIcs.ICALP.2021.143},
  annote =	{Keywords: Differential Calculus, Integration, Lambda Calculus, Incremental Computation, Adaptive Computing}
}
Document
Distributed and Robust Support Vector Machine

Authors: Yangwei Liu, Hu Ding, Ziyun Huang, and Jinhui Xu

Published in: LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)


Abstract
In this paper, we consider the distributed version of Support Vector Machine (SVM) under the coordinator model, where all input data (i.e., points in R^d space) of SVM are arbitrarily distributed among k nodes in some network with a coordinator which can communicate with all nodes. We investigate two variants of this problem, with and without outliers. For distributed SVM without outliers, we prove a lower bound on the communication complexity and give a distributed (1-epsilon)-approximation algorithm to reach this lower bound, where epsilon is a user specified small constant. For distributed SVM with outliers, we present a (1-epsilon)-approximation algorithm to explicitly remove the influence of outliers. Our algorithm is based on a deterministic distributed top t selection algorithm with communication complexity of O(k log (t)) in the coordinator model. Experimental results on benchmark datasets confirm the theoretical guarantees of our algorithms.

Cite as

Yangwei Liu, Hu Ding, Ziyun Huang, and Jinhui Xu. Distributed and Robust Support Vector Machine. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 54:1-54:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{liu_et_al:LIPIcs.ISAAC.2016.54,
  author =	{Liu, Yangwei and Ding, Hu and Huang, Ziyun and Xu, Jinhui},
  title =	{{Distributed and Robust Support Vector Machine}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{54:1--54:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Hong, Seok-Hee},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.54},
  URN =		{urn:nbn:de:0030-drops-68221},
  doi =		{10.4230/LIPIcs.ISAAC.2016.54},
  annote =	{Keywords: Distributed Algorithm, Communication Complexity, Robust Algorithm, SVM}
}
Document
Finding Global Optimum for Truth Discovery: Entropy Based Geometric Variance

Authors: Hu Ding, Jing Gao, and Jinhui Xu

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)


Abstract
Truth Discovery is an important problem arising in data analytics related fields such as data mining, database, and big data. It concerns about finding the most trustworthy information from a dataset acquired from a number of unreliable sources. Due to its importance, the problem has been extensively studied in recent years and a number techniques have already been proposed. However, all of them are of heuristic nature and do not have any quality guarantee. In this paper, we formulate the problem as a high dimensional geometric optimization problem, called Entropy based Geometric Variance. Relying on a number of novel geometric techniques (such as Log-Partition and Modified Simplex Lemma), we further discover new insights to this problem. We show, for the first time, that the truth discovery problem can be solved with guaranteed quality of solution. Particularly, we show that it is possible to achieve a (1+eps)-approximation within nearly linear time under some reasonable assumptions. We expect that our algorithm will be useful for other data related applications.

Cite as

Hu Ding, Jing Gao, and Jinhui Xu. Finding Global Optimum for Truth Discovery: Entropy Based Geometric Variance. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 34:1-34:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{ding_et_al:LIPIcs.SoCG.2016.34,
  author =	{Ding, Hu and Gao, Jing and Xu, Jinhui},
  title =	{{Finding Global Optimum for Truth Discovery: Entropy Based Geometric Variance}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{34:1--34:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.34},
  URN =		{urn:nbn:de:0030-drops-59264},
  doi =		{10.4230/LIPIcs.SoCG.2016.34},
  annote =	{Keywords: geometric optimization, data mining, high dimension, entropy}
}
Document
Using Self-learning and Automatic Tuning to Improve the Performance of Sexual Genetic Algorithms for Constraint Satisfaction Problems

Authors: Hu Xu, Karen Petrie, and Iain Murray

Published in: OASIcs, Volume 35, 2013 Imperial College Computing Student Workshop


Abstract
Currently the parameters in a constraint solver are often selected by hand by experts in the field; these parameters might include the level of preprocessing to be used and the variable ordering heuristic. The efficient and automatic choice of a preprocessing level for a constraint solver is a step towards making constraint programming a more widely accessible technology. Self-learning sexual genetic algorithms are a new approach combining a self-learning mechanism with sexual genetic algorithms in order to suggest or predict a suitable solver configuration for large scale problems by learning from the same class of small scale problems. In this paper, Self-learning Sexual genetic algorithms are applied to create an automatic solver configuration mechanism for solving various constraint problems. The starting population of self-learning sexual genetic algorithms will be trained through experience on small instances. The experiments in this paper are a proof-of-concept for the idea of combining sexual genetic algorithms with a self-learning strategy to aid in parameter selection for constraint programming.

Cite as

Hu Xu, Karen Petrie, and Iain Murray. Using Self-learning and Automatic Tuning to Improve the Performance of Sexual Genetic Algorithms for Constraint Satisfaction Problems. In 2013 Imperial College Computing Student Workshop. Open Access Series in Informatics (OASIcs), Volume 35, pp. 128-135, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


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@InProceedings{xu_et_al:OASIcs.ICCSW.2013.128,
  author =	{Xu, Hu and Petrie, Karen and Murray, Iain},
  title =	{{Using Self-learning and Automatic Tuning to Improve the Performance of Sexual Genetic Algorithms for Constraint Satisfaction Problems}},
  booktitle =	{2013 Imperial College Computing Student Workshop},
  pages =	{128--135},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-63-7},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{35},
  editor =	{Jones, Andrew V. and Ng, Nicholas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ICCSW.2013.128},
  URN =		{urn:nbn:de:0030-drops-42811},
  doi =		{10.4230/OASIcs.ICCSW.2013.128},
  annote =	{Keywords: Self-learning Genetic Algorithm, Sexual Genetic algorithm, Constraint Programming, Parameter Tuning}
}
Document
Self-Learning Genetic Algorithm For Constrains Satisfaction Problems

Authors: Hu Xu and Karen Petrie

Published in: OASIcs, Volume 28, 2012 Imperial College Computing Student Workshop


Abstract
The efficient choice of a preprocessing level can reduce the search time of a constraint solver to find a solution to a constraint problem. Currently the parameters in constraint solver are often picked by hand by experts in the field. Genetic algorithms are a robust machine learning technology for problem optimization such as function optimization. Self-learning Genetic Algorithm are a strategy which suggests or predicts the suitable preprocessing method for large scale problems by learning from the same class of small scale problems. In this paper Self-learning Genetic Algorithms are used to create an automatic preprocessing selection mechanism for solving various constraint problems. The experiments in the paper are a proof of concept for the idea of combining genetic algorithm self-learning ability with constraint programming to aid in the parameter selection issue.

Cite as

Hu Xu and Karen Petrie. Self-Learning Genetic Algorithm For Constrains Satisfaction Problems. In 2012 Imperial College Computing Student Workshop. Open Access Series in Informatics (OASIcs), Volume 28, pp. 156-162, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


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@InProceedings{xu_et_al:OASIcs.ICCSW.2012.156,
  author =	{Xu, Hu and Petrie, Karen},
  title =	{{Self-Learning Genetic Algorithm For Constrains Satisfaction Problems}},
  booktitle =	{2012 Imperial College Computing Student Workshop},
  pages =	{156--162},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-48-4},
  ISSN =	{2190-6807},
  year =	{2012},
  volume =	{28},
  editor =	{Jones, Andrew V.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ICCSW.2012.156},
  URN =		{urn:nbn:de:0030-drops-37808},
  doi =		{10.4230/OASIcs.ICCSW.2012.156},
  annote =	{Keywords: Self-learning Genetic Algorithm, Constraint Programming, Parameter Tuning}
}
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