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Sampling in Combinatorial and Geometric Set Systems

Bibliographic Details
Title: Sampling in Combinatorial and Geometric Set Systems
Description: Understanding the behavior of basic sampling techniques and intrinsic geometric attributes of data is an invaluable skill that is in high demand for both graduate students and researchers in mathematics, machine learning, and theoretical computer science. The last ten years have seen significant progress in this area, with many open problems having been resolved during this time. These include optimal lower bounds for epsilon-nets for many geometric set systems, the use of shallow-cell complexity to unify proofs, simpler and more efficient algorithms, and the use of epsilon-approximations for construction of coresets, to name a few. This book presents a thorough treatment of these probabilistic, combinatorial, and geometric methods, as well as their combinatorial and algorithmic applications. It also revisits classical results, but with new and more elegant proofs. While mathematical maturity will certainly help in appreciating the ideas presented here, only a basic familiarity with discrete mathematics, probability, and combinatorics is required to understand the material.
Authors: Nabil H. Mustafa
Resource Type: eBook.
Subjects: Geometry--Data processing
Categories: MATHEMATICS / Combinatorics, MATHEMATICS / Geometry / General
Database: eBook Index
FullText Text:
  Availability: 0
Header DbId: edsebk
DbLabel: eBook Index
An: 3146783
RelevancyScore: 962
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 962.24267578125
IllustrationInfo
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  Data: Sampling in Combinatorial and Geometric Set Systems
– Name: Abstract
  Label: Description
  Group: Ab
  Data: Understanding the behavior of basic sampling techniques and intrinsic geometric attributes of data is an invaluable skill that is in high demand for both graduate students and researchers in mathematics, machine learning, and theoretical computer science. The last ten years have seen significant progress in this area, with many open problems having been resolved during this time. These include optimal lower bounds for epsilon-nets for many geometric set systems, the use of shallow-cell complexity to unify proofs, simpler and more efficient algorithms, and the use of epsilon-approximations for construction of coresets, to name a few. This book presents a thorough treatment of these probabilistic, combinatorial, and geometric methods, as well as their combinatorial and algorithmic applications. It also revisits classical results, but with new and more elegant proofs. While mathematical maturity will certainly help in appreciating the ideas presented here, only a basic familiarity with discrete mathematics, probability, and combinatorics is required to understand the material.
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  Data: <searchLink fieldCode="DE" term="%22Geometry--Data+processing%22">Geometry--Data processing</searchLink>
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PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=3146783
RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 519.2
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Geometry--Data processing
        Type: general
    Titles:
      – TitleFull: Sampling in Combinatorial and Geometric Set Systems
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Nabil H. Mustafa
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            NameFull: Nabil H. Mustafa
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2022
            – D: 09
              M: 02
              Type: profile
              Y: 2022
          Identifiers:
            – Type: isbn-print
              Value: 9781470461560
            – Type: isbn-electronic
              Value: 9781470468736
          Numbering:
            – Type: volume
              Value: 00265
          Titles:
            – TitleFull: Sampling in Combinatorial and Geometric Set Systems
              Type: main
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