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020 _a9783031190742
_9978-3-031-19074-2
024 7 _a10.1007/978-3-031-19074-2
_2doi
050 4 _aQ336
072 7 _aUN
_2bicssc
072 7 _aCOM021000
_2bisacsh
072 7 _aUN
_2thema
082 0 4 _a005.7
_223
100 1 _aHrycej, Tomas.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aMathematical Foundations of Data Science
_h[electronic resource] /
_cby Tomas Hrycej, Bernhard Bermeitinger, Matthias Cetto, Siegfried Handschuh.
250 _a1st ed. 2023.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2023.
300 _aXIII, 213 p. 108 illus., 98 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTexts in Computer Science,
_x1868-095X
505 0 _a1. Data Science and its Tasks -- 2. Application Specific Mappings and Measuring the Fit to Data -- 3. Data Processing by Neural Networks -- 4. Learning and Generalization -- 5. Numerical Algorithms for Network Learning -- 6. Specific Problems of Natural Language Processing -- 7. Specific Problems of Computer Vision.
520 _aAlthough it is widely recognized that analyzing large volumes of data by intelligent methods may provide highly valuable insights, the practical success of data science has led to the development of a sometimes confusing variety of methods, approaches and views. This practical textbook aims to point out the most important principles of data analysis from the mathematical point of view. Specifically, it selected these questions for exploring: Which are the principles necessary to understand the implications of an application, and which are necessary to understand the conditions for the success of methods used? Theory is presented only to the degree necessary to apply it properly, striving for the balance between excessive complexity and oversimplification. Its primary focus is on principles crucial for application success. Topics and features: Focuses on approaches supported by mathematical arguments, rather thansole computing experiences Investigates conditions under which numerical algorithms used in data science operate, and what performance can be expected from them Considers key data science problems: problem formulation including optimality measure; learning and generalization in relationships to training set size and number of free parameters; and convergence of numerical algorithms Examines original mathematical disciplines (statistics, numerical mathematics, system theory) as they are specifically relevant to a given problem Addresses the trade-off between model size and volume of data available for its identification and its consequences for model parameterization Investigates the mathematical principles involved with natural language processing and computer vision Keeps subject coverage intentionally compact, focusing on key issues of each topic to encourage full comprehension of the entire book Although this core textbook aims directly at students of computer science and/or data science, it will be of real appeal, too, to researchers in the field who want to gain a proper understanding of the mathematical foundations “beyond” the sole computing experience.
650 0 _aArtificial intelligence
_xData processing.
650 0 _aComputer science
_xMathematics.
650 0 _aDiscrete mathematics.
650 0 _aComputer arithmetic and logic units.
650 1 4 _aData Science.
650 2 4 _aDiscrete Mathematics in Computer Science.
650 2 4 _aMathematical Applications in Computer Science.
650 2 4 _aArithmetic and Logic Structures.
700 1 _aBermeitinger, Bernhard.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aCetto, Matthias.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aHandschuh, Siegfried.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031190735
776 0 8 _iPrinted edition:
_z9783031190759
776 0 8 _iPrinted edition:
_z9783031190766
830 0 _aTexts in Computer Science,
_x1868-095X
856 4 0 _uhttps://doi.org/10.1007/978-3-031-19074-2
912 _aZDB-2-SCS
912 _aZDB-2-SXCS
942 _cSPRINGER
999 _c185020
_d185020