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Mathematics of Data [Hardback]

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  • Formāts: Hardback, 325 pages, height x width: 254x178 mm, weight: 755 g
  • Sērija : IAS/Park City Mathematics Series
  • Izdošanas datums: 30-Nov-2018
  • Izdevniecība: American Mathematical Society
  • ISBN-10: 1470435756
  • ISBN-13: 9781470435752
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  • Hardback
  • Cena: 141,85 €
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Mathematics of DataPalielināt
  • Formāts: Hardback, 325 pages, height x width: 254x178 mm, weight: 755 g
  • Sērija : IAS/Park City Mathematics Series
  • Izdošanas datums: 30-Nov-2018
  • Izdevniecība: American Mathematical Society
  • ISBN-10: 1470435756
  • ISBN-13: 9781470435752
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781470435752.html
Keywords:
Data science is a highly interdisciplinary field, incorporating ideas from applied mathematics, statistics, probability, and computer science, as well as many other areas. This book gives an introduction to the mathematical methods that form the foundations of machine learning and data science, presented by leading experts in computer science, statistics, and applied mathematics. Although the chapters can be read independently, they are designed to be read together as they lay out algorithmic, statistical, and numerical approaches in diverse but complementary ways.

This book can be used both as a text for advanced undergraduate and beginning graduate courses, and as a survey for researchers interested in understanding how applied mathematics broadly defined is being used in data science. It will appeal to anyone interested in the interdisciplinary foundations of machine learning and data science.
1 Introduction
2(1)
2 Linear Algebra
3(8)
2.1 Basics
3(1)
2.2 Norms
4(1)
2.3 Vector norms
4(1)
2.4 Induced matrix norms
5(1)
2.5 The Frobenius norm
6(1)
2.6 The Singular Value Decomposition
7(2)
2.7 SVD and Fundamental Matrix Spaces
9(1)
2.8 Matrix Schatten norms
9(1)
2.9 The Moore-Penrose pseudoinverse
10(1)
2.10 References
11(1)
3 Discrete Probability
11(5)
3.1 Random experiments: basics
11(1)
3.2 Properties of events
12(1)
3.3 The union bound
12(1)
3.4 Disjoint events and independent events
12(1)
3.5 Conditional probability
12(1)
3.6 Random variables
13(1)
3.7 Probability mass function and cumulative distribution function
13(1)
3.8 Independent random variables
14(1)
3.9 Expectation of a random variable
14(1)
3.10 Variance of a random variable
14(1)
3.11 Markov's inequality
15(1)
3.12 The Coupon Collector Problem
16(1)
3.13 References
16(1)
4 Randomized Matrix Multiplication
16(8)
4.1 Analysis of the RandMatrixMultiply algorithm
18(3)
4.2 Analysis of the algorithm for nearly optimal probabilities
21(1)
4.3 Bounding the two norm
21(3)
4.4 References
24(1)
5 RandNLA Approaches for Regression Problems
24(12)
5.1 The Randomized Hadamard Transform
25(1)
5.2 The main algorithm and main theorem
26(2)
5.3 RandNLA algorithms as preconditioners
28(3)
5.4 The proof of Theorem 5.2.2
31(4)
5.5 The running time of the RandLeastSquares algorithm
35(1)
5.6 References
36(1)
6 A RandNLA Algorithm for Low-rank Matrix Approximation
36
6.1 The main algorithm and main theorem
37(3)
6.2 An alternative expression for the error
40(1)
6.3 A structural inequality
41(1)
6.4 Completing the proof of Theorem 6.1.1
42(5)
6.5 Running time
47(1)
6.6 References
47
Michael W. Mahoney, University of California, Berkeley, CA.

John C. Duchi, Stanford University, CA.

Anna C. Gilbert, University of Michigan, Ann Arbor, MI.