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E-grāmata: Python for Probability, Statistics, and Machine Learning

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  • Formāts: PDF+DRM
  • Izdošanas datums: 29-Jun-2019
  • Izdevniecība: Springer Nature Switzerland AG
  • Valoda: eng
  • ISBN-13: 9783030185459
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Python for Probability, Statistics, and Machine LearningPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 29-Jun-2019
  • Izdevniecība: Springer Nature Switzerland AG
  • Valoda: eng
  • ISBN-13: 9783030185459
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This book, fully updated for Python version 3.6+, covers the key ideas that link probability, statistics, and machine learning illustrated using Python modules in these areas.  All the figures and numerical results are reproducible using the Python codes provided. The author develops key intuitions in machine learning by working meaningful examples using multiple analytical methods and Python codes, thereby connecting theoretical concepts to concrete implementations. Detailed proofs for certain important results are also provided. Modern Python modules like Pandas, Sympy, Scikit-learn, Tensorflow, and Keras are applied to simulate and visualize important machine learning concepts like the bias/variance trade-off, cross-validation, and regularization. Many abstract mathematical ideas, such as convergence in probability theory, are developed and illustrated with numerical examples.  This updated edition now includes the Fisher Exact Test and the Mann-Whitney-Wilcoxon Test. A new section on survival analysis has been included as well as substantial development of Generalized Linear Models. The new deep learning section for image processing includes an in-depth discussion of gradient descent methods that underpin all deep learning algorithms.   As with the prior edition, there are new and updated *Programming Tips* that the illustrate effective Python modules and methods for scientific programming and machine learning. There are 445 run-able code blocks with corresponding outputs that have been tested for accuracy.  Over 158 graphical visualizations (almost all generated using Python) illustrate the concepts that are developed both in code and in mathematics. We also discuss and use key Python modules such as Numpy, Scikit-learn, Sympy,  Scipy, Lifelines, CvxPy, Theano, Matplotlib, Pandas, Tensorflow, Statsmodels,  and Keras. This book is suitable for anyone with an undergraduate-level exposure to probability, statistics, or machine learning and with rudimentary knowledge of Python programming.

Recenzijas

The book is aimed primarily at intermediate or advanced Python programmers . this work is a generally sound and comprehensive overview of the areas it covers. We recommend it to Python programmers interested in growing in these areas or experts in these areas interested in learning how to deal with them in Python. (Eugene Callahan and Yujia Zhang, Computing Reviews, October 15, 2020)

1 Getting Started with Scientific Python
1(38)
1.1 Installation and Setup
2(2)
1.2 Numpy
4(13)
1.2.1 Numpy Arrays and Memory
6(3)
1.2.2 Numpy Matrices
9(1)
1.2.3 Numpy Broadcasting
10(3)
1.2.4 Numpy Masked Arrays
13(1)
1.2.5 Floating-Point Numbers
13(4)
1.2.6 Numpy Optimizations and Prospectus
17(1)
1.3 Matplotlib
17(3)
1.3.1 Alternatives to Matplotlib
19(1)
1.3.2 Extensions to Matplotlib
20(1)
1.4 IPython
20(2)
1.5 Jupyter Notebook
22(2)
1.6 Scipy
24(1)
1.7 Pandas
25(5)
1.7.1 Series
25(2)
1.7.2 Dataframe
27(3)
1.8 Sympy
30(2)
1.9 Interfacing with Compiled Libraries
32(1)
1.10 Integrated Development Environments
33(1)
1.11 Quick Guide to Performance and Parallel Programming
34(3)
1.12 Other Resources
37(2)
References
38(1)
2 Probability
39(84)
2.1 Introduction
39(16)
2.1.1 Understanding Probability Density
40(1)
2.1.2 Random Variables
41(5)
2.1.3 Continuous Random Variables
46(3)
2.1.4 Transformation of Variables Beyond Calculus
49(2)
2.1.5 Independent Random Variables
51(2)
2.1.6 Classic Broken Rod Example
53(2)
2.2 Projection Methods
55(3)
2.2.1 Weighted Distance
57(1)
2.3 Conditional Expectation as Projection
58(7)
2.3.1 Appendix
64(1)
2.4 Conditional Expectation and Mean Squared Error
65(3)
2.5 Worked Examples of Conditional Expectation and Mean Square Error Optimization
68(15)
2.5.1 Example
69(3)
2.5.2 Example
72(3)
2.5.3 Example
75(3)
2.5.4 Example
78(1)
2.5.5 Example
79(3)
2.5.6 Example
82(1)
2.6 Useful Distributions
83(12)
2.6.1 Normal Distribution
83(1)
2.6.2 Multinomial Distribution
84(2)
2.6.3 Chi-square Distribution
86(3)
2.6.4 Poisson and Exponential Distributions
89(1)
2.6.5 Gamma Distribution
90(1)
2.6.6 Beta Distribution
91(2)
2.6.7 Dirichlet-Multinomial Distribution
93(2)
2.7 Information Entropy
95(6)
2.7.1 Information Theory Concepts
96(2)
2.7.2 Properties of Information Entropy
98(1)
2.7.3 Kullback--Leibler Divergence
99(1)
2.7.4 Cross-Entropy as Maximum Likelihood
100(1)
2.8 Moment Generating Functions
101(3)
2.9 Monte Carlo Sampling Methods
104(9)
2.9.1 Inverse CDF Method for Discrete Variables
105(2)
2.9.2 Inverse CDF Method for Continuous Variables
107(1)
2.9.3 Rejection Method
108(5)
2.10 Sampling Importance Resampling
113(2)
2.11 Useful Inequalities
115(8)
2.11.1 Markov's Inequality
115(1)
2.11.2 Chebyshev's Inequality
116(2)
2.11.3 Hoeffding's Inequality
118(2)
References
120(3)
3 Statistics
123(114)
3.1 Introduction
123(1)
3.2 Python Modules for Statistics
124(2)
3.2.1 Scipy Statistics Module
124(1)
3.2.2 Sympy Statistics Module
125(1)
3.2.3 Other Python Modules for Statistics
126(1)
3.3 Types of Convergence
126(7)
3.3.1 Almost Sure Convergence
126(3)
3.3.2 Convergence in Probability
129(2)
3.3.3 Convergence in Distribution
131(1)
3.3.4 Limit Theorems
132(1)
3.4 Estimation Using Maximum Likelihood
133(14)
3.4.1 Setting Up the Coin-Flipping Experiment
135(10)
3.4.2 Delta Method
145(2)
3.5 Hypothesis Testing and P-Values
147(19)
3.5.1 Back to the Coin-Flipping Example
149(3)
3.5.2 Receiver Operating Characteristic
152(2)
3.5.3 P-Values
154(1)
3.5.4 Test Statistics
155(8)
3.5.5 Testing Multiple Hypotheses
163(1)
3.5.6 Fisher Exact Test
163(3)
3.6 Confidence Intervals
166(3)
3.7 Linear Regression
169(14)
3.7.1 Extensions to Multiple Covariates
178(5)
3.8 Maximum A-Posteriori
183(5)
3.9 Robust Statistics
188(7)
3.10 Bootstrapping
195(6)
3.10.1 Parametric Bootstrap
200(1)
3.11 Gauss--Markov
201(4)
3.12 Nonparametric Methods
205(23)
3.12.1 Kernel Density Estimation
205(2)
3.12.2 Kernel Smoothing
207(6)
3.12.3 Nonparametric Regression Estimators
213(1)
3.12.4 Nearest Neighbors Regression
214(4)
3.12.5 Kernel Regression
218(1)
3.12.6 Curse of Dimensionality
219(2)
3.12.7 Nonparametric Tests
221(7)
3.13 Survival Analysis
228(9)
3.13.1 Example
231(5)
References
236(1)
4 Machine Learning
237(144)
4.1 Introduction
237(1)
4.2 Python Machine Learning Modules
237(4)
4.3 Theory of Learning
241(27)
4.3.1 Introduction to Theory of Machine Learning
244(5)
4.3.2 Theory of Generalization
249(1)
4.3.3 Worked Example for Generalization/Approximation Complexity
250(6)
4.3.4 Cross-Validation
256(4)
4.3.5 Bias and Variance
260(5)
4.3.6 Learning Noise
265(3)
4.4 Decision Trees
268(13)
4.4.1 Random Forests
275(2)
4.4.2 Boosting Trees
277(4)
4.5 Boosting Trees
281(4)
4.5.1 Boosting Trees
281(4)
4.6 Logistic Regression
285(10)
4.7 Generalized Linear Models
295(5)
4.8 Regularization
300(11)
4.8.1 Ridge Regression
304(5)
4.8.2 Lasso Regression
309(2)
4.9 Support Vector Machines
311(6)
4.9.1 Kernel Tricks
315(2)
4.10 Dimensionality Reduction
317(8)
4.10.1 Independent Component Analysis
321(4)
4.11 Clustering
325(4)
4.12 Ensemble Methods
329(5)
4.12.1 Bagging
329(2)
4.12.2 Boosting
331(3)
4.13 Deep Learning
334(47)
4.13.1 Introduction to Tensorflow
343(7)
4.13.2 Understanding Gradient Descent
350(13)
4.13.3 Image Processing Using Convolutional Neural Networks
363(16)
References
379(2)
Notation 381(2)
Index 383
Dr. José Unpingco completed his PhD at the University of California, San Diego in 1997 and has since worked in industry as an engineer, consultant, and instructor on a wide-variety of advanced data processing and analysis topics, with deep experience in machine learning and statistics. As the onsite technical director for large-scale Signal and Image Processing for the Department of Defense (DoD), he spearheaded the DoD-wide adoption of scientific Python. He also trained over 600 scientists and engineers to effectively utilize Python for a wide range of scientific topics -- from weather modeling to antenna analysis. Dr. Unpingco is the cofounder and Senior Director for Data Science at a non-profit Medical Research Organization in San Diego, California. He also teaches programming for data analysis at the University of California, San Diego for engineering undergraduate/graduate students. He is author of Python for Signal Processing (Springer 2014) and Python for Probability, Statistics, and Machine Learning (2016) 
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