发帖
雷达卡
by José Unpingco (Author)
About the Author
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)
About this book
This textbook, fully updated to feature Python version 3.7, covers the key ideas that link probability, statistics, and machine learning illustrated using Python modules. The entire text, including all the figures and numerical results, is reproducible using the Python codes and their associated Jupyter/IPython notebooks, which are provided as supplementary downloads. 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. The update features full coverage of Web-based scientific visualization with Bokeh Jupyter Hub; Fisher Exact, Cohen’s D and Rank-Sum Tests; Local Regression, Spline, and Additive Methods; and Survival Analysis, Stochastic Gradient Trees, and Neural Networks and Deep Learning. Modern Python modules like Pandas, Sympy, and Scikit-learn 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 book is suitable for classes in probability, statistics, or machine learning and requires only rudimentary knowledge of Python programming.
Brief contents
1 Getting Started with Scientific Python 1
1.1 Installation and Setup 2
1.2 Numpy. 4
1.2.1 Numpy Arrays and Memory 6
1.2.2 Numpy Matrices 9
1.2.3 Numpy Broadcasting 10
1.2.4 Numpy Masked Arrays. 13
1.2.5 Floating-Point Numbers 13
1.2.6 Numpy Optimizations and Prospectus 17
1.3 Matplotlib 17
1.3.1 Alternatives to Matplotlib 19
1.3.2 Extensions to Matplotlib 20
1.4 IPython 20
1.5 Jupyter Notebook 22
1.6 Scipy 24
1.7 Pandas 25
1.7.1 Series 25
1.7.2 Dataframe 27
1.8 Sympy 30
1.9 Interfacing with Compiled Libraries 32
1.10 Integrated Development Environments 33
1.11 Quick Guide to Performance and Parallel Programming 34
1.12 Other Resources 37
References 38
2 Probability 39
.1 Introduction 39
2.1.1 Understanding Probability Density 40
2.1.2 Random Variables 41
2.1.3 Continuous Random Variables 46
2.1.4 Transformation of Variables Beyond Calculus 49
2.1.5 Independent Random Variables 51
2.1.6 Classic Broken Rod Example 53
2.2 Projection Methods 55
2.2.1 Weighted Distance 57
2.3 Conditional Expectation as Projection 58
2.3.1 Appendix 64
2.4 Conditional Expectation and Mean Squared Error 65
2.5 Worked Examples of Conditional Expectation and Mean Square Error Optimization 68
2.5.1 Example 69
2.5.2 Example 72
2.5.3 Example 75
2.5.4 Example 78
2.5.5 Example 79
2.5.6 Example 82
2.6 Useful Distributions 83
2.6.1 Normal Distribution 83
2.6.2 Multinomial Distribution. 84
2.6.3 Chi-square Distribution 86
2.6.4 Poisson and Exponential Distributions 89
2.6.5 Gamma Distribution 90
2.6.6 Beta Distribution 91
2.6.7 Dirichlet-Multinomial Distribution 93
2.7 Information Entropy 95
2.7.1 Information Theory Concepts 96
2.7.2 Properties of Information Entropy 98
2.7.3 Kullback–Leibler Divergence 99
2.7.4 Cross-Entropy as Maximum Likelihood 100
2.8 Moment Generating Functions 101
2.9 Monte Carlo Sampling Methods 104
2.9.1 Inverse CDF Method for Discrete Variables. 105
2.9.2 Inverse CDF Method for Continuous Variables 107
2.9.3 Rejection Method 108
2.10 Sampling Importance Resampling 113
2.11 Useful Inequalities 115
2.11.1 Markov’s Inequality 115
2.11.2 Chebyshev’s Inequality. 116
2.11.3 Hoeffding’s Inequality 118
References 120
3 Statistics 123
3.1 Introduction 123
3.2 Python Modules for Statistics 124
3.2.1 Scipy Statistics Module 124
3.2.2 Sympy Statistics Module 125
3.2.3 Other Python Modules for Statistics 126
3.3 Types of Convergence 126
3.3.1 Almost Sure Convergence 126
3.3.2 Convergence in Probability 129
3.3.3 Convergence in Distribution 131
3.3.4 Limit Theorems 132
.4 Estimation Using Maximum Likelihood 133
3.4.1 Setting Up the Coin-Flipping Experiment 135
3.4.2 Delta Method 145
3.5 Hypothesis Testing and P-Values. 147
3.5.1 Back to the Coin-Flipping Example. 149
3.5.2 Receiver Operating Characteristic 152
3.5.3 P-Values 154
3.5.4 Test Statistics 155
3.5.5 Testing Multiple Hypotheses 163
3.5.6 Fisher Exact Test 163
3.6 Confidence Intervals 166
3.7 Linear Regression 169
3.7.1 Extensions to Multiple Covariates 178
3.8 Maximum A-Posteriori 183
3.9 Robust Statistics 188
3.10 Bootstrapping 195
3.10.1 Parametric Bootstrap 200
3.11 Gauss–Markov 201
3.12 Nonparametric Methods 205
3.12.1 Kernel Density Estimation 205
3.12.2 Kernel Smoothing 207
3.12.3 Nonparametric Regression Estimators 213
3.12.4 Nearest Neighbors Regression 214
3.12.5 Kernel Regression 218
3.12.6 Curse of Dimensionality 219
3.12.7 Nonparametric Tests 221
3.13 Survival Analysis 228
3.13.1 Example 231
References 236
4 Machine Learning 237
4.1 Introduction 237
4.2 Python Machine Learning Modules 237
4.3 Theory of Learning 241
4.3.1 Introduction to Theory of Machine Learning 244
4.3.2 Theory of Generalization 249
4.3.3 Worked Example for Generalization/Approximation Complexity 250
4.3.4 Cross-Validation 256
4.3.5 Bias and Variance 260
4.3.6 Learning Noise 265
4.4 Decision Trees 268
4.4.1 Random Forests 275
4.4.2 Boosting Trees 277
4.5 Boosting Trees 281
4.5.1 Boosting Trees 281
4.6 Logistic Regression. 285
4.7 Generalized Linear Models 295
4.8 Regularization 300
4.8.1 Ridge Regression 304
4.8.2 Lasso Regression 309
4.9 Support Vector Machines 311
4.9.1 Kernel Tricks 315
4.10 Dimensionality Reduction 317
4.10.1 Independent Component Analysis 321
4.11 Clustering 325
4.12 Ensemble Methods 329
4.12.1 Bagging 329
4.12.2 Boosting 331
4.13 Deep Learning 334
4.13.1 Introduction to Tensorflow 343
4.13.2 Understanding Gradient Descent 350
4.13.3 Image Processing Using Convolutional Neural Networks 363
References 379
Notation 381
Index 383
Pages: 384 pages
Publisher: Springer; 2nd ed. 2019 edition (September 1, 2019)
Language: English
ISBN-10: 3030185443
ISBN-13: 978-3030185442
PDF version
Springer__Python for Probability, Statistics, and Machine Learning, 2nd.pdf
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EPUB version
Springer__Python for Probability, Statistics, and Machine Learning, 2nd.epub
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