Preface |
|
ix | |
|
|
|
1 About the Book and Supporting Material |
|
|
3 | (38) |
|
1.1 What Do Data Mining, Machine Learning, and Knowledge Discovery Mean? |
|
|
3 | (2) |
|
1.2 What Is This Book About? |
|
|
5 | (3) |
|
1.3 An Incomplete Survey of the Relevant Literature |
|
|
8 | (4) |
|
1.4 Introduction to the Python Language and the Git Code Management Tool |
|
|
12 | (1) |
|
1.5 Description of Surveys and Data Sets Used in Examples |
|
|
13 | (16) |
|
1.6 Plotting and Visualizing the Data in This Book |
|
|
29 | (6) |
|
1.7 How to Efficiently Use This Book |
|
|
35 | (6) |
|
|
37 | (4) |
|
2 Fast Computation on Massive Data Sets |
|
|
41 | (24) |
|
2.1 Data Types and Data Management Systems |
|
|
41 | (1) |
|
2.2 Analysis of Algorithmic Efficiency |
|
|
42 | (2) |
|
2.3 Seven Types of Computational Problem |
|
|
44 | (1) |
|
2.4 Eight Strategies for Speeding Things Up |
|
|
45 | (3) |
|
2.5 Case Studies: Speedup Strategies in Practice |
|
|
48 | (17) |
|
|
60 | (5) |
|
II Statistical Frameworks and Exploratory Data Analysis |
|
|
|
3 Probability and Statistical Distributions |
|
|
65 | (50) |
|
3.1 Brief Overview of Probability and Random Variables |
|
|
66 | (7) |
|
3.2 Descriptive Statistics |
|
|
73 | (7) |
|
3.3 Common Univariate Distribution Functions |
|
|
80 | (18) |
|
3.4 The Central Limit Theorem |
|
|
98 | (2) |
|
3.5 Bivariate and Multivariate Distribution Functions |
|
|
100 | (8) |
|
3.6 Correlation Coefficients |
|
|
108 | (3) |
|
3.7 Random Number Generation for Arbitrary Distributions |
|
|
111 | (4) |
|
|
114 | (1) |
|
4 Classical Statistical Inference |
|
|
115 | (50) |
|
4.1 Classical vs. Bayesian Statistical Inference |
|
|
115 | (1) |
|
4.2 Maximum Likelihood Estimation (MLE) |
|
|
116 | (7) |
|
4.3 The Goodness of Fit and Model Selection |
|
|
123 | (3) |
|
4.4 ML Applied to Gaussian Mixtures: The Expectation Maximization Algorithm |
|
|
126 | (6) |
|
4.5 Confidence Estimates: The Bootstrap and the Jackknife |
|
|
132 | (3) |
|
|
135 | (6) |
|
4.7 Comparison of Distributions |
|
|
141 | (12) |
|
4.8 Nonparametric Modeling and Histograms |
|
|
153 | (4) |
|
4.9 Selection Effects and Luminosity Function Estimation |
|
|
157 | (5) |
|
|
162 | (3) |
|
|
162 | (3) |
|
5 Bayesian Statistical Inference |
|
|
165 | (78) |
|
5.1 Introduction to the Bayesian Method |
|
|
166 | (4) |
|
|
170 | (4) |
|
5.3 Bayesian Parameter Uncertainty Quantification |
|
|
174 | (1) |
|
5.4 Bayesian Model Selection |
|
|
175 | (5) |
|
5.5 Nonuniform Priors: Eddington, Malmquist, and Lutz--Kelker Biases |
|
|
180 | (5) |
|
5.6 Simple Examples of Bayesian Analysis: Parameter Estimation |
|
|
185 | (26) |
|
5.7 Simple Examples of Bayesian Analysis: Model Selection |
|
|
211 | (6) |
|
5.8 Numerical Methods for Complex Problems (MCMC) |
|
|
217 | (11) |
|
5.9 Hierarchical Bayesian Modeling |
|
|
228 | (4) |
|
5.10 Approximate Bayesian Computation |
|
|
232 | (2) |
|
5.11 Summary of Pros and Cons for Classical and Bayesian Methods |
|
|
234 | (9) |
|
|
237 | (6) |
|
III Data Mining and Machine Learning |
|
|
|
6 Searching for Structure in Point Data |
|
|
243 | (38) |
|
6.1 Nonparametric Density Estimation |
|
|
244 | (7) |
|
6.2 Nearest-Neighbor Density Estimation |
|
|
251 | (2) |
|
6.3 Parametric Density Estimation |
|
|
253 | (10) |
|
6.4 Finding Clusters in Data |
|
|
263 | (6) |
|
6.5 Correlation Functions |
|
|
269 | (4) |
|
6.6 Which Density Estimation and Clustering Algorithms Should I Use? |
|
|
273 | (8) |
|
|
277 | (4) |
|
7 Dimensionality and Its Reduction |
|
|
281 | (30) |
|
7.1 The Curse of Dimensionality |
|
|
281 | (2) |
|
7.2 The Data Sets Used in This Chapter |
|
|
283 | (1) |
|
7.3 Principal Component Analysis |
|
|
283 | (12) |
|
7.4 Nonnegative Matrix Factorization |
|
|
295 | (2) |
|
|
297 | (7) |
|
7.6 Independent Component Analysis and Projection Pursuit |
|
|
304 | (2) |
|
7.7 Which Dimensionality Reduction Technique Should I Use? |
|
|
306 | (5) |
|
|
309 | (2) |
|
8 Regression and Model Fitting |
|
|
311 | (42) |
|
8.1 Formulation of the Regression Problem |
|
|
311 | (4) |
|
8.2 Regression for Linear Models |
|
|
315 | (6) |
|
8.3 Regularization and Penalizing the Likelihood |
|
|
321 | (5) |
|
8.4 Principal Component Regression |
|
|
326 | (1) |
|
|
327 | (1) |
|
8.6 Locally Linear Regression |
|
|
328 | (1) |
|
|
329 | (2) |
|
8.8 Uncertainties in the Data |
|
|
331 | (1) |
|
8.9 Regression That Is Robust to Outliers |
|
|
332 | (5) |
|
8.10 Gaussian Process Regression |
|
|
337 | (4) |
|
8.11 Overfitting, Underrating, and Cross-Validation |
|
|
341 | (8) |
|
8.12 Which Regression Method Should I Use? |
|
|
349 | (4) |
|
|
351 | (2) |
|
|
353 | (46) |
|
9.1 Data Sets Used in This Chapter |
|
|
353 | (1) |
|
9.2 Assigning Categories: Classification |
|
|
354 | (2) |
|
9.3 Generative Classification |
|
|
356 | (10) |
|
9.4 K-Nearest-Neighbor Classifier |
|
|
366 | (1) |
|
9.5 Discriminative Classification |
|
|
367 | (3) |
|
9.6 Support Vector Machines |
|
|
370 | (3) |
|
|
373 | (8) |
|
9.8 Deep Learning and Neural Networks |
|
|
381 | (10) |
|
9.9 Evaluating Classifiers: ROC Curves |
|
|
391 | (2) |
|
9.10 Which Classifier Should I Use? |
|
|
393 | (6) |
|
|
397 | (2) |
|
|
399 | (68) |
|
10.1 Main Concepts for Time Series Analysis |
|
|
400 | (1) |
|
10.2 Modeling Toolkit for Time Series Analysis |
|
|
401 | (19) |
|
10.3 Analysis of Periodic Time Series |
|
|
420 | (27) |
|
10.4 Temporally Localized Signals |
|
|
447 | (2) |
|
10.5 Analysis of Stochastic Processes |
|
|
449 | (10) |
|
10.6 Which Method Should I Use for Time Series Analysis? |
|
|
459 | (8) |
|
|
460 | (7) |
|
|
|
A An Introduction to Scientific Computing with Python |
|
|
467 | (38) |
|
A.1 A Brief History of Python |
|
|
467 | (1) |
|
|
468 | (2) |
|
A.3 Getting Started with Python |
|
|
470 | (12) |
|
A.4 IPython: The Basics of Interactive Computing |
|
|
482 | (2) |
|
A.5 Introduction to NumPy |
|
|
484 | (5) |
|
A.6 Visualization with Matplotlib |
|
|
489 | (3) |
|
A.7 Overview of Useful NumPy/SciPy Modules |
|
|
492 | (5) |
|
A.8 Efficient Coding with Python and NumPy |
|
|
497 | (4) |
|
A.9 Wrapping Existing code in Python |
|
|
501 | (1) |
|
|
502 | (3) |
|
B AstroML: Machine Learning for Astronomy |
|
|
505 | (4) |
|
|
505 | (1) |
|
|
505 | (1) |
|
B.3 Tools Included in AstroML v1.0 |
|
|
506 | (1) |
|
B.4 Open Source Deep Learning Libraries |
|
|
507 | (2) |
|
C Astronomical Flux Measurements and Magnitudes |
|
|
509 | (4) |
|
C.1 The Definition of the Specific Flux |
|
|
509 | (1) |
|
C.2 Wavelength Window Function for Astronomical Measurements |
|
|
509 | (1) |
|
C.3 The Astronomical Magnitude Systems |
|
|
510 | (3) |
|
D SQL Query for Downloading SDSS Data |
|
|
513 | (2) |
|
E Approximating the Fourier Transform with the FFT |
|
|
515 | (6) |
|
|
518 | (3) |
Visual Figure Index |
|
521 | (8) |
Index |
|
529 | |