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Data Science in Theory and Practice

Techniques for Big Data Analytics and Complex Data Sets

Mariani, Maria Cristina / Tweneboah, Osei Kofi / Beccar-Varela, Maria Pia

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1. Auflage Dezember 2021
400 Seiten, Hardcover
Wiley & Sons Ltd

ISBN: 978-1-119-67468-9
John Wiley & Sons

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DATA SCIENCE IN THEORY AND PRACTICE

EXPLORE THE FOUNDATIONS OF DATA SCIENCE WITH THIS INSIGHTFUL NEW RESOURCE

Data Science in Theory and Practice delivers a comprehensive treatment of the mathematical and statistical models useful for analyzing data sets arising in various disciplines, like banking, finance, health care, bioinformatics, security, education, and social services. Written in five parts, the book examines some of the most commonly used and fundamental mathematical and statistical concepts that form the basis of data science. The authors go on to analyze various data transformation techniques useful for extracting information from raw data, long memory behavior, and predictive modeling.

The book offers readers a multitude of topics all relevant to the analysis of complex data sets. Along with a robust exploration of the theory underpinning data science, it contains numerous applications to specific and practical problems. The book also provides examples of code algorithms in R and Python and provides pseudo-algorithms to port the code to any other language.

Ideal for students and practitioners without a strong background in data science, readers will also learn from topics like:
* Analyses of foundational theoretical subjects, including the history of data science, matrix algebra and random vectors, and multivariate analysis
* A comprehensive examination of time series forecasting, including the different components of time series and transformations to achieve stationarity
* Introductions to both the R and Python programming languages, including basic data types and sample manipulations for both languages
* An exploration of algorithms, including how to write one and how to perform an asymptotic analysis
* A comprehensive discussion of several techniques for analyzing and predicting complex data sets

Perfect for advanced undergraduate and graduate students in Data Science, Business Analytics, and Statistics programs, Data Science in Theory and Practice will also earn a place in the libraries of practicing data scientists, data and business analysts, and statisticians in the private sector, government, and academia.

List of Figures xvii

List of Tables xxi

Preface xxiii

1 Background of Data Science 1

1.1 Introduction 1

1.2 Origin of Data Science 2

1.3 Who is a Data Scientist? 2

1.4 Big Data 3

1.4.1 Characteristics of Big Data 4

1.4.2 Big Data Architectures 4

2 Matrix Algebra and Random Vectors 7

2.1 Introduction 7

2.2 Some Basics of Matrix Algebra 7

2.2.1 Vectors 7

2.2.2 Matrices 8

2.3 Random Variables and Distribution Functions 12

2.3.1 The Dirichlet Distribution 15

2.3.2 Multinomial Distribution 17

2.3.3 Multivariate Normal Distribution 18

2.4 Problems 19

3 Multivariate Analysis 21

3.1 Introduction 21

3.2 Multivariate Analysis: Overview 21

3.3 Mean Vectors 22

3.4 Variance-Covariance Matrices 24

3.5 Correlation Matrices 26

3.6 Linear Combinations of Variables 28

3.6.1 Linear Combinations of Sample Means 29

3.6.2 Linear Combinations of Sample Variance and Covariance 29

3.6.3 Linear Combinations of Sample Correlation 30

3.7 Problems 31

4 Time Series Forecasting 35

4.1 Introduction 35

4.2 Terminologies 36

4.3 Components of Time Series 39

4.3.1 Seasonal 39

4.3.2 Trend 40

4.3.3 Cyclical 41

4.3.4 Random 42

4.4 Transformations to Achieve Stationarity 42

4.5 Elimination of Seasonality via Differencing 44

4.6 Additive and Multiplicative Models 44

4.7 Measuring Accuracy of Different Time Series Techniques 45

4.7.1 Mean Absolute Deviation 46

4.7.2 Mean Absolute Percent Error 46

4.7.3 Mean Square Error 47

4.7.4 Root Mean Square Error 48

4.8 Averaging and Exponential Smoothing Forecasting Methods 48

4.8.1 Averaging Methods 49

4.8.1.1 Simple Moving Averages 49

4.8.1.2 Weighted Moving Averages 51

4.8.2 Exponential Smoothing Methods 54

4.8.2.1 Simple Exponential Smoothing 54

4.8.2.2 Adjusted Exponential Smoothing 55

4.9 Problems 57

5 Introduction to R 61

5.1 Introduction 61

5.2 Basic Data Types 62

5.2.1 Numeric Data Type 62

5.2.2 Integer Data Type 62

5.2.3 Character 63

5.2.4 Complex Data Types 63

5.2.5 Logical Data Types 64

5.3 Simple Manipulations - Numbers and Vectors 64

5.3.1 Vectors and Assignment 64

5.3.2 Vector Arithmetic 65

5.3.3 Vector Index 66

5.3.4 Logical Vectors 67

5.3.5 Missing Values 68

5.3.6 Index Vectors 69

5.3.6.1 Indexing with Logicals 69

5.3.6.2 A Vector of Positive Integral Quantities 69

5.3.6.3 A Vector of Negative Integral Quantities 69

5.3.6.4 Named Indexing 70

5.3.7 Other Types of Objects 70

5.3.7.1 Matrices 70

5.3.7.2 List 72

5.3.7.3 Factor 73

5.3.7.4 Data Frames 75

5.3.8 Data Import 76

5.3.8.1 Excel File 76

5.3.8.2 CSV File 76

5.3.8.3 Table File 77

5.3.8.4 Minitab File 77

5.3.8.5 SPSS File 77

5.4 Problems 78

6 Introduction to Python 81

6.1 Introduction 81

6.2 Basic Data Types 82

6.2.1 Number Data Type 82

6.2.1.1 Integer 82

6.2.1.2 Floating-Point Numbers 83

6.2.1.3 Complex Numbers 84

6.2.2 Strings 84

6.2.3 Lists 85

6.2.4 Tuples 86

6.2.5 Dictionaries 86

6.3 Number Type Conversion 87

6.4 Python Conditions 87

6.4.1 If Statements 88

6.4.2 The Else and Elif Clauses 89

6.4.3 The While Loop 90

6.4.3.1 The Break Statement 91

6.4.3.2 The Continue Statement 91

6.4.4 For Loops 91

6.4.4.1 Nested Loops 92

6.5 Python File Handling: Open, Read, and Close 93

6.6 Python Functions 93

6.6.1 Calling a Function in Python 94

6.6.2 Scope and Lifetime of Variables 94

6.7 Problems 95

7 Algorithms 97

7.1 Introduction 97

7.2 Algorithm - Definition 97

7.3 How toWrite an Algorithm 98

7.3.1 Algorithm Analysis 99

7.3.2 Algorithm Complexity 99

7.3.3 Space Complexity 100

7.3.4 Time Complexity 100

7.4 Asymptotic Analysis of an Algorithm 101

7.4.1 Asymptotic Notations 102

7.4.1.1 Big O Notation 102

7.4.1.2 The Omega Notation, Omega 102

7.4.1.3 The Theta Notation 102

7.5 Examples of Algorithms 104

7.6 Flowchart 104

7.7 Problems 105

8 Data Preprocessing and Data Validations 109

8.1 Introduction 109

8.2 Definition - Data Preprocessing 109

8.3 Data Cleaning 110

8.3.1 Handle Missing Data 110

8.3.2 Types of Missing Data 110

8.3.2.1 Missing Completely at Random 110

8.3.2.2 Missing at Random 110

8.3.2.3 Missing Not at Random 111

8.3.3 Techniques for Handling the Missing Data 111

8.3.3.1 Listwise Deletion 111

8.3.3.2 Pairwise Deletion 111

8.3.3.3 Mean Substitution 112

8.3.3.4 Regression Imputation 112

8.3.3.5 Multiple Imputation 112

8.3.4 Identify Outliers and Noisy Data 113

8.3.4.1 Binning 113

8.3.4.2 Box Plot 113

8.4 Data Transformations 115

8.4.1 Min-Max Normalization 115

8.4.2 Z-score Normalization 115

8.5 Data Reduction 116

8.6 Data Validations 117

8.6.1 Methods for Data Validation 117

8.6.1.1 Simple Statistical Criterion 117

8.6.1.2 Fourier Series Modeling and SSC 118

8.6.1.3 Principal Component Analysis and SSC 118

8.7 Problems 119

9 Data Visualizations 121

9.1 Introduction 121

9.2 Definition - Data Visualization 121

9.2.1 Scientific Visualization 123

9.2.2 Information Visualization 123

9.2.3 Visual Analytics 124

9.3 Data Visualization Techniques 126

9.3.1 Time Series Data 126

9.3.2 Statistical Distributions 127

9.3.2.1 Stem-and-Leaf Plots 127

9.3.2.2 Q-Q Plots 127

9.4 Data Visualization Tools 129

9.4.1 Tableau 129

9.4.2 Infogram 130

9.4.3 Google Charts 132

9.5 Problems 133

10 Binomial and Trinomial Trees 135

10.1 Introduction 135

10.2 The Binomial Tree Method 135

10.2.1 One Step Binomial Tree 136

10.2.2 Using the Tree to Price a European Option 139

10.2.3 Using the Tree to Price an American Option 140

10.2.4 Using the Tree to Price Any Path Dependent Option 141

10.3 Binomial Discrete Model 141

10.3.1 One-Step Method 141

10.3.2 Multi-step Method 144

10.3.2.1 Example: European Call Option 145

10.4 Trinomial Tree Method 146

10.4.1 What is the Meaning of Little o and Big O? 147

10.5 Problems 147

11 Principal Component Analysis 151

11.1 Introduction 151

11.2 Background of Principal Component Analysis 151

11.3 Motivation 152

11.3.1 Correlation and Redundancy 152

11.3.2 Visualization 153

11.4 The Mathematics of PCA 153

11.4.1 The Eigenvalues and Eigenvectors 156

11.5 How PCAWorks 159

11.5.1 Algorithm 160

11.6 Application 161

11.7 Problems 162

12 Discriminant and Cluster Analysis 165

12.1 Introduction 165

12.2 Distance 165

12.3 Discriminant Analysis 166

12.3.1 Kullback-Leibler Divergence 167

12.3.2 Chernoff Distance 167

12.3.3 Application - Seismic Time Series 169

12.3.4 Application - Financial Time Series 171

12.3.4.1 Background of Data and Analysis 171

12.4 Cluster Analysis 173

12.4.1 Partitioning Algorithms 174

12.4.2 k-Means Algorithm 174

12.4.3 k-Medoids Algorithm 175

12.4.4 Application - Seismic Time Series 176

12.4.5 Application - Financial Time Series 176

12.5 Problems 177

13 Multidimensional Scaling 179

13.1 Introduction 179

13.2 Motivation 180

13.3 Number of Dimensions and Goodness of Fit 182

13.4 Proximity Measures 183

13.5 Metric Multidimensional Scaling 183

13.5.1 The Classical Solution 184

13.6 Nonmetric Multidimensional Scaling 186

13.6.1 Shepard-Kruskal Algorithm 186

13.7 Problem 187

14 Classification and Tree-Based Methods 191

14.1 Introduction 191

14.2 An Overview of Classification 191

14.2.1 The Classification Problem 192

14.2.2 Logistic Regression Model 192

14.2.2.1 l1 Regularization 193

14.2.2.2 l2 Regularization 194

14.3 Linear Discriminant Analysis 194

14.3.1 Optimal Classification and Estimation of Gaussian Distribution 195

14.4 Tree-Based Methods 197

14.4.1 One Single Decision Tree 197

14.4.2 Random Forest 198

14.5 Applications 200

14.6 Problems 202

15 Association Rules 205

15.1 Introduction 205

15.2 Market Basket Analysis 205

15.3 Terminologies 207

15.3.1 Itemset and Support Count 207

15.3.2 Frequent Itemset 207

15.3.3 Closed Frequent Itemset 207

15.3.4 Maximal Frequent Itemset 207

15.3.5 Association Rule 208

15.3.6 Rule Evaluation Metrics 208

15.4 The Apriori Algorithm 209

15.4.1 An example of the Apriori Algorithm 211

15.5 Applications 213

15.5.1 Confidence 214

15.5.2 Lift 215

15.5.3 Conviction 215

15.6 Problems 215

16 Support Vector Machines 219

16.1 Introduction 219

16.2 The Maximal Margin Classifier 219

16.3 Classification Using a Separating Hyperplane 223

16.4 Kernel Functions 225

16.5 Applications 225

16.6 Problems 227

17 Neural Networks 231

17.1 Introduction 231

17.2 Perceptrons 231

17.3 Feed Forward Neural Network 231

17.4 Recurrent Neural Networks 233

17.5 Long Short-Term Memory 234

17.5.1 Residual Connections 235

17.5.2 Loss Functions 236

17.5.3 Stochastic Gradient Descent 236

17.5.4 Regularization - Ensemble Learning 237

17.6 Application 237

17.6.1 Emergent and Developed Market 237

17.6.2 The Lehman Brothers Collapse 237

17.6.3 Methodology 238

17.6.4 Analyses of Data 238

17.6.4.1 Results of the Emergent Market Index 238

17.6.4.2 Results of the Developed Market Index 238

17.7 Significance of Study 239

17.8 Problems 240

18 Fourier Analysis 245

18.1 Introduction 245

18.2 Definition 245

18.3 Discrete Fourier Transform 246

18.4 The Fast Fourier Transform (FFT) Method 247

18.5 Dynamic Fourier Analysis 250

18.5.1 Tapering 251

18.5.2 Daniell Kernel Estimation 252

18.6 Applications of the Fourier Transform 253

18.6.1 Modeling Power Spectrum of Financial Returns Using Fourier

Transforms 253

18.6.1.1 Background of Data 255

18.6.2 Application of Dynamic Fourier Analysis 255

18.6.3 Image Compression 259

18.7 Problems 259

19 Wavelets Analysis 261

19.1 Introduction 261

19.1.1 Wavelets Transform 262

19.2 DiscreteWavelets Transforms (DWT) 264

19.2.1 HaarWavelets 265

19.2.1.1 Haar Functions 265

19.2.1.2 Haar Transform Matrix 266

19.2.2 DaubechiesWavelets 267

19.3 Applications of theWavelets Transform 268

19.3.1 Discriminating Between Mining Explosions and Cluster of

Earthquakes 269

19.3.1.1 Background of Data 269

19.3.1.2 Results 269

19.3.2 Finance 271

19.3.3 Damage Detection in Frame Structures 275

19.3.4 Image Compression 275

19.3.5 Seismic Signals 275

19.4 Problems 276

20 Stochastic Analysis 279

20.1 Introduction 279

20.2 Necessary Definitions from Probability Theory 279

20.3 Stochastic Processes 280

20.3.1 The Index Set 281

20.3.2 The State Space 281

20.3.3 Stationary and Independent Components 281

20.3.4 Stationary and Independent Increments 282

20.3.5 Filtration and Standard Filtration 283

20.4 Examples of Stochastic Processes 284

20.4.1 Markov Chains 284

20.4.1.1 Examples of Markov Processes 286

20.4.1.2 The Chapman-Kolmogorov Equation 287

20.4.1.3 Classification of States 288

20.4.1.4 Limiting Probabilities 289

20.4.1.5 Branching Processes 291

20.4.1.6 Time Homogeneous Chains 293

20.4.2 Martingales 293

20.4.3 Simple RandomWalk 294

20.4.4 The Brownian Motion (Wiener Process) 294

20.5 Measurable Functions and Expectations 294

20.5.1 Radon-Nikodym Theorem and Conditional Expectation 296

20.6 Problems 299

21 Fractal Analysis - Lévy, Hurst, DFA, DEA 301

21.1 Introduction and Definitions 301

21.2 Lévy Processes 301

21.2.1 Examples of Lévy Processes 304

21.2.1.1 The Poisson Process (Jumps) 305

21.2.1.2 The Compound Poisson Process 305

21.2.1.3 Inverse Gaussian (IG) Process 306

21.2.1.4 The Gamma Process 307

21.2.2 Exponential Lévy Models 307

21.2.3 Subordination of Lévy Processes 308

21.2.4 Stable Distributions 309

21.3 Lévy Flight Models 311

21.4 Rescaled Range Analysis (Hurst Analysis) 312

21.5 Detrended Fluctuation Analysis (DFA) 315

21.6 Diffusion Entropy Analysis (DEA) 316

21.6.1 Estimation Procedure 317

21.6.1.1 The Shannon Entropy 317

21.6.2 The H-alpha Relationship for the Truncated Lévy Flight 319

21.7 Application - Characterization of Volcanic Time Series 321

21.7.1 Background of Volcanic Data 321

21.7.2 Results 321

21.8 Problems 323

22 Stochastic Differential Equations 325

22.1 Introduction 325

22.2 Stochastic Differential Equations (SDEs) 325

22.2.1 Solution Methods of SDEs 326

22.3 Examples 335

22.3.1 Modeling Asset Prices 335

22.3.2 Modeling the Magnitude of Earthquake Series 336

22.4 Multidimensional Stochastic Differential Equations 337

22.4.1 The multidimensional Ornstein-Uhlenbeck Processes 337

22.4.2 Solution of the Ornstein-Uhlenbeck Process 338

22.5 Simulation of Stochastic Differential Equations 340

22.5.1 Euler-Maruyama Scheme for Approximating Stochastic Differential

Equations 340

22.5.2 Euler-Milstein Scheme for Approximating Stochastic Differential

Equations 341

22.6 Problems 343

23 Ethics: With Great Power Comes Great Responsibility 345

23.1 Introduction 345

23.2 Data Science Ethical Principles 346

23.2.1 Enhance Value in Society 346

23.2.2 Avoiding Harm 346

23.2.3 Professional Competence 347

23.2.4 Increasing Trustworthiness 348

23.2.5 Maintaining Accountability and Oversight 348

23.3 Data Science Code of Professional Conduct 348

23.4 Application 350

23.4.1 Project Planning 350

23.4.2 Data Preprocessing 350

23.4.3 Data Management 350

23.4.4 Analysis and Development 351

23.5 Problems 351

Bibliography 353

Index 359
MARIA CRISTINA MARIANI, PHD, is Shigeko K. Chan Distinguished Professor and Chair in the Department of Mathematical Sciences at The University of Texas at El Paso. She currently focuses her research on Stochastic Analysis, Differential Equations and Machine Learning with applications to Big Data and Complex Data sets arising in Public Health, Geophysics, Finance and others. Dr. Mariani is co-author of other Wiley books including Quantitative Finance.

OSEI KOFI TWENEBOAH, PHD, is Assistant Professor of Data Science at Ramapo College of New Jersey. His main research is Stochastic Analysis, Machine Learning and Scientific Computing with applications to Finance, Health Sciences, and Geophysics.

MARIA PIA BECCAR-VARELA, PHD, is Associate Professor of Instruction in the Department of Mathematical Sciences at the University of Texas at El Paso. Her research interests include Differential Equations, Stochastic Differential Equations, Wavelet Analysis and Discriminant Analysis applied to Finance, Health Sciences, and Earthquake Studies.

M. C. Mariani, University of Texas at El Paso, United States; O. K. Tweneboah, Ramapo College of New Jersey, Mahwah, United States; M. P. Beccar-Varela, University of Texas at El Paso, United States