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.

Table of Contents:
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 5 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 69 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, Ω 102 7.4.1.3 The Θ 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 Handling 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 Identifying Outliers and Noisy Data 113 8.3.4.1 Binning 113 8.3.4.2 Box and Whisker 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 145 10.3.2.1 Example: European Call Option 146 10.4 Trinomial Tree Method 147 10.4.1 What is the Meaning of Little o and Big O? 148 10.5 Problems 148 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 12.4 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 Problems 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 208 15.3.5 Association Rule 208 15.3.6 Rule Evaluation Metrics 208 15.4 The Apriori Algorithm 210 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 216 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 18.6.2 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 264 19.2.1 HaarWavelets 265 19.2.1.1 Haar Functions 265 19.2.1.2 Haar Transform Matrix 266 19.2.2 Daubechies Wavelets 267 19.3 Applications of the Wavelets Transform 269 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 285 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 289 20.4.1.4 Limiting Probabilities 290 20.4.1.5 Branching Processes 291 20.4.1.6 Time Homogeneous Chains 293 20.4.2 Martingales 294 20.4.3 Simple Random Walk 294 20.4.4 The Brownian Motion (Wiener Process) 294 20.5 Measurable Functions and Expectations 295 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–𝛼 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 325 22.2.1 Solution Methods of SDEs 326 22.3 Examples 335 22.3.1 Modeling Asset Prices 335 22.3.2 Modeling 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