Foundations of Predictive Analytics

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ISBN: 9781439869468 | 1439869464
Cover: Hardcover
Copyright: 2/15/2012

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Written by industry experts, this book introduces the various concepts, theorems, and algorithms widely used in statistical data analysis and data mining. It covers important topics in data mining, machine learning, and statistical pattern recognition, including linear and nonlinear regression models, time series analysis, and variable selection. The text also explores key topics that are not extensively covered in similar books, such as copula functions, incremental regression, censored data models, Dempster-Shafer theory, survival data analysis, and GARCH.

List of Figures	p. xv
List of Tables	p. xvii
Preface	p. xix
Introduction	p. 1
What Is a Model?	p. 1
What Is a Statistical Model?	p. 2
The Modeling Process	p. 3
Modeling Pitfalls	p. 4
Characteristics of Good Modelers	p. 5
The Future of Predictive Analytics	p. 7
Properties of Statistical Distributions	p. 9
Fundamental Distributions	p. 9
Uniform Distribution	p. 9
Details of the Normal (Gaussian) Distribution	p. 10
Lognormal Distribution	p. 19
¿ Distribution	p. 20
Chi-Squared Distribution	p. 22
Non-Central Chi-Squared Distribution	p. 25
Student's t-Distribution	p. 28
Multivariate t-Distribution	p. 29
F-Distribution	p. 31
Binomial Distribution	p. 31
Poisson Distribution	p. 32
Exponential Distribution	p. 32
Geometric Distribution	p. 33
Hypergeometric Distribution	p. 33
Negative Binomial Distribution	p. 34
Inverse Gaussian (IG) Distribution	p. 35
Normal Inverse Gaussian (NIG) Distribution	p. 36
Central Limit Theorem	p. 38
Estimate of Mean, Variance, Skewness, and Kurtosis from Sample Data	p. 40
Estimate of the Standard Deviation of the Sample Mean	p. 40
(Pseudo) Random Number Generators	p. 41
Mersenne Twister Pseudorandom Number Generator	p. 42
Box-Muller Transform for Generating a Normal Distribution	p. 42
Transformation of a Distribution Function	p. 43
Distribution of a Function of Random Variables	p. 43
Z = X + Y	p. 44
Z = XY	p. 44
(Z₁,Z₂,…,Z_n) = (X₁,X₂,…,X_n) Y	p. 44
Z = X/Y	p. 45
Z = max(X,Y)	p. 45
Z = min(X,Y)	p. 45
Moment Generating Function	p. 46
Moment Generating Function of Binomial Distribution	p. 46
Moment Generating Function of Normal Distribution	p. 47
Moment Generating Function of the ¿ Distribution	p. 47
Moment Generating Function of Chi-Square Distribution	p. 47
Moment Generating Function of the Poisson Distribution	p. 48
Cumulant Generating Function	p. 48
Characteristic Function	p. 50
Relationship between Cumulative Function and Characteristic Function	p. 51
Characteristic Function of Normal Distribution	p. 52
Characteristic Function of ¿ Distribution	p. 52
Chebyshev's Inequality	p. 53
Markov's Inequality	p. 54
Gram-Charlier Series	p. 54
Edgeworth Expansion	p. 55
Cornish-Fisher Expansion	p. 56
Lagrange Inversion Theorem	p. 56
Cornish-Fisher Expansion	p. 57
Copula Functions	p. 58
Gaussian Copula	p. 60
t-Copula	p. 61
Archimedean Copula	p. 62
Important Matrix Relationships	p. 63
Pseudo-Inverse of a Matrix	p. 63
A Lemma of Matrix Inversion	p. 64
Identity for a Matrix Determinant	p. 66
Inversion of Partitioned Matrix	p. 66
Determinant of Partitioned Matrix	p. 67
Matrix Sweep and Partial Correlation	p. 67
Singular Value Decomposition (SVD)	p. 69
Diagonalization of a Matrix	p. 71
Spectral Decomposition of a Positive Semi-Definite Matrix	p. 75
Normalization in Vector Space	p. 76
Conjugate Decomposition of a Symmetric Definite Matrix	p. 77
Cholesky Decomposition	p. 77
Cauchy-Schwartz Inequality .	p. 80
Relationship of Correlation among Three Variables	p. 81
Linear Modeling and Regression	p. 83
Properties of Maximum Likelihood Estimators	p. 84
Likelihood Ratio Test	p. 87
Wald Test	p. 87
Lagrange Multiplier Statistic	p. 88
Linear Regression	p. 88
Ordinary Least Squares (OLS) Regression	p. 89
Interpretation of the Coefficients of Linear Regression	p. 95
Regression on Weighted Data	p. 97
Incrementally Updating a Regression Model with Additional Data	p. 100
Partitioned Regression	p. 101
How Does the Regression Change When Adding One More Variable?	p. 101
Linearly Restricted Least Squares Regression	p. 103
Significance of the Correlation Coefficient	p. 105
Partial Correlation	p. 105
Ridge Regression	p. 105
Fisher's Linear Discriminant Analysis	p. 106
Principal Component Regression (PCR)	p. 109
Factor Analysis	p. 110
Partial Least Squares Regression (PLSR)	p. 111
Generalized Linear Model (GLM)	p. 113
Logistic Regression: Binary	p. 116
Logistic Regression: Multiple Nominal	p. 119
Logistic Regression: Proportional Multiple Ordinal	p. 121
Fisher Scoring Method for Logistic Regression . .	p. 123
Tobit Model: A Censored Regression Model	p. 125
Some Properties of the Normal Distribution	p. 125
Formulation of the Tobit Model	p. 126
Nonlinear Modeling	p. 129
Naive Bayesian Classifier	p. 129
Neural Network	p. 131
Back Propagation Neural Network	p. 131
Segmentation and Tree Models	p. 137
Segmentation	p. 137
Tree Models	p. 138
Sweeping to Find the Best Cutpoint	p. 140
Impurity Measure of a Population: Entropy and Gini Index	p. 143
Chi-Square Splitting Rule	p. 147
Implementation of Decision Trees	p. 148
Additive Models	p. 151
Boosted Tree	p. 153
Least Squares Regression Boosting Tree	p. 154
Binary Logistic Regression Boosting Tree	p. 155
Support Vector Machine (SVM)	p. 158
Wolfe Dual	p. 158
Linearly Separable Problem	p. 159
Linearly Inseparable Problem	p. 161
Constructing Higher-Dimensional Space and Kernel	p. 162
Model Output	p. 163
C-Support Vector Classification (C-SVC) for Classification	p. 164
¿-Support Vector Regression (¿-SVR) for Regression	p. 164
The Probability Estimate	p. 167
Fuzzy Logic System	p. 168
A Simple Fuzzy Logic System	p. 168
Clustering	p. 169
K Means, Fuzzy C Means	p. 170
Nearest Neighbor, K Nearest Neighbor (KNN	p. 171
Comments on Clustering Methods	p. 171
Time Series Analysis	p. 173
Fundamentals of Forecasting	p. 173
Box-Cox Transformation	p. 174
Smoothing Algorithms	p. 175
Convolution of Linear Filters	p. 176
Linear Difference Equation	p. 177
The Autocovariance Function and Autocorrelation Function	p. 178
The Partial Autocorrelation Function	p. 179
ARIMA Models	p. 181
MA(q) Process	p. 182
AR(p) Process	p. 184
ARMA(p, q) Process	p. 186
Survival Data Analysis	p. 187
Sampling Method	p. 190
Exponentially Weighted Moving Average (EWMA) and GARCH(1, 1)	p. 191
Exponentially Weighted Moving Average (EWMA)	p. 191
ARCH and GARCH Models	p. 192
Data Preparation and Variable Selection	p. 195
Data Quality and Exploration	p. 196
Variable Scaling and Transformation	p. 197
How to Bin Variables .	p. 197
Equal Interval	p. 198
Equal Population	p. 198
Tree Algorithms	p. 199
Interpolation in One and Two Dimensions	p. 199
Weight of Evidence (WOE) Transformation	p. 200
Variable Selection Overview	p. 204
Missing Data Imputation	p. 206
Stepwise Selection Methods	p. 207
Forward Selection in Linear Regression	p. 208
Forward Selection in Logistic Regression	p. 208
Mutual Information, KL Distance	p. 209
Detection of Multicollinearity	p. 210
Model Goodness Measures	p. 213
Training, Testing, Validation	p. 213
Continuous Dependent Variable	p. 215
Example: Linear Regression	p. 217
Binary Dependent Variable (Two-Group Classification)	p. 218
Kolmogorov-Smirnov (KS) Statistic	p. 218
Confusion Matrix	p. 220
Concordant and Discordant	p. 221
R² for Logistic Regression	p. 223
AIC and SBC	p. 224
Hosmer-Lemeshow Goodness-of-Fit Test	p. 224
Example: Logistic Regression	p. 225
Population Stability Index Using Relative Entropy	p. 227
Optimization Methods	p. 231
Lagrange Multiplier	p. 232
Gradient Descent Method	p. 234
Newton-Raphson Method	p. 236
Conjugate Gradient Method	p. 238
Quasi-Newton Method	p. 240
Genetic Algorithms (GA)	p. 242
Simulated Annealing	p. 242
Linear Programming	p. 243
Nonlinear Programming (NLP)	p. 247
General Nonlinear Programming (GNLP)	p. 248
Lagrange Dual Problem	p. 249
Quadratic Programming (QP)	p. 250
Linear Complementarity Programming (LCP	p. 254
Sequential Quadratic Programming (SQP)	p. 256
Nonlinear Equations	p. 263
Expectation-Maximization (EM) Algorithm	p. 264
Optimal Design of Experiment	p. 268
Miscellaneous Topics	p. 271
Multidimensional Scaling	p. 271
Simulation	p. 274
Odds Normalization and Score Transformation	p. 278
Reject Inference	p. 280
Dempster-Shafer Theory of Evidence	p. 281
Some Properties in Set Theory	p. 281
Basic Probability Assignment, Belief Function, and Plausibility Function	p. 282
Dempster-Shafer's Rule of Combination	p. 285
Applications of Dempster-Shafer Theory of Evidence: Multiple Classifier Function	p. 287
Useful Mathematical Relations	p. 291
Information Inequality	p. 291
Relative Entropy	p. 291
Saddle-Point Method	p. 292
Stirling's Formula	p. 293
Convex Function and Jensen's Inequality	p. 294
DataMinerXL - Microsoft Excel Add-In for Building Predictive Models	p. 299
Overview	p. 299
Utility Functions	p. 299
Data Manipulation Functions	p. 300
Basic Statistical Functions	p. 300
Modeling Functions for All Models	p. 301
Weight of Evidence Transformation Functions	p. 301
Linear Regression Functions	p. 302
Partial Least Squares Regression Functions	p. 302
Logistic Regression Functions	p. 303
Time Series Analysis Functions	p. 303
Naive Bayes Classifier Functions	p. 303
Tree-Based Model Functions	p. 304
Clustering and Segmentation Functions	p. 304
Neural Network Functions	p. 304
Support Vector Machine Functions	p. 304
Optimization Functions	p. 305
Matrix Operation Functions	p. 305
Numerical Integration Functions	p. 306
Excel Built-in Statistical Distribution Functions	p. 306
Bibliography	p. 309
Index	p. 313
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Foundations of Predictive Analytics

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Table of Contents

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