Statistical inference and machine learning for big data / / Mayer Alvo

• Record Nr.: UNISA996499866303316
• Autore: Alvo Mayer
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2022]; ©2022
• ISBN: 9783031067846; 9783031067839
• Descrizione fisica: 1 online resource (442 pages)
• Collana: Springer series in the data sciences
• Disciplina: 005.7
• Soggetti: Big data; Machine learning; Mathematical statistics; Dades massives; Aprenentatge automàtic; Estadística matemàtica; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Acknowledgments -- Contents -- List of Acronyms -- List of Nomenclatures -- List of Figures -- List of Tables -- I. Introduction to Big Data -- 1. Examples of Big Data -- 1.1. Multivariate Data -- 1.2. Categorical Data -- 1.3. Environmental Data -- 1.4. Genetic Data -- 1.5. Time Series Data -- 1.6. Ranking Data -- 1.7. Social Network Data -- 1.8. Symbolic Data -- 1.9. Image Data -- II. Statistical Inference for Big Data -- 2. Basic Concepts in Probability -- 2.1. Pearson System of Distributions -- 2.2. Modes of Convergence -- 2.3. Multivariate Central Limit Theorem -- 2.4. Markov Chains -- 3. Basic Concepts in Statistics -- 3.1. Parametric Estimation -- 3.2. Hypothesis Testing -- 3.3. Classical Bayesian Statistics -- 4. Multivariate Methods -- 4.1. Matrix Algebra -- 4.2. Multivariate Analysis as a Generalization of Univariate Analysis -- 4.2.1. The General Linear Model -- 4.2.2. One Sample Problem -- 4.2.3. Two-Sample Problem -- 4.3. Structure in Multivariate Data Analysis -- 4.3.1. ; Principal Component Analysis -- 4.3.2. Factor Analysis -- 4.3.3. Canonical Correlation -- 4.3.4. Linear Discriminant Analysis -- 4.3.5. Multidimensional Scaling -- 4.3.6. Copula Methods -- 5. Nonparametric Statistics -- 5.1. Goodness-of-Fit Tests -- 5.2. Linear Rank Statistics -- 5.3. U Statistics -- 5.4. Hoeffding's Combinatorial Central Limit Theorem -- 5.5. Nonparametric Tests -- 5.5.1. One-Sample Tests of Location -- 5.5.2. Confidence Interval for the Median -- 5.5.3. Wilcoxon Signed Rank Test -- 5.6. Multi-Sample Tests -- 5.6.1. Two-Sample Tests for Location -- 5.6.2. Multi-Sample Test for Location -- 5.6.3. Tests for Dispersion -- 5.7. Compatibility -- 5.8. Tests for Ordered Alternatives -- 5.9. A Unified Theory of Hypothesis Testing -- 5.9.1. Umbrella Alternatives -- 5.9.2. Tests for Trend in Proportions -- 5.10. Randomized Block Designs.; 5.11. Density Estimation -- 5.11.1. Univariate Kernel Density Estimation -- 5.11.2. The Rank Transform -- 5.11.3. Multivariate Kernel Density Estimation -- 5.12. Spatial Data Analysis -- 5.12.1. Spatial Prediction -- 5.12.2. Point Poisson Kriging of Areal Data -- 5.13. Efficiency -- 5.13.1. Pitman Efficiency -- 5.13.2. Application of Le Cam's Lemmas -- 5.14. Permutation Methods -- 6. Exponential Tilting and Its Applications -- 6.1. Neyman Smooth Tests -- 6.2. Smooth Models for Discrete Distributions -- 6.3. Rejection Sampling -- 6.4. Tweedie's Formula: Univariate Case -- 6.5. Tweedie's Formula: Multivariate Case -- 6.6. The Saddlepoint Approximation and Notions of Information -- 7. Counting Data Analysis -- 7.1. Inference for Generalized Linear Models -- 7.2. Inference for Contingency Tables -- 7.3. Two-Way Ordered Classifications -- 7.4. Survival Analysis -- 7.4.1. Kaplan-Meier Estimator -- 7.4.2. Modeling Survival Data -- 8. Time Series Methods -- 8.1. Classical Methods of Analysis -- 8.2. State Space Modeling -- 9. Estimating Equations -- 9.1. Composite Likelihood -- 9.2. Empirical Likelihood -- 9.2.1. Application to One-Sample Ranking Problems -- 9.2.2. Application to Two-Sample Ranking Problems -- 10. Symbolic Data Analysis -- 10.1. Introduction -- 10.2. Some Examples -- 10.3. Interval Data -- 10.3.1. Frequency -- 10.3.2. Sample Mean and Sample Variance -- 10.3.3. Realization In SODAS -- 10.4. Multi-nominal Data -- 10.4.1. Frequency -- 10.5. Symbolic Regression -- 10.5.1. Symbolic Regression for Interval Data -- 10.5.2. Symbolic Regression for Modal Data -- 10.5.3. Symbolic Regression in SODAS -- 10.6. Cluster Analysis -- 10.7. Factor Analysis -- 10.8. Factorial Discriminant Analysis -- 10.9. Application to Parkinson's Disease -- 10.9.1. Data Processing -- 10.9.2. Result Analysis -- 10.9.2.1. Viewer -- 10.9.2.2. Descriptive Statistics.; 10.9.2.3. Symbolic Regression Analysis -- 10.9.2.4. Symbolic Clustering -- 10.9.2.5. Principal Component Analysis -- 10.9.3. Comparison with Classical Method -- 10.10. Application to Cardiovascular Disease Analysis -- 10.10.1. Results of the Analysis -- 10.10.2. Comparison with the Classical Method -- III. Machine Learning for Big Data -- 11. Tools for Machine Learning -- 11.1. Regression Models -- 11.2. Simple Linear Regression -- 11.2.1. Least Squares Method -- 11.2.2. Statistical Inference on Regression Coefficients -- 11.2.3. Verifying the Assumptions on the Error Terms -- 11.3. Multiple Linear Regression -- 11.3.1. Multiple Linear Regression Model -- 11.3.2. Normal Equations -- 11.3.3. Statistical Inference on Regression Coefficients -- 11.3.4. Model Fit Evaluation -- 11.4. Regression in Machine Learning -- 11.4.1. Optimization for Linear Regression in Machine Learning -- 11.4.1.1. Gradient Descent -- 11.4.1.2. Feature Standardization -- 11.4.1.3. Computing Cost on a Test Set -- 11.5. Classification Models -- 11.5.1. Logistic Regression -- 11.5.1.1. Optimization with Maximal Likelihood for Logistic Regression -- ; 11.5.1.2. Statistical Inference -- 11.5.2. Logistic Regression for Binary Classification -- 11.5.2.1. Kullback-Leibler Divergence -- 11.5.3. Logistic Regression with Multiple Response Classes -- 11.5.4. Regularization for Regression Models in Machine Learning -- 11.5.4.1. Ridge Regression -- 11.5.4.2. Lasso Regression -- 11.5.4.3. The Choice of Regularization Method -- 11.5.5. Support Vector Machines (SVM) -- 11.5.5.1. Introduction -- 11.5.5.2. Finding the Optimal Hyperplane -- 11.5.5.3. SVM for Nonlinearly Separable Data Sets -- 11.5.5.4. Illustrating SVM -- 12. Neural Networks -- 12.1. Feed-Forward Networks -- 12.1.1. Motivation -- 12.1.2. Introduction to Neural Networks -- 12.1.3. Building a Deep Feed-Forward Network.; 12.1.4. Learning in Deep Networks -- 12.1.4.1. Quantitative Model -- 12.1.4.2. Binary Classification Model -- 12.1.5. Generalization -- 12.1.5.1. A Machine Learning Approach to Generalization -- 12.2. Recurrent Neural Networks -- 12.2.1. Building a Recurrent Neural Network -- 12.2.2. Learning in Recurrent Networks -- 12.2.3. Most Common Design Structures of RNNs -- 12.2.4. Deep RNN -- 12.2.5. Bidirectional RNN -- 12.2.6. Long-Term Dependencies and LSTM RNN -- 12.2.7. Reduction for Exploding Gradients -- 12.3. Convolution Neural Networks -- 12.3.1. Convolution Operator for Arrays -- 12.3.1.1. Properties of the Convolution Operator -- 12.3.2. Convolution Layers -- 12.3.3. Pooling Layers -- 12.4. Text Analytics -- 12.4.1. Introduction -- 12.4.2. General Architecture -- IV. Computational Methods for Statistical Inference -- 13. Bayesian Computation Methods -- 13.1. Data Augmentation Methods -- 13.2. Metropolis-Hastings Algorithm -- 13.3. Gibbs Sampling -- 13.4. EM Algorithm -- 13.4.1. Application to Ranking -- 13.4.2. Extension to Several Populations -- 13.5. Variational Bayesian Methods -- 13.5.1. Optimization of the Variational Distribution -- 13.6. Bayesian Nonparametric Methods -- 13.6.1. Dirichlet Prior -- 13.6.2. The Poisson-Dirichlet Prior -- 13.6.3. Simulation of Bayesian Posterior Distributions -- 13.6.4. Other Applications -- Bibliography -- Index.