Theoretical Foundation of Data Science presents the latest in data science, an area that is penetrating into virtually every discipline of science, engineering, and medicine, and is a fast evolving field. Practitioners, researchers, and graduate students often have difficulty in understanding the foundation of data science. In order to have a deep understanding of data science, a strong understanding of statistical analysis and machine learning is a must. This book introduces the commonly used statistical principles behind many machine learning and data mining algorithms, the connections of those principles, and the connections of those principles to commonly utilized data analytic algorithms. Presents an ideal guide for readers that want to go deep into the basics of statistics and probability and how it applies to data sciencellustrates the connection of widely used data analytics methods and statistical and computational principlesPresents applied examples from several disciplines including, but not limited to, computer science, engineering and medicineDiscusses extensive experimental results using real application datasets to demonstrate the performance of statistical and machine learning techniques INDICE: Preface i 1 Probability Theory and LLN 1 1.1 Basic Probability Theory 1.2 Law of Large Numbers 1.3 Moment generating function 2 Maximum Likelihood Estimation 5 2.1 Maximum Likelihood Estimator 2.2 Properties of MLE 3 Linear Regression 10 3.1 Linear Regression in One Dimensional Space 3.2 Linear Regression in High Dimensional Space 3.3 Least Square Fitting and Maximum Likelihood Estimation 3.4 Linear Regression with Least Squre Fitting is Consistent 3.5 Generalization Error of Prediction Estimation 3.6 Avoid Overfitting 4 Ridge Regression 15 4.1 Unstable Parameter Estiamtion in Linear Regression 4.2 Ridge regression 4.3 Kernel regression: Non-linear Regression with Linear Relationship 5 Linear Classification 18 5.1 Logistic regression 5.2 Recall Kernel regression 6 Akaike Information Criterion(AIC) 22 6.1 Preliminaries 6.2 Why MLE does not work 7 Support Vector Machines 24 7.1 Large Margin Classifier 7.2 Hinge Loss and Regularized Loss Function Minimization 7.3 Probabilistic Approximately Correct (PAC) 8 Statistical Learning Theory 28 8.1 Rademacher Complexity 8.2 Bound on Rademacher Complexity for Kernel-Based Hypothesis 9 Statistical Decision Theory 31 9.1 Risk 10 Exchangeability 34 10.1 Prior Exchangeability (Independence) 10.2 Bernoulli R.V. & Exchangeability 10.2.1 Example 10.2.2 Thought Experiment 11 Bayesian Linear Regression 36 11.1 Multi-Dimensional Gaussian 11.2 Conditional Gaussian 11.3 Bayesian Linear Regression 12 Gaussian Process 41 13 Ensemble learning 43 13.1 Weak classifier 13.2 Ada boost 13.3 Alternative approach 14 Optimization 45 14.1 Machine Learning from an Optimization Perspective A Real Number and Vector Space 47 A.1 Natural number A.2 Integers A.3 Rational number A.4 Real number B Vector Space 50 B.1 Function space B.2 Function convergence C Advanced Probability and SLLN 53 C.1 Measure Theory C.1.1 Measurable Sets and Events C.2.2 Measures and Probability C.3.3 Measurable Functions and Random Variables C.2 Types of Convergence C.2.1 Convergence of Events C.2.2 Convergence of Random Variables C.3 Strong Law of Large Numbers
- ISBN: 978-0-12-803655-6
- Editorial: Morgan Kaufmann
- Encuadernacion: Rústica
- Páginas: 256
- Fecha Publicación: 15/09/2016
- Nº Volúmenes: 1
- Idioma: Inglés