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This book is a concise but thorough introduction to the tools commonly used in pattern recognition and Machine Learning, including classification, dimensionality reduction, regression, and clustering, as well as recent popular topics such as deep neural networks and Gaussian process regression. The Second Edition is thoroughly revised, featuring a new chapter on the emerging topic of physics-informed Machine Learning and additional material on deep neural networks.
Combining theory and practice, this book is suitable for the graduate or advanced undergraduate level classroom and self-study. It fills the need of a mathematically-rigorous text that is relevant to the practitioner as well, with datasets from applications in bioinformatics and materials informatics used throughout to illustrate the theory. These datasets are available from the book website to be used in end-of-chapter coding assignments based on Python and Keras/Tensorflow. All plots in the text were generated using Python scripts and Jupyter notebooks, which can be downloaded from the book website.
Introduction
Optimal Classifcation
Sample-Based Classifcation
Parametric Classifcation
Nonparametric Classifcation
Function-Approximation Classifcation
Error Estimation for Classifcation
Model Selection for Classifcation
Dimensionality Reduction
Clustering
Regression
Physics-Informed Machine Learning
Appendix
A1 Probability Theory
Asymptotic Theorems
A2 Basic Matrix Theory
A3 Basic Lagrange-Multiplier Optimization
A4 Proof of the Cover-Hart Theorem
A5 Proof of Stone’s Theorem
A6 Proof of the Vapnik-Chervonenkis Theorem
A7 Proof of Convergence of the EM Algorithm
A8 Data Sets Used in the Book