Machine Learning for the Physical Sciences: Fundamentals and Prototyping with Julia

Preface

    List of Figures

    List of Table

    SECTION I Foundations

        Chapter 1 Multivariate Calculus

            1.1 Vectors, matrices, and tensors

            1.2 Mappings and spaces

            1.3 Matrix calculus

                1.3.1 Notation

                1.3.2 Affine Map

        Chapter 2 Probability Theory

            2.1 Probability space

                2.1.1 Random Variables

                2.1.2 Conditional Probability

                2.1.3 Probability Distribution

            2.2 Information

                2.2.1 Statistical Divergence

                2.2.2 Maximum Likelihood

            2.3 Kernel density estimation

                2.3.1 Bandwidth

            2.4 Markov chains

                2.4.1 Hidden Markov Models

    SECTION II  Unsupervised Learning

        Chapter 3 Dimensionality Reduction

            3.1 Principal component analysis

                3.1.1 Correlation Matrix

                3.1.2 Explained Variance

                3.1.3 Projection on New Basis

            3.2 Singular value decomposition

                3.2.1 Pseudoinverse

            3.3 Kernel PCA

            3.4 Independent component analysis

        Chapter 4 Cluster Analysis

            4.1 K-Means and k-Medoids

                4.1.1 Silhouette

            4.2 DBScan

            4.3 Hierarchical clustering

                4.3.1 AGNES

                4.3.2 DIANA

            4.4 Spectral clustering

        Chapter 5 Vector Quantization Techniques

            5.1 Simple vector quantization

            5.2 Self-organizing map

            5.3 Neural gas

                5.3.1 Growing Neural Gas

            5.4 Voronoi and Delaunay diagrams

    SECTION III Supervised Learning

        Chapter 6 Regression Models

            6.1 Bias-variance trade-off

            6.2 Simple linear regression

                6.2.1 Goodness of Fit

            6.3 Multivariate linear regression

                6.3.1 Bayesian Approach

            6.4 Regularization

                6.4.1 Least Angle Regression

            6.5 Non-linear regression

            6.6 Gaussian process regression

        Chapter 7 Classification

            7.1 Logistic regression

            7.2 Classification and regression trees

                7.2.1 Boosting

            7.3 Support vector machines

                7.3.1 Soft Margins

            7.4 Naïve Bayes

    SECTION IV Neuronal-Inspired Learning

        Chapter 8 Feedforward Networks

            8.1 McCulloch-Pitts artificial neuron

                8.1.1 Perceptron

            8.2 Multilayer perceptron

                8.2.1 Optimization Strategies

            8.3 Autoencoders and generative Models

                8.3.1 Variational Autoencoders

                8.3.2 Diffusion Models

                8.3.3 Generative-Adversarial Networks

        Chapter 9 Advanced Network Architectures

            9.1 Convolutional neural networks

            9.2 Recurrent networks

                9.2.1 Attention Mechanism

            9.3 Hopfield network

                9.3.1 Training

                9.3.2 Energy and Asynchronous Update

                9.3.3 Capacity and Cross-Talk

            9.4 Boltzmann machines

    SECTION V Reinforcement Learning

        Chapter 10 Value Methods

            10.1 Dynamic programming

            10.2 Monte Carlo and temporal difference

                10.2.1 Exploitation vs. Exploration

            10.3 SARSA and Q-Learning

        Chapter 11 Gradient Methods

            11.1 REINFORCE

                11.1.1 A Simple Game

            11.2 Actor-critic

                11.2.1 Advantage Actor-Critic

            11.3 Trust region methods

    SECTION VI Optimization

        Chapter 12 Population-Based Metaheuristic Methods

            12.1 Genetic algorithms and evolution strategy

                12.1.1 Selection

                12.1.2 Crossover

                12.1.3 Mutation

                12.1.4 Survivor Selection and Termination

            12.2 Particle swarm optimization

            12.3 Stigmergy algorithms

        Chapter 13 Local Search Methods

            13.1 Amoeba optimization

            13.2 Simmulated annealing

            13.3 Closing remarks

    Appendix A Sufficient Statistic

    Appendix B Graphs

    Appendix C Sequential Minimization Optimization

    Appendix D Algorithmic Differentiation

    Appendix E Batch Normalizing Transform

    Appendix F Divergence of two Gaussian Distributions

    Appendix G Continuous-time Bellman\'s Equation

    Appendix H Conjugate Gradient

    Appendix I Importance Sampling

    References

    Index