b. Hybrid EP-variational inference methods D. Laplace approximation 1. Gaussian approximation to the posterior a. Taylor series expansion and local curvature b. Multivariate Gaussian approximation 2. Hessian matrix and its computation a. Finite differences and automatic differentiation b. Quasi-Newton methods and Hessian-free optimization IV. Model Selection and Evaluation A. Bayesian model selection 1. Bayes factors and marginal likelihood a. Laplace approximation and importance sampling for marginal likelihood b. Savage-Dickey density ratio and harmonic mean estimator 2. Bayesian information criterion (BIC) and its variants a. Schwarz criterion and its derivation b. Deviance information criterion (DIC) and its limitations 3. Bayesian model averaging and its applications a. Posterior model probabilities and model uncertainty b. Bayesian model combination and ensemble learning B. Cross-validation and information criteria 1. Leave-one-out cross-validation (LOO-CV) a. Exact LOO-CV and its computational challenges b. Pareto-smoothed importance sampling (PSIS) for LOO-CV 2. Watanabe-Akaike information criterion (WAIC) a. Pointwise predictive accuracy and effective number of parameters b. Comparison with other information criteria C. Bayesian optimization for hyperparameter tuning 1. Acquisition functions and their properties a. Expected improvement, probability of improvement, and upper confidence bound b. Entropy search and knowledge gradient methods 2. Gaussian process-based optimization a. Surrogate modeling with Gaussian processes b. Batch Bayesian optimization and parallel evaluations V. Applications of Bayesian Machine Learning A. Bayesian active learning 1. Uncertainty sampling and query strategies a. Least confidence, margin sampling, and entropy-based methods b. Expected model change and expected error reduction 2. Bayesian optimization for active learning a. Information-theoretic acquisition functions b. Multi-task and transfer learning in active learning B. Bayesian reinforcement learning 1. Bayesian Q-learning and value function approximation a. Gaussian process regression for Q-function modeling b. Bayesian deep Q-networks and uncertainty-aware exploration 2. Thompson sampling and posterior sampling reinforcement learning a. Exploration-exploitation trade-off and regret analysis b. Contextual bandits and multi-armed bandits 3. Bayesian policy search and model-based reinforcement learning a. Gaussian process dynamics models and model predictive control b. Variational inference for policy optimization C. Bayesian deep learning 1. Bayesian convolutional neural networks a. Variational inference and Monte Carlo dropout for CNNs b. Uncertainty estimation and calibration in deep learning 2. Bayesian recurrent neural networks a. Variational inference and stochastic gradient variational Bayes for RNNs b. Bayesian long short-term memory (LSTM) and gated recurrent units (GRUs) 3. Variational autoencoders and generative models a. Bayesian variational autoencoders and their extensions b. Bayesian generative adversarial networks (GANs) and adversarial variational Bayes VI. Software and Tools for Bayesian Machine Learning A. Probabilistic programming languages 1. Stan and its ecosystem a. Hamiltonian Monte Carlo and variational inference in Stan b. R and Python interfaces for Stan (RStan and PyStan) 2. PyMC3 and its features a. Theano-based probabilistic programming in Python b. Variational inference and Gaussian processes in PyMC3 3. Edward and TensorFlow Probability a. Probabilistic programming with TensorFlow b. Variational inference, MCMC, and probabilistic layers in TFP B. Bayesian libraries and frameworks 1. GPflow and GPy for Gaussian processes a. Sparse Gaussian processes and variational inference in GPflow b. Kernel design and hyperparameter optimization in GPy 2. BayesOpt and GPyOpt for Bayesian optimization a. Gaussian process-based optimization in Python and MATLAB b. Parallel and batch Bayesian optimization with GPyOpt 3. PyBayes and BayesPy for general Bayesian modeling a. Variational inference and expectation propagation in PyBayes b. Modular and extensible Bayesian modeling with BayesPy This expanded map delves deeper into each topic, providing more granular details and sub-topics within each section. It covers a wider range of Bayesian models, inference methods, and applications, as well as additional software tools and libraries. The map also includes more mathematical and algorithmic details, such as specific optimization techniques, sampling methods, and model evaluation metrics. With this level of detail, the map serves as a comprehensive reference for researchers and practitioners working in the field of Bayesian machine learning. Here is an expanded and more detailed map of the field of evolutionary machine learning: Evolutionary Machine Learning ├── Evolutionary Algorithms │ ├── Genetic Algorithms (GAs) │ │ ├── Representation │ │ │ ├── Binary Encoding │ │ │ ├── Real-Valued Encoding │ │ │ ├── Permutation Encoding │ │ │ └── Tree Encoding │ │ ├── Selection Methods │ │ │ ├── Roulette Wheel Selection │ │ │ ├── Stochastic Universal Sampling │ │ │ ├── Tournament Selection │ │ │ ├── Rank Selection │ │ │ ├── Boltzmann Selection │ │ │ └── Elitism │ │ ├── Crossover Operators │ │ │ ├── Single-Point Crossover │ │ │ ├── Two-Point Crossover │ │ │ ├── Multi-Point Crossover │ │ │ ├── Uniform Crossover │ │ │ ├── Arithmetic Crossover │ │ │ ├── Blend Crossover (BLX-α) │ │ │ ├── Simulated Binary Crossover (SBX) │ │ │ └── Partially Mapped Crossover (PMX) │ │ ├── Mutation Operators │ │ │ ├── Bit-Flip Mutation │ │ │ ├── Gaussian Mutation │ │ │ ├── Uniform Mutation │ │ │ ├── Swap Mutation │ │ │ ├── Scramble Mutation │ │ │ ├── Inversion Mutation │ │ │ └── Polynomial Mutation │ │ └── Constraint Handling Techniques │ │ ├── Penalty Functions │ │ ├── Repair Mechanisms │ │ ├── Decoder-Based Approaches │ │ └── Multi-Objective Approaches │ │ │ ├── Genetic Programming (GP) │ │ ├── Tree-Based GP │ │ │ ├── Function Set │ │ │ ├── Terminal Set │ │ │ ├── Initialization Methods │ │ │ │ ├── Full Initialization │ │ │ │ ├── Grow Initialization │ │ │ │ └── Ramped Half-and-Half Initialization │ │ │ ├── Crossover Methods │ │ │ │ ├── Subtree Crossover │ │ │ │ ├── Size-Fair Crossover │ │ │ │ └── Homologous Crossover │ │ │ └── Mutation Methods │ │ │ ├── Subtree Mutation │ │ │ ├── Point Mutation │ │ │ ├── Hoist Mutation │ │ │ └── Shrink Mutation │ │ ├── Linear GP │ │ │ ├── Machine Code GP │ │ │ └── Finite State Machine GP │ │ ├── Graph-Based GP │ │ │ ├── Cartesian GP │ │ │ └── Parallel Distributed GP │ │ └── Grammar-Based GP │ │ ├── Context-Free Grammar GP │ │ ├── Attribute Grammar GP │ │ └── Grammatical Evolution │ │ │ ├── Evolution Strategies (ES) │ │ ├── (1+1)-ES │ │ ├── (μ+λ)-ES │ │ ├── (μ,λ)-ES │ │ ├── Covariance Matrix Adaptation ES (CMA-ES) │ │ │ ├── Single-Objective CMA-ES │ │ │ └── Multi-Objective CMA-ES │ │ ├── Natural Evolution Strategies (NES) │ │ │ ├── Exponential NES (xNES) │ │ │ └── Separable NES (sNES) │ │ └── Evolutionary Gradient Search (EGS) │ │ │ └── Differential Evolution (DE) │ ├── Mutation Strategies │ │ ├── DE/rand/1 │ │ ├── DE/best/1 │ │ ├── DE/current-to-best/1 │ │ ├── DE/best/2 │ │ ├── DE/rand/2 │ │ └── DE/current-to-rand/1 │ ├── Crossover Methods │ │ ├── Binomial Crossover │ │ └── Exponential Crossover │ ├── Parameter Adaptation │ │ ├── Self-Adaptive DE │ │ ├── Adaptive DE (jDE) │ │ └── Fuzzy Adaptive DE (FADE) │ └── Constrained Optimization │ ├── Constraint Handling Techniques │ └── Multi-Objective DE ├── Evolutionary Neural Networks │ ├── Neuroevolution │ │ ├── Direct Encoding │ │ │ ├── Fixed Topology │ │ │ │ ├── Conventional Neuroevolution (CNE) │ │ │ │ ├── Symbiotic Adaptive Neuroevolution (SANE) │ │ │ │ └── Evolutionary Programming with Neural Networks (EPNN) │ │ │ └── Variable Topology │ │ │ ├── NeuroEvolution of Augmenting Topologies (NEAT) │ │ │ ├── HyperNEAT │ │ │ ├── Evolutionary Acquisition of Neural Topologies (EANT) │ │ │ └── Genetic Algorithm for Evolving Network Topology (GANET) │ │ └── Indirect Encoding │ │ ├── Developmental Encoding │ │ │ ├── Cellular Encoding │ │ │ ├── Graph Generation Grammar Encoding │ │ │ └── L-System Encoding │ │ ├── Grammatical Encoding │ │ │ ├── Cellular Automata-Based Encoding │ │ │ └── Lindenmayer System-Based Encoding │ │ └── Parametric Encoding │ │ ├── Compositional Pattern Producing Networks (CPPNs) │ │ └── Artificial Gene Regulatory Networks (AGRNs) │ │ │ ├── Evolutionary Training of Neural Networks │ │ ├── Evolutionary Optimization of Weights │ │ │ ├── Conventional Neuroevolution │ │ │ ├── Cooperative Coevolution │ │ │ ├── Memetic Algorithms │ │ │ └── Lamarckian Evolution │ │ ├── Evolutionary Optimization of Architectures │ │ │ ├── Evolutionary Neural Architecture Search (ENAS) │ │ │ ├── Neural Architecture Search by Evolutionary Algorithms (NASEA) │ │ │ └── Evolutionary Deep Intelligence (EDI) │ │ └── Evolutionary Optimization of Learning Rules │ │ ├── Evolved Plasticity Rules │ │ ├── Evolved Hebbian Learning Rules │ │ └── Evolved Gradient Descent Rules │ │ │ └── Evolutionary Feature Selection and Extraction │ ├── Evolutionary Feature Selection │ │ ├── Filter Approaches │ │ ├── Wrapper Approaches │ │ └── Embedded Approaches │ └── Evolutionary Feature Extraction │ ├── Linear Feature Extraction │ │ ├── Evolutionary Principal Component Analysis (EPCA) │ │ └── Evolutionary Linear Discriminant Analysis (ELDA) │ └── Nonlinear Feature Extraction │ ├── Evolutionary Kernel Principal Component Analysis (EKPCA) │ └── Evolutionary Manifold Learning ├── Evolutionary Fuzzy Systems │ ├── Evolutionary Design of Fuzzy Rules │ │ ├── Michigan Approach │ │ ├── Pittsburgh Approach │ │ └── Iterative Rule Learning Approach │ ├── Evolutionary Optimization of Fuzzy Membership Functions │ │ ├── Parameterized Membership Functions │ │ ├── Linguistic Hedges │ │ └── Hierarchical Fuzzy Systems │ └── Evolutionary Tuning of Fuzzy System Parameters │ ├── Evolutionary Tuning of Fuzzy Inference Systems │ ├── Evolutionary Tuning of Fuzzy Classifiers │ └── Evolutionary Tuning of Fuzzy Clusterers ├── Evolutionary Swarm Intelligence │ ├── Particle Swarm Optimization (PSO) │ │ ├── Variants and Extensions │ │ │ ├── Binary PSO │ │ │ ├── Continuous PSO │ │ │ ├── Discrete PSO │ │ │ ├── Constrained PSO │ │ │ ├── Multi-Objective PSO │ │ │ ├── Adaptive PSO │ │ │ ├── Hybrid PSO │ │ │ ├── Bare Bones PSO │ │ │ ├── Fully Informed Particle Swarm (FIPS) │ │ │ └── Comprehensive Learning PSO (CLPSO) │ │ └── Applications │ │ ├── Function Optimization │ │ ├── Neural Network Training │ │ ├── Feature Selection │ │ ├── Scheduling │ │ ├── Image Processing │ │ └── Robotics │ │ │ └── Ant Colony Optimization (ACO) │ ├── Ant System (AS) │ ├── Ant Colony System (ACS) │ ├── MAX-MIN Ant System (MMAS) │ ├── Rank-Based Ant System (ASrank) │ ├── Continuous Orthogonal Ant Colony (COAC) │ ├── Recursive Ant Colony Optimization (RACO) │ └── Applications │ ├── Traveling Salesman Problem (TSP) │ ├── Quadratic Assignment Problem (QAP) │ ├── Vehicle Routing Problem (VRP) │ ├── Job-Shop Scheduling Problem (JSSP) │ ├── Graph Coloring │ └── Data Mining ├── Evolutionary Multi-Objective Optimization │ ├── Dominance-Based Approaches │ │ ├── Non-Dominated Sorting Genetic Algorithm (NSGA) │ │ │ ├── NSGA-II │ │ │ └── NSGA-III │ │ ├── Strength Pareto Evolutionary Algorithm (SPEA) │ │ │ ├── SPEA2 │ │ │ └── SPEA2+ │ │ ├── Pareto Archived Evolution Strategy (PAES) │ │ ├── Pareto Envelope-Based Selection Algorithm (PESA) │ │ │ ├── PESA-I │ │ │ └── PESA-II │ │ └── Niched Pareto Genetic Algorithm (NPGA) │ │ │ ├── Decomposition-Based Approaches │ │ ├── MOEA/D │ │ │ ├── MOEA/D-DE │ │ │ ├── MOEA/D-DRA │ │ │ └── MOEA/D-M2M │ │ ├── NSGA-III │ │ ├── Reference Vector Guided Evolutionary Algorithm (RVEA) │ │ └── θ-Dominance Based Evolutionary Algorithm (θ-DEA) │ │ │ ├── Indicator-Based Approaches │ │ ├── Hypervolume Indicator │ │ │ ├── S-Metric Selection Evolutionary Multi-Objective Algorithm (SMS-EMOA) │ │ │ └── Hypervolume Estimation Algorithm for Multi-Objective Optimization (HypE) │ │ ├── R2 Indicator │ │ │ └── R2-EMOA │ │ ├── Epsilon Indicator │ │ │ ├── Epsilon-Dominance Evolutionary Algorithm (ε-MOEA) │ │ │ └── Additive Epsilon Indicator Algorithm (IBEA+) │ │ └── Inverted Generational Distance (IGD) │ │ └── IGD+-EMOA │ │ │ └── Preference-Based Approaches │ ├── Reference Point Methods │ │ ├── R-NSGA-II │ │ └── g-NSGA-II │ ├── Light Beam Search │ ├── Interactive EMO │ └── Progressively Interactive EMO ├── Evolutionary Machine Learning Applications │ ├── Supervised Learning │ │ ├── Classification │ │ │ ├── Evolutionary Feature Selection for Classification │ │ │ ├── Evolutionary Ensemble Learning │ │ │ ├── Evolutionary Rule-Based Classification │ │ │ └── Evolutionary Neural Network Classifiers │ │ └── Regression │ │ ├── Evolutionary Feature Selection for Regression │ │ ├── Evolutionary Symbolic Regression │ │ └── Evolutionary Neural Network Regression │ │ │ ├── Unsupervised Learning │ │ ├── Clustering │ │ │ ├── Evolutionary K-Means Clustering │ │ │ ├── Evolutionary Fuzzy C-Means Clustering │ │ │ ├── Evolutionary Hierarchical Clustering │ │ │ └── Evolutionary Spectral Clustering │ │ ├── Dimensionality Reduction │ │ │ ├── Evolutionary Principal Component Analysis (EPCA) │ │ │ ├── Evolutionary Manifold Learning │ │ │ └── Evolutionary Autoencoder │ │ └── Feature Learning │ │ ├── Evolutionary Sparse Coding │ │ └── Evolutionary Deep Belief Networks (DBNs) │ │ │ ├── Reinforcement Learning │ │ ├── Policy Search │ │ │ ├── Evolutionary Policy Gradient Methods │ │ │ ├── Evolutionary Actor-Critic Methods │ │ │ └── Evolutionary Reward Shaping │ │ └── Value Function Approximation │ │ ├── Evolutionary Q-Learning │ │ ├── Evolutionary SARSA │ │ └── Evolutionary Deep Q-Networks (DQNs) │ │ │ ├── Optimization │ │ ├── Numerical Optimization │ │ │ ├── Unconstrained Optimization │ │ │ └── Constrained Optimization │ │ ├── Combinatorial Optimization │ │ │ ├── Traveling Salesman Problem (TSP) │ │ │ ├── Knapsack Problem │ │ │ ├── Scheduling Problems │ │ │ └── Vehicle Routing Problem (VRP) │ │ └── Multi-Objective Optimization │ │ ├── Engineering Design Optimization │ │ ├── Portfolio Optimization │ │ └── Environmental/Economic Dispatch │ │ │ └── Other Applications ││ └── Other Applications │ ├── Time Series Prediction │ │ ├── Evolutionary Recurrent Neural Networks │ │ ├── Evolutionary Echo State Networks │ │ └── Evolutionary Long Short-Term Memory (LSTM) Networks │ ├── Anomaly Detection │ │ ├── Evolutionary One-Class Classification │ │ ├── Evolutionary Outlier Detection │ │ └── Evolutionary Novelty Detection │ ├── Image Processing │ │ ├── Evolutionary Image Segmentation │ │ ├── Evolutionary Image Enhancement │ │ ├── Evolutionary Image Compression │ │ └── Evolutionary Image Retrieval │ └── Natural Language Processing │ ├── Evolutionary Text Classification │ ├── Evolutionary Named Entity Recognition │ ├── Evolutionary Sentiment Analysis │ └── Evolutionary Machine Translation └── Evolutionary Machine Learning Theory ├── Convergence Analysis │ ├── Schema Theory │ ├── Markov Chain Analysis │ └── Dynamical Systems Analysis ├── Computational Complexity │ ├── Time Complexity │ └── Space Complexity ├── No Free Lunch Theorem │ ├── NFL for Optimization │ └── NFL for Machine Learning ├── Fitness Landscape Analysis │ ├── Fitness Distance Correlation (FDC) │ ├── Epistasis │ ├── Ruggedness and Neutrality │ └── Deception and Multimodality ├── Evolutionary Dynamics │ ├── Exploration vs. Exploitation │ ├── Diversity Maintenance │ ├── Premature Convergence │ └── Evolutionary Stability ├── Scalability and Efficiency │ ├── Parallel Evolutionary Algorithms │ ├── Distributed Evolutionary Algorithms │ ├── GPU Acceleration │ └── Surrogate-Assisted Evolutionary Algorithms ├── Evolutionary Multitasking │ ├── Multifactorial Optimization │ └── Evolutionary Transfer Learning ├── Evolutionary Meta-Learning │ ├── Evolutionary Algorithm Configuration │ ├── Evolutionary Hyperparameter Optimization │ └── Evolutionary AutoML └── Theoretical Foundations ├── Evolutionary Game Theory ├── Evolutionary Multi-Objective Optimization Theory ├── Evolutionary Learning Theory └── Evolutionary Computation Theory This expanded map provides a more comprehensive view of the field of evolutionary machine learning, including additional sub-branches, techniques, algorithms, and application areas. The map covers a wide range of topics, from the fundamentals of evolutionary algorithms to their applications in various domains of machine learning, as well as theoretical aspects and advanced concepts such as evolutionary multitasking and meta-learning. Please note that given the vast nature of the field, even this expanded map may not exhaustively cover every single aspect or the most recent developments in evolutionary machine learning. However, it aims to provide a broad and structured overview of the key areas and topics within the field. [Quanta Magazine](https://www.quantamagazine.org/ai-starts-to-sift-through-string-theorys-near-endless-possibilities-20240423/) Inner workings of transformers [[2405.00208] A Primer on the Inner Workings of Transformer-based Language Models](https://arxiv.org/abs/2405.00208) book: [[2402.03175] The Matrix: A Bayesian learning model for LLMs](https://arxiv.org/abs/2402.03175)