"Here is a gigantic map of Bayesian machine learning: ```mermaid graph TD A[Bayesian Machine Learning] --> B[Bayesian Inference] A --> C[Probabilistic Graphical Models] A --> D[Bayesian Nonparametrics] A --> E[Bayesian Optimization] A --> F[Bayesian Deep Learning] B --> B1[Bayes' Theorem] B --> B2[Bayesian Parameter Estimation] B --> B3[Bayesian Model Selection] B --> B4[Bayesian Hypothesis Testing] B --> B5[Bayesian Decision Theory] C --> C1[Bayesian Networks] C --> C2[Markov Random Fields] C --> C3[Hidden Markov Models] C --> C4[Conditional Random Fields] C --> C5[Factor Graphs] C --> C6[Plate Notation] C --> C7[Junction Tree Algorithm] C --> C8[Belief Propagation] C --> C9[Variational Inference] C --> C10[Markov Chain Monte Carlo (MCMC)] D --> D1[Dirichlet Process] D --> D2[Chinese Restaurant Process] D --> D3[Indian Buffet Process] D --> D4[Gaussian Process] D --> D5[Pitman-Yor Process] D --> D6[Beta Process] D --> D7[Hierarchical Dirichlet Process] D --> D8[Nested Chinese Restaurant Process] E --> E1[Gaussian Process Optimization] E --> E2[Thompson Sampling] E --> E3[Upper Confidence Bound (UCB)] E --> E4[Expected Improvement] E --> E5[Entropy Search] E --> E6[Bayesian Active Learning] E --> E7[Multi-armed Bandits] E --> E8[Bayesian Experimental Design] F --> F1[Bayesian Neural Networks] F --> F2[Variational Autoencoders (VAEs)] F --> F3[Bayesian Convolutional Neural Networks] F --> F4[Bayesian Recurrent Neural Networks] F --> F5[Gaussian Process Deep Learning] F --> F6[Deep Bayesian Active Learning] F --> F7[Bayesian Transfer Learning] F --> F8[Bayesian Reinforcement Learning] B1 --> B1a[Prior Probability] B1 --> B1b[Likelihood] B1 --> B1c[Posterior Probability] B1 --> B1d[Evidence] B2 --> B2a[Maximum a Posteriori (MAP) Estimation] B2 --> B2b[Bayesian Least Squares] B2 --> B2c[Kalman Filter] B2 --> B2d[Particle Filter] B3 --> B3a[Bayes Factor] B3 --> B3b[Bayesian Information Criterion (BIC)] B3 --> B3c[Akaike Information Criterion (AIC)] B3 --> B3d[Deviance Information Criterion (DIC)] B4 --> B4a[Bayes Factor Hypothesis Testing] B4 --> B4b[Bayesian t-test] B4 --> B4c[Bayesian ANOVA] B4 --> B4d[Bayesian A/B Testing] B5 --> B5a[Expected Utility] B5 --> B5b[Risk] B5 --> B5c[Loss Functions] B5 --> B5d[Bayesian Decision Rules] C1 --> C1a[Naive Bayes] C1 --> C1b[Tree-Augmented Naive Bayes (TAN)] C1 --> C1c[Bayesian Belief Networks] C1 --> C1d[Dynamic Bayesian Networks] C2 --> C2a[Ising Model] C2 --> C2b[Potts Model] C2 --> C2c[Gaussian Markov Random Fields] C2 --> C2d[Conditional Markov Random Fields] C3 --> C3a[Discrete Hidden Markov Models] C3 --> C3b[Continuous Hidden Markov Models] C3 --> C3c[Hidden Semi-Markov Models] C3 --> C3d[Infinite Hidden Markov Models] C4 --> C4a[Linear-chain Conditional Random Fields] C4 --> C4b[General Conditional Random Fields] C4 --> C4c[Skip-chain Conditional Random Fields] C4 --> C4d[Higher-order Conditional Random Fields] C5 --> C5a[Sum-Product Algorithm] C5 --> C5b[Max-Product Algorithm] C5 --> C5c[Loopy Belief Propagation] C5 --> C5d[Tree-reweighted Belief Propagation] C6 --> C6a[Bayesian Plate Models] C6 --> C6b[Nested Plate Models] C6 --> C6c[Overlapping Plate Models] C6 --> C6d[Hierarchical Plate Models] C7 --> C7a[Clique Tree] C7 --> C7b[Hugin Algorithm] C7 --> C7c[Shenoy-Shafer Algorithm] C7 --> C7d[Lauritzen-Spiegelhalter Algorithm] C8 --> C8a[Sum-Product Message Passing] C8 --> C8b[Max-Product Message Passing] C8 --> C8c[Generalized Belief Propagation] C8 --> C8d[Expectation Propagation] C9 --> C9a[Mean Field Variational Inference] C9 --> C9b[Stochastic Variational Inference] C9 --> C9c[Variational Bayes] C9 --> C9d[Variational Message Passing] C10 --> C10a[Metropolis-Hastings Algorithm] C10 --> C10b[Gibbs Sampling] C10 --> C10c[Hamiltonian Monte Carlo] C10 --> C10d[Reversible Jump MCMC] D1 --> D1a[Stick-breaking Construction] D1 --> D1b[Pólya Urn Scheme] D1 --> D1c[Chinese Restaurant Process] D1 --> D1d[Dirichlet Process Mixture Models] D2 --> D2a[Table Assignment] D2 --> D2b[Dish Selection] D2 --> D2c[Table Sharing] D2 --> D2d[Hierarchical Chinese Restaurant Process] D3 --> D3a[Latent Feature Allocation] D3 --> D3b[Infinite Latent Feature Models] D3 --> D3c[Nonparametric Factor Analysis] D3 --> D3d[Nonparametric Matrix Factorization] D4 --> D4a[Gaussian Process Regression] D4 --> D4b[Gaussian Process Classification] D4 --> D4c[Sparse Gaussian Processes] D4 --> D4d[Multi-output Gaussian Processes] D5 --> D5a[Power-law Clustering] D5 --> D5b[Pitman-Yor Language Models] D5 --> D5c[Hierarchical Pitman-Yor Processes] D5 --> D5d[Pitman-Yor Process Mixture Models] D6 --> D6a[Indian Buffet Process] D6 --> D6b[Beta-Bernoulli Process] D6 --> D6c[Hierarchical Beta Process] D6 --> D6d[Dependent Indian Buffet Process] D7 --> D7a[Hierarchical Dirichlet Process Mixture Models] D7 --> D7b[Hierarchical Dirichlet Process Hidden Markov Models] D7 --> D7c[Hierarchical Dirichlet Process Topic Models] D7 --> D7d[Hierarchical Dirichlet Process Regression] D8 --> D8a[Hierarchical Clustering] D8 --> D8b[Nested Hierarchical Dirichlet Process] D8 --> D8c[Nested Chinese Restaurant Franchise] D8 --> D8d[Bayesian Hierarchical Clustering] E1 --> E1a[Bayesian Optimization with Gaussian Processes] E1 --> E1b[Bayesian Optimization with Random Forests] E1 --> E1c[Bayesian Optimization with Deep Neural Networks] E1 --> E1d[Batch Bayesian Optimization] E2 --> E2a[Bernoulli Thompson Sampling] E2 --> E2b[Gaussian Thompson Sampling] E2 --> E2c[Contextual Thompson Sampling] E2 --> E2d[Hierarchical Thompson Sampling] E3 --> E3a[UCB1] E3 --> E3b[UCB-V] E3 --> E3c[KL-UCB] E3 --> E3d[Bayes-UCB] E4 --> E4a[Probability of Improvement] E4 --> E4b[Expected Improvement] E4 --> E4c[Entropy Search] E4 --> E4d[Predictive Entropy Search] E5 --> E5a[Max-value Entropy Search] E5 --> E5b[Fast Information-theoretic Bayesian Optimization] E5 --> E5c[Output Space Entropy Search] E5 --> E5d[Predictive Entropy Search with Constraints] E6 --> E6a[Bayesian Active Learning by Disagreement] E6 --> E6b[Bayesian Active Learning with Dirichlet Process Prior] E6 --> E6c[Bayesian Active Learning for Optimization] E6 --> E6d[Bayesian Active Learning with Gaussian Processes] E7 --> E7a[Bayesian Multi-armed Bandits] E7 --> E7b[Contextual Multi-armed Bandits] E7 --> E7c[Bayesian Dueling Bandits] E7 --> E7d[Infinite-armed Bandits] E8 --> E8a[Bayesian Optimal Experimental Design] E8 --> E8b[Bayesian Active Learning for Experimental Design] E8 --> E8c[Bayesian Optimization for Experimental Design] E8 --> E8d[Bayesian Sequential Experimental Design] F1 --> F1a[Variational Bayesian Neural Networks] F1 --> F1b[Probabilistic Backpropagation] F1 --> F1c[Bayesian Neural Network Ensembles] F1 --> F1d[Bayesian Dropout] F2 --> F2a[Variational Autoencoder] F2 --> F2b[Conditional Variational Autoencoder] F2 --> F2c[Importance Weighted Autoencoder] F2 --> F2d[Disentangled Variational Autoencoder] F3 --> F3a[Bayesian Convolutional Neural Networks] F3 --> F3b[Variational Bayesian Convolutional Neural Networks] F3 --> F3c[Bayesian Convolutional Autoencoders] F3 --> F3d[Bayesian Convolutional Generative Adversarial Networks] F4 --> F4a[Bayesian Recurrent Neural Networks] F4 --> F4b[Variational Bayesian Recurrent Neural Networks] F4 --> F4c[Bayesian Long Short-Term Memory Networks] F4 --> F4d[Bayesian Gated Recurrent Units] F5 --> F5a[Deep Gaussian Processes] F5 --> F5b[Convolutional Gaussian Processes] F5 --> F5c[Recurrent Gaussian Processes] F5 --> F5d[Variational Deep Gaussian Processes] F6 --> F6a[Bayesian Active Learning with Deep Neural Networks] F6 --> F6b[Deep Bayesian Active Learning by Disagreement] F6 --> F6c[Bayesian Optimization for Deep Active Learning] F6 --> F6d[Bayesian Deep Active Learning with Gaussian Processes] F7 --> F7a[Bayesian Transfer Learning with Gaussian Processes] F7 --> F7b[Bayesian Transfer Learning with Deep Neural Networks] F7 --> F7c[Bayesian Multi-task Learning] F7 --> F7d[Bayesian Domain Adaptation] F8 --> F8a[Bayesian Q-learning] F8 --> F8b[Bayesian Actor-Critic] F8 --> F8c[Bayesian Model-based Reinforcement Learning] F8 --> F8d[Bayesian Inverse Reinforcement Learning] ``` This map provides a comprehensive overview of the key concepts, techniques, and algorithms in Bayesian machine learning. It covers the main areas of Bayesian inference, probabilistic graphical models, Bayesian nonparametrics, Bayesian optimization, and Bayesian deep learning, along with their various sub-topics and related methods. Please note that this map is not exhaustive and there may be additional concepts and techniques within each area of Bayesian machine learning. However, it aims to capture the most important and widely used approaches in the field." "Here is a gigantic map of evolutionary machine learning in markdown format: # Evolutionary Machine Learning ## Evolutionary Computation ### Genetic Algorithms - Selection - Fitness-proportionate selection - Tournament selection - Rank-based selection - Crossover - Single-point crossover - Two-point crossover - Uniform crossover - Mutation - Bit-flip mutation - Gaussian mutation - Swap mutation - Applications - Optimization problems - Feature selection - Neural architecture search ### Genetic Programming - Representation - Tree-based representation - Linear representation - Graph-based representation - Genetic Operators - Crossover - Subtree crossover - Homologous crossover - Mutation - Subtree mutation - Point mutation - Applications - Symbolic regression - Classification - Control systems ### Evolution Strategies - Representation - Real-valued vectors - Mutation - Gaussian mutation - Covariance matrix adaptation (CMA-ES) - Recombination - Intermediate recombination - Discrete recombination - Applications - Continuous optimization - Reinforcement learning ### Differential Evolution - Mutation - DE/rand/1 - DE/best/1 - DE/current-to-best/1 - Crossover - Binomial crossover - Exponential crossover - Selection - Greedy selection - Applications - Global optimization - Multiobjective optimization ## Neuroevolution ### Direct Encoding - Fixed Topology - Evolving weights - Variable Topology - NEAT (NeuroEvolution of Augmenting Topologies) - Historical markings - Speciation - Crossover - Mutation - Add node - Add connection - Modify weights - HyperNEAT (Hypercube-based NEAT) - Compositional pattern producing networks (CPPNs) - Substrate - Indirect encoding ### Indirect Encoding - Developmental Encoding - Cellular Encoding - L-systems - Generative Encoding - Compressed Weight Matrices - Fourier-type Representations ## Evolving Machine Learning Models ### Evolving Neural Networks - Architecture Search - Layer types - Hyperparameters - Connectivity patterns - Weight Initialization - Activation Functions ### Evolving Decision Trees - Tree Structure - Splitting criteria - Leaf nodes - Feature Selection - Pruning ### Evolving Ensemble Models - Ensemble Composition - Homogeneous ensembles - Heterogeneous ensembles - Combination Methods - Voting - Averaging - Stacking ## Hybrid Approaches ### Memetic Algorithms - Local Search - Hill climbing - Simulated annealing - Baldwinian Learning - Lamarckian Learning ### Evolutionary Reinforcement Learning - Policy Search - Neuroevolution for policy representation - Value Function Approximation - Evolving Q-functions - Actor-Critic Methods - Evolving actor and critic networks ### Evolutionary Transfer Learning - Domain Adaptation - Multitask Learning - Lifelong Learning ## Applications - Image Classification - Natural Language Processing - Robotics and Control - Game Playing - Optimization and Scheduling - Bioinformatics and Computational Biology - Finance and Economics This map provides a comprehensive overview of the field of evolutionary machine learning, covering key techniques, algorithms, and applications. It can serve as a reference for researchers and practitioners working in this area, helping them navigate the various subfields and understand the relationships between different approaches." "Here is a gigantic map on self-organizing machine learning: # Self-Organizing Machine Learning ## Introduction - Definition of self-organizing machine learning - Importance and applications of self-organizing systems - Historical background and key milestones ## Foundations ### Artificial Neural Networks (ANNs) - Feedforward neural networks - Recurrent neural networks (RNNs) - Convolutional neural networks (CNNs) - Activation functions and learning rules ### Unsupervised Learning - Clustering algorithms (e.g., k-means, hierarchical clustering) - Dimensionality reduction techniques (e.g., PCA, t-SNE) - Association rule learning - Anomaly detection ## Self-Organizing Neural Networks ### Kohonen Self-Organizing Maps (SOMs) - Architecture and learning algorithm - Visualization and interpretation of SOMs - Variants and extensions (e.g., growing SOMs, hierarchical SOMs) ### Adaptive Resonance Theory (ART) Networks - ART1 for binary input patterns - ART2 for analog input patterns - Fuzzy ART for handling uncertainty - ARTMAP for supervised learning ### Growing Neural Gas (GNG) Networks - Incremental network growth and adaptation - Topology representation and preservation - Applications in clustering and visualization ## Deep Learning and Self-Organization ### Deep Belief Networks (DBNs) - Restricted Boltzmann Machines (RBMs) - Layerwise pretraining and fine-tuning - Applications in feature learning and generative modeling ### Autoencoders - Undercomplete and overcomplete autoencoders - Denoising autoencoders - Variational autoencoders (VAEs) - Applications in dimensionality reduction and representation learning ### Self-Organizing Deep Neural Networks - Deep SOMs and deep ART networks - Hierarchical feature learning and abstraction - Unsupervised pretraining for deep networks ## Applications and Case Studies - Image and video analysis - Natural language processing - Bioinformatics and genomics - Robotics and autonomous systems - Anomaly detection and fraud detection - Recommender systems and personalization ## Challenges and Future Directions - Scalability and computational efficiency - Interpretability and explainability - Integration with other learning paradigms (e.g., reinforcement learning) - Unsupervised representation learning for complex data - Self-organization in continual and lifelong learning ## Conclusion - Recap of key concepts and techniques - Potential impact and future prospects of self-organizing machine learning - Call for further research and exploration in the field This map covers the main topics, techniques, and applications related to self-organizing machine learning. It begins with the foundations, including artificial neural networks and unsupervised learning, and then delves into specific self-organizing neural network architectures like SOMs, ART networks, and GNG networks. The map also explores the integration of self-organization with deep learning, highlighting approaches such as DBNs, autoencoders, and self-organizing deep neural networks. Finally, it discusses various applications, challenges, and future directions in the field." "Gibbs free energy, denoted as G, is a thermodynamic potential that combines enthalpy (H) (total heat content of a system) and entropy (S) into a single value. It is defined by the equation: G = H - TS where T is the absolute temperature. The change in Gibbs free energy (ΔG) for a process is equal to the change in enthalpy (ΔH) minus the product of the temperature and the change in entropy (ΔS): ΔG = ΔH - TΔS ΔG is a measure of the thermodynamic favorability of a process: - If ΔG < 0, the process is thermodynamically favored (spontaneous)[1]. - If ΔG > 0, the process is not thermodynamically favored (non-spontaneous) and requires an input of energy to occur. - If ΔG = 0, the process is at equilibrium. ΔG represents the maximum amount of non-expansion work that can be extracted from a thermodynamic system at constant temperature and pressure[4]. A negative ΔG means a reaction will release free energy that can be used to do useful work[5]. Gibbs free energy is an important concept in chemistry and biology for understanding the energetics and spontaneity of processes like chemical reactions and phase changes[2][3]. It was originally developed in the 1870s by American scientist Josiah Willard Gibbs[4]. Citations: [1] [Khan Academy](https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:applications-of-thermodynamics/x2eef969c74e0d802:gibbs-free-energy-and-thermodynamic-favorability/v/introduction-to-gibbs-free-energy) [2] [Gibbs Free Energy - Definition, Equations, 2nd Law of Thermodynamics](https://byjus.com/jee/gibbs-free-energy/) [3] [Gibbs (Free) Energy - Chemistry LibreTexts](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_%28Physical_and_Theoretical_Chemistry%29/Thermodynamics/Energies_and_Potentials/Free_Energy/Gibbs_%28Free%29_Energy) [4] [Gibbs free energy - Wikipedia](https://en.wikipedia.org/wiki/Gibbs_free_energy) [5] [Gibbs Free Energy - YouTube](https://www.youtube.com/watch?v=DPjMPeU5OeM) " [How Physics Found a Geometric Structure for Math to Play With | Quanta Magazine](https://www.quantamagazine.org/how-physics-gifted-math-with-a-new-geometry-20200729/) "Symplectic geometry is a branch of differential geometry that studies symplectic manifolds, which are smooth manifolds equipped with a closed, nondegenerate 2-form called the symplectic form[1]. The study of symplectic manifolds is motivated by classical mechanics, where the phase space of a closed system can be modeled as a symplectic manifold[1]. Some key points about symplectic geometry: - Symplectic manifolds are necessarily even-dimensional and orientable, since the nondegeneracy of the symplectic form implies it is a volume form[4]. - Locally, all symplectic manifolds are indistinguishable due to the closedness condition on the symplectic form[4]. - Symplectic geometry provides the mathematical language for areas of physics like Hamiltonian mechanics, geometric quantization, and geometrical optics[3][5]. - Special submanifolds called Lagrangian submanifolds, which are half-dimensional, play a central role and can be thought of as "classical points"[3]. - While symplectic geometry is called "geometry", it is less clear what the geometric content is compared to Riemannian geometry, as notions like the symplectic form seem more algebraic than geometric[2]. One view is that the "geometry" comes from studying the symmetries, namely the symplectomorphism groups[2]. So in summary, symplectic geometry is the study of even-dimensional manifolds with a symplectic form, motivated by physics, but with rich mathematical structure and deep connections to other areas of geometry and topology. Citations: [1] [Symplectic manifold - Wikipedia](https://en.wikipedia.org/wiki/Symplectic_manifold) [2] [What is so geometric about symplectic geometry? - MathOverflow](https://mathoverflow.net/questions/394211/what-is-so-geometric-about-symplectic-geometry) [3] [symplectic geometry in nLab](https://ncatlab.org/nlab/show/symplectic%2Bgeometry) [4] https://people.math.ethz.ch/~acannas/Papers/lsg.pdf [5] [Symplectic Geometry | SpringerLink](https://link.springer.com/chapter/10.1007/978-3-662-06791-8_1) "