--- Examples: Zero-shot learning, Transfer learning, Domain adaptation --- Key assumption: Causal structure is invariant across domains - Applications of Causal ML -- Healthcare and biomedicine --- Drug discovery: Identify causal mechanisms of action --- Personalized medicine: Estimate individual treatment effects --- Epidemiology: Disentangle causes of diseases --- Randomized Controlled Trials: Improve efficiency and generalizability -- Advertising and marketing --- Attribution modeling: Estimate causal impact of advertising touchpoints --- Incrementality testing: Measure causal effect of marketing interventions --- Customer journey optimization: Identify causal bottlenecks and opportunities --- Uplift modeling: Predict individual-level response to treatment -- Economics and social sciences --- Policy evaluation: Estimate causal impact of interventions --- Generalizability: Transport causal effects across contexts --- Counterfactual analysis: Reason about alternative historical scenarios --- Skill acquisition: Infer causal role of training -- Reinforcement learning and robotics --- Causal model-based RL: Learn causal models of environment for planning --- Transfer learning: Adapt causal knowledge to new tasks or domains --- Counterfactual reasoning: Imagine alternative actions and their consequences --- Safe exploration: Design interventions to efficiently and safely explore environment -- Fairness and Interpretability --- Counterfactual fairness: Ensure decisions are fair under counterfactual reasoning --- Path-specific counterfactual fairness: Disentangle fair and unfair causal pathways --- Counterfactual explanations: Explain decisions using counterfactual scenarios --- Causal concept activation vectors: Interpret causal influence of concepts on model predictions - Challenges and Future Directions -- Scaling to high-dimensional and nonlinear settings -- Learning causal structure from complex, heterogeneous data (images, text, etc.) -- Combining causal reasoning with deep learning and reinforcement learning -- Developing user-friendly software libraries and benchmarks for causal ML -- Bridging gap between theory and practice of causal inference in industry settings -- Incorporating domain knowledge and human expertise into causal discovery process -- Ensuring safety, fairness, and robustness of causal ML systems -- Advancing philosophical foundations and addressing conceptual controversies -- Fostering interdisciplinary collaboration and knowledge sharing This expanded mind map delves deeper into the technical details and practical considerations surrounding causal inference in machine learning. It covers a wider range of methods for learning causal structures, estimating causal effects, and reasoning counterfactually. It also highlights emerging areas such as causal representation learning and transfer, and discusses applications across diverse domains including healthcare, marketing, economics, and robotics. Furthermore, it touches on key challenges and future directions for the field, emphasizing the need for scalable and flexible methods, integration with other areas of ML, and the importance of fairness, safety, and interpretability. The map underscores the multidisciplinary nature of causal ML, drawing from statistics, computer science, economics, philosophy, and domain expertise. Of course, even this expanded view is not exhaustive, as causal inference is a rich and rapidly evolving field. However, it aims to provide a comprehensive overview of the key concepts, methods, and applications, and to highlight the potential for causal reasoning to enhance the capabilities and impact of machine learning systems. Sure, here's an even more gigantic and detailed map of Bayesian artificial intelligence: Bayesian AI Fundamentals - Bayes' Theorem - Prior probability P(H) - Conjugate priors - Noninformative priors (e.g. Jeffreys prior) - Empirical Bayes methods - Likelihood P(E|H) - Likelihood functions for common distributions - Maximum likelihood estimation (MLE) - Marginal likelihood P(E) - Integration techniques (e.g. Monte Carlo, quadrature) - Posterior probability P(H|E) - Maximum a posteriori (MAP) estimation - Credible intervals - Bayesian inference - Parameter estimation - Conjugate priors and posteriors - Markov chain Monte Carlo (MCMC) methods - Metropolis-Hastings algorithm - Gibbs sampling - Hamiltonian Monte Carlo (HMC) - Variational inference (VI) - Mean-field approximation - Stochastic variational inference (SVI) - Hypothesis testing - Bayes factors - Bayesian model averaging (BMA) - Model selection - Bayesian information criterion (BIC) - Akaike information criterion (AIC) - Minimum description length (MDL) principle - Bayesian networks - Directed acyclic graphs (DAGs) - Moralization and triangulation - Conditional probability tables (CPTs) - Parameter learning with Dirichlet priors - D-separation and Markov blankets - Faithfulness and causal sufficiency assumptions - Exact inference - Variable elimination - Clique tree propagation - Recursive conditioning - Approximate inference - Loopy belief propagation - Variational methods (e.g. mean-field, structured) - Particle-based methods (e.g. likelihood weighting, importance sampling) Probabilistic Graphical Models - Markov random fields - Pairwise and higher-order potentials - Hammersley-Clifford theorem - Ising and Potts models - Factor graphs - Sum-product and max-product algorithms - Belief propagation - Pearl's message passing algorithm - Generalized belief propagation (GBP) - Junction tree algorithm - Chordal graphs and clique trees - Gaussian graphical models - Covariance selection and graphical lasso - Conditional independence in Gaussian distributions - Latent variable models - Mixture models - Gaussian mixture models (GMMs) - Bayesian Gaussian mixture models - Infinite mixture models with Dirichlet process priors - Hidden Markov models - Forward-backward algorithm - Viterbi algorithm - Bayesian HMMs with hierarchical Dirichlet process priors - Kalman filters - Linear Gaussian state-space models - Extended and unscented Kalman filters for nonlinear systems - Latent Dirichlet allocation - Collapsed Gibbs sampling - Variational Bayes for LDA - Structure learning - Score-based approaches - Bayesian Dirichlet score - Bayesian information criterion (BIC) - Minimum description length (MDL) - Constraint-based approaches - PC and IC algorithms - Markov blanket discovery - Hybrid approaches - Max-min hill climbing (MMHC) - Greedy equivalence search (GES) Bayesian Nonparametrics - Dirichlet process (DP) - Chinese restaurant process - Infinite mixture models - Hierarchical clustering with DPs - Stick-breaking construction - Slice sampling for DP mixtures - Hierarchical Dirichlet process (HDP) - Chinese restaurant franchise - Infinite hidden Markov models - Pitman-Yor process - Power-law clustering behavior - Language modeling applications - Gaussian process (GP) - Covariance functions - Squared exponential - Matérn - Periodic - Rational quadratic - Spectral mixture - GP regression and classification - Exact and approximate inference - Sparse GP methods (e.g. inducing points, variational) - Multi-output and deep GPs - Bayesian optimization with GPs - Indian buffet process (IBP) - Infinite latent feature models - Nonparametric binary matrix factorization - Beta process - Infinite feature allocation models - Bayesian nonparametric factor analysis Bayesian Deep Learning - Bayesian neural networks - Bayes by Backprop - Probabilistic backpropagation - Markov chain Monte Carlo (MCMC) - Stochastic gradient Langevin dynamics (SGLD) - Hamiltonian Monte Carlo (HMC) - No-U-Turn Sampler (NUTS) - Laplace approximation - Kronecker-factored approximate curvature (KFAC) - Expectation propagation - Assumed Density Filtering (ADF) - Deterministic Expectation Propagation (DEP) - Uncertainty estimation and calibration - Monte Carlo dropout - Ensemble methods - Bayesian model averaging - Bayesian convolutional neural networks - Variational Bayesian CNNs - Gaussian process CNNs - Bayesian ResNets and DenseNets - Bayesian recurrent neural networks - Bayesian LSTMs and GRUs - Variational RNNs with latent variables - Bayesian attention mechanisms - Bayesian reinforcement learning - Bayesian Q-learning - Bayesian deep Q-networks (BDQN) - Variational Bayes for Q-learning - Thompson sampling - Posterior sampling RL (PSRL) - Bootstrapped Thompson sampling - Bayesian model-based RL - Gaussian process dynamic programming (GPDP) - Bayes-Adaptive Markov Decision Processes (BAMDPs) - Bayesian optimization for hyperparameter tuning - Gaussian process bandits - Entropy search and predictive entropy search - Multi-objective and constrained Bayesian optimization Bayesian Active Learning - Uncertainty sampling - Least confidence, margin, and entropy sampling - Query-by-committee - Gibbs sampling and variational inference committees - Expected model change - Expected gradient length (EGL) - Expected error reduction - Bayesian active learning by disagreement (BALD) - Bayesian optimal experimental design - Information-theoretic design criteria (e.g. D-optimality, mutual information) Applications - Bayesian forecasting and time series analysis - Bayesian vector autoregression (BVAR) - Bayesian dynamic linear models (DLMs) - Gaussian process time series models - Bayesian A/B testing - Beta-binomial and Dirichlet-multinomial models - Expected loss and value of information criteria - Bayesian recommender systems - Bayesian Personalized Ranking (BPR) - Collaborative topic modeling - Hierarchical Poisson factorization - Bayesian natural language processing - Topic modeling - Latent Dirichlet allocation (LDA) - Hierarchical Dirichlet process (HDP) topic models - Supervised topic models (e.g. labeled LDA, DiscLDA) - Word embeddings - Bayesian skip-gram and CBOW models - Gaussian embedding models - Bayesian language models and smoothing techniques - Bayesian computer vision - Image segmentation - Gaussian process and Dirichlet process mixture models - Bayesian nonparametric scene parsing - Object detection and tracking - Bayesian filtering and smoothing (e.g. Kalman, particle filters) - Bayesian non-parametric object models (e.g. IBP, beta-Bernoulli process) - Pose estimation and 3D reconstruction - Bayesian structure from motion - Gaussian process implicit surfaces - Bayesian bioinformatics - Bayesian hierarchical models for microarray data - Gaussian process models for gene networks - Protein structure prediction - Bayesian nonparametric models for sequence and structure motifs - Dirichlet process mixture models for protein families - Genome-wide association studies (GWAS) - Bayesian variable selection and model averaging - Gaussian process models for genetic associations - Bayesian robotics - Simultaneous localization and mapping (SLAM) - Extended and unscented Kalman filters - Rao-Blackwellized particle filters - Gaussian process occupancy maps - Motion planning under uncertainty - Partially observable Markov decision processes (POMDPs) - Bayesian reinforcement learning for adaptive control - Bayesian nonparametric models for robot skill learning - Dirichlet process mixture models for trajectory clustering - Indian buffet process for feature learning in robotic grasping Foundational Concepts - Conditional probability and Bayes' rule - Random variables and probability distributions - Expectation, variance, and covariance - Limit theorems and convergence results - Kullback-Leibler (KL) divergence - Rényi entropy and divergences - Information geometry - Statistical machine learning - Supervised and unsupervised learning - Bias-variance tradeoff and regularization - Cross-validation and model selection - PAC learning and VC theory - Computational complexity - Time and space complexity classes (e.g. P, NP, PSPACE) - Tractability and approximability of inference problems - Complexity of learning (e.g. PAC learning, computational learning theory) This expanded map dives deeper into each subtopic, providing a more comprehensive view of the vast field of Bayesian AI. It covers additional techniques, algorithms, and applications across various domains. However, even this highly detailed representation is not exhaustive, as the field is constantly evolving with new research and advances. Bayesian methods offer a principled and flexible framework for modeling uncertainty, learning from data, and making predictions. They have been successfully applied to a wide range of problems in machine learning, from fundamental research to real-world applications in science, engineering, and industry. Exploring and understanding these topics requires a solid foundation in probability theory, statistics, and computer science. Specialized expertise is often necessary to effectively apply Bayesian techniques to specific domains and problem settings. Despite its size and complexity, this map can serve as a useful guide and reference for researchers and practitioners working in Bayesian AI, helping to navigate the key concepts, methods, and applications in this exciting and rapidly growing field. Here is an even more detailed and expanded map of Bayesian machine learning: I. Foundations of Bayesian Machine Learning 1. Basic concepts a. Random variables and probability distributions b. Joint, marginal, and conditional probability c. Independence and conditional independence 2. Bayes' theorem and its applications a. Prior, likelihood, and posterior distributions b. Bayesian updating and sequential learning 3. Expectation, variance, and other moments a. Properties and computation of expectation and variance b. Covariance and correlation B. Bayesian inference 1. Conjugate priors and their properties a. Beta-Bernoulli, Gamma-Poisson, and other conjugate pairs b. Sufficient statistics and exponential family distributions 2. Maximum a posteriori (MAP) estimation a. Optimization techniques for MAP estimation b. Regularization and sparsity-inducing priors 3. Bayesian credible intervals and hypothesis testing a. Highest posterior density (HPD) intervals b. Bayes factors and model comparison C. Bayesian decision theory 1. Loss functions and risk minimization a. Squared error, absolute error, and 0-1 loss b. Asymmetric and custom loss functions 2. Optimal decision rules and Bayes risk a. Minimizing expected loss b. Connections to information theory and entropy II. Bayesian Models A. Bayesian linear regression 1. Model formulation and assumptions a. Likelihood function and noise distribution b. Prior distributions for regression coefficients 2. Conjugate priors and closed-form posterior updates a. Normal-Inverse-Gamma prior b. Reference priors and Jeffreys prior 3. Predictive distribution and uncertainty quantification a. Posterior predictive distribution b. Bayesian model averaging for prediction B. Bayesian logistic regression 1. Model formulation and assumptions a. Bernoulli likelihood and logit link function b. Gaussian and Laplace priors for coefficients 2. Laplace approximation for posterior inference a. Gaussian approximation to the posterior b. Hessian matrix and its computation 3. Variational inference for logistic regression a. Evidence lower bound (ELBO) and mean-field approximation b. Stochastic variational inference and mini-batch updates C. Bayesian neural networks 1. Model formulation and assumptions a. Network architecture and activation functions b. Prior distributions for weights and biases 2. Variational inference for Bayesian neural networks a. Reparameterization trick and stochastic gradient variational Bayes (SGVB) b. Normalizing flows and invertible transformations 3. Monte Carlo dropout as a Bayesian approximation a. Dropout as a variational approximation b. Uncertainty estimation and model averaging with dropout D. Gaussian processes 1. Gaussian process regression a. Kernel functions and their properties b. Exact inference and computational complexity 2. Gaussian process classification a. Laplace approximation and expectation propagation b. Variational inference for GP classification 3. Covariance functions and hyperparameter optimization a. Stationary and non-stationary covariance functions b. Automatic relevance determination (ARD) and lengthscale hyperparameters E. Bayesian nonparametric models 1. Dirichlet process mixture models a. Chinese restaurant process and stick-breaking construction b. Variational inference and Gibbs sampling for DPMM 2. Hierarchical Dirichlet process a. Nested clustering and topic modeling applications b. Variational inference and collapsed Gibbs sampling for HDP 3. Indian buffet process and latent feature models a. Beta process and stick-breaking construction b. Variational inference and MCMC for IBP III. Approximate Inference Methods A. Variational inference 1. Evidence lower bound (ELBO) and Jensen's inequality a. Derivation and interpretation of the ELBO b. Optimization techniques for maximizing the ELBO 2. Mean-field approximation and factorized variational families a. Coordinate ascent variational inference (CAVI) b. Structured variational inference and beyond mean-field 3. Stochastic variational inference and mini-batch updates a. Noisy gradient estimates and learning rate schedules b. Variance reduction techniques and control variates B. Markov chain Monte Carlo (MCMC) methods 1. Metropolis-Hastings algorithm a. Proposal distributions and acceptance probabilities b. Adaptive MCMC and optimal scaling a. Conditional distributions and full conditionals b. Collapsed Gibbs sampling and Rao-Blackwellization 3. Hamiltonian Monte Carlo and its variants a. Hamiltonian dynamics and leapfrog integrator b. No-U-Turn Sampler (NUTS) and adaptive HMC C. Expectation propagation 1. Message passing and factor graphs a. Sum-product algorithm and belief propagation b. Convergence and accuracy of EP 2. Moment matching and exponential family distributions a. Gaussian EP and its extensions