Probabilistic Graphical Models

  1. Learning: From Data to Models
    1. Parameter Learning
      1. Complete Data Scenarios
        1. Maximum Likelihood Estimation (MLE)
          1. Likelihood Function
            1. Log-Likelihood Optimization
              1. Analytical Solutions
                1. Numerical Optimization Methods
                2. Bayesian Parameter Estimation
                  1. Prior Distributions
                    1. Posterior Distributions
                      1. Conjugate Priors
                        1. Hyperparameter Selection
                        2. Regularization Techniques
                          1. L1 and L2 Regularization
                            1. Ridge and Lasso Regression
                              1. Bayesian Interpretation
                            2. Incomplete Data Scenarios
                              1. Missing Data Mechanisms
                                1. Missing Completely at Random (MCAR)
                                  1. Missing at Random (MAR)
                                    1. Missing Not at Random (MNAR)
                                    2. Expectation-Maximization (EM) Algorithm
                                      1. E-step: Expectation Computation
                                        1. M-step: Maximization
                                          1. Convergence Properties
                                            1. Variants and Extensions
                                            2. Gradient-Based Optimization
                                              1. Stochastic Gradient Descent
                                                1. Handling Latent Variables
                                                  1. Variational EM
                                                2. Specialized Learning Scenarios
                                                  1. Online Learning
                                                    1. Sequential Parameter Updates
                                                      1. Forgetting Factors
                                                      2. Transfer Learning
                                                        1. Parameter Sharing
                                                          1. Domain Adaptation
                                                      3. Structure Learning
                                                        1. Problem Formulation
                                                          1. The Structure Learning Problem
                                                            1. Search Space Complexity
                                                              1. Identifiability Issues
                                                                1. Evaluation Metrics
                                                              2. Score-Based Methods
                                                                1. Scoring Functions
                                                                  1. Likelihood-Based Scores
                                                                    1. Penalized Likelihood
                                                                      1. Bayesian Information Criterion (BIC)
                                                                        1. Akaike Information Criterion (AIC)
                                                                        2. Search Algorithms
                                                                          1. Greedy Hill-Climbing
                                                                            1. Local Search Strategies
                                                                              1. Neighborhood Definitions
                                                                                1. Local Optima Issues
                                                                                2. Simulated Annealing
                                                                                  1. Temperature Schedules
                                                                                    1. Exploration vs. Exploitation
                                                                                    2. Genetic Algorithms
                                                                                      1. Crossover and Mutation
                                                                                  2. Constraint-Based Methods
                                                                                    1. Independence Testing
                                                                                      1. Statistical Tests for Independence
                                                                                        1. Chi-Square Tests
                                                                                          1. Mutual Information Tests
                                                                                            1. Conditional Independence Tests
                                                                                            2. The PC Algorithm
                                                                                              1. Skeleton Discovery
                                                                                                1. Edge Orientation
                                                                                                  1. Complexity Analysis
                                                                                                  2. FCI Algorithm
                                                                                                    1. Handling Latent Variables
                                                                                                      1. Partial Ancestral Graphs
                                                                                                    2. Hybrid Methods
                                                                                                      1. Combining Scores and Constraints
                                                                                                        1. Max-Min Hill-Climbing (MMHC)
                                                                                                          1. Three-Phase Algorithms
                                                                                                          2. Bayesian Structure Learning
                                                                                                            1. Priors over Graph Structures
                                                                                                              1. Uniform Priors
                                                                                                                1. Structural Priors
                                                                                                                2. Posterior Inference for Structures
                                                                                                                  1. MCMC over Structures
                                                                                                                    1. Model Averaging

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                                                                                                              3. Inference: Answering Queries

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                                                                                                              5. Advanced Topics and Specialized Models