Probabilistic Graphical Models

  1. Advanced Topics and Specialized Models
    1. Temporal and Sequential Models
      1. Dynamic Bayesian Networks (DBNs)
        1. Temporal Structure
          1. Time Slices
            1. Inter-slice Dependencies
              1. Unrolling in Time
              2. Two-Timeslice Bayesian Networks (2TBNs)
                1. Stationary Assumptions
                  1. Transition Models
                  2. Applications
                    1. Time Series Modeling
                      1. State Tracking
                        1. Prediction
                      2. Hidden Markov Models (HMMs)
                        1. Model Components
                          1. State Variables
                            1. Observation Variables
                              1. Transition Probabilities
                                1. Emission Probabilities
                                2. The Three Fundamental Problems
                                  1. Evaluation Problem
                                    1. Forward Algorithm
                                      1. Backward Algorithm
                                      2. Decoding Problem
                                        1. Viterbi Algorithm
                                          1. Dynamic Programming Approach
                                          2. Learning Problem
                                            1. Baum-Welch Algorithm
                                              1. EM for HMMs
                                            2. Extensions and Variants
                                              1. Higher-Order HMMs
                                                1. Factorial HMMs
                                                  1. Hierarchical HMMs
                                                2. State-Space Models
                                                  1. Kalman Filters
                                                    1. Linear-Gaussian Systems
                                                      1. State-Space Equations
                                                        1. Prediction and Update Steps
                                                          1. Optimality Properties
                                                          2. Extended Kalman Filter (EKF)
                                                            1. Nonlinear System Handling
                                                              1. Linearization Approach
                                                                1. Limitations
                                                                2. Unscented Kalman Filter (UKF)
                                                                  1. Sigma Point Methods
                                                                    1. Unscented Transform
                                                                      1. Advantages over EKF
                                                                      2. Particle Filters
                                                                        1. Sequential Monte Carlo
                                                                          1. Importance Sampling Framework
                                                                            1. Resampling Strategies
                                                                        2. Causal Inference and Causal Models
                                                                          1. Causal Graphical Models
                                                                            1. Causal DAGs
                                                                              1. Causal Interpretation of Edges
                                                                                1. Structural Causal Models
                                                                                2. Causal vs. Statistical Relationships
                                                                                  1. Correlation vs. Causation
                                                                                    1. Confounding Variables
                                                                                  2. Causal Identification
                                                                                    1. The do-operator
                                                                                      1. Interventions and Manipulations
                                                                                        1. Do-calculus Rules
                                                                                        2. Backdoor Criterion
                                                                                          1. Confounding Control
                                                                                            1. Adjustment Sets
                                                                                            2. Frontdoor Criterion
                                                                                              1. Mediation-Based Identification
                                                                                              2. Instrumental Variables
                                                                                                1. Definition and Applications
                                                                                                  1. Two-Stage Least Squares
                                                                                                2. Causal Discovery
                                                                                                  1. Constraint-Based Causal Discovery
                                                                                                    1. PC Algorithm for Causal Graphs
                                                                                                      1. FCI for Latent Confounders
                                                                                                      2. Score-Based Causal Discovery
                                                                                                        1. GES Algorithm
                                                                                                          1. Causal Scoring Functions
                                                                                                        2. Counterfactual Reasoning
                                                                                                          1. Structural Causal Models (SCMs)
                                                                                                            1. Structural Equations
                                                                                                              1. Exogenous Variables
                                                                                                              2. Counterfactual Queries
                                                                                                                1. Definition and Computation
                                                                                                                  1. Three-Level Hierarchy
                                                                                                              3. Discriminative Models
                                                                                                                1. Conditional Random Fields (CRFs)
                                                                                                                  1. Discriminative vs. Generative Models
                                                                                                                    1. Modeling Differences
                                                                                                                      1. Advantages and Disadvantages
                                                                                                                      2. Linear-Chain CRFs
                                                                                                                        1. Structure and Parameterization
                                                                                                                          1. Feature Functions
                                                                                                                            1. Training and Inference
                                                                                                                            2. General CRFs
                                                                                                                              1. Arbitrary Graph Structures
                                                                                                                                1. Clique Templates
                                                                                                                                2. Applications
                                                                                                                                  1. Sequence Labeling
                                                                                                                                    1. Named Entity Recognition
                                                                                                                                      1. Part-of-Speech Tagging
                                                                                                                                        1. Image Segmentation
                                                                                                                                      2. Maximum Entropy Models
                                                                                                                                        1. Principle of Maximum Entropy
                                                                                                                                          1. Feature-Based Models
                                                                                                                                            1. Relationship to CRFs
                                                                                                                                          2. Decision Making and Utility
                                                                                                                                            1. Influence Diagrams
                                                                                                                                              1. Components and Structure
                                                                                                                                                1. Decision Nodes
                                                                                                                                                  1. Chance Nodes
                                                                                                                                                    1. Utility Nodes
                                                                                                                                                    2. Semantics and Evaluation
                                                                                                                                                      1. Expected Utility Maximization
                                                                                                                                                        1. Solution Algorithms
                                                                                                                                                      2. Multi-Attribute Utility Theory
                                                                                                                                                        1. Utility Functions
                                                                                                                                                          1. Risk Preferences
                                                                                                                                                            1. Multi-Objective Decision Making
                                                                                                                                                          2. Value of Information
                                                                                                                                                            1. Expected Value of Perfect Information
                                                                                                                                                              1. Expected Value of Sample Information
                                                                                                                                                                1. Applications in Decision Analysis
                                                                                                                                                                2. Sequential Decision Making
                                                                                                                                                                  1. Markov Decision Processes (MDPs)
                                                                                                                                                                    1. States, Actions, and Rewards
                                                                                                                                                                      1. Policy Optimization
                                                                                                                                                                      2. Partially Observable MDPs (POMDPs)
                                                                                                                                                                        1. Belief States
                                                                                                                                                                          1. Policy Representation

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                                                                                                                                                                    4. Learning: From Data to Models

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                                                                                                                                                                    1. Foundations of Probabilistic Graphical Models