Probabilistic Programming and Data Structures

  1. Inference Algorithms for Probabilistic Programming
    1. Exact Inference Methods
      1. Variable Elimination
        1. Sum-Product Algorithm
          1. Elimination Ordering
            1. Computational Complexity
              1. Limitations and Scalability
              2. Junction Tree Algorithm
                1. Tree Decomposition
                  1. Message Passing
                    1. Clique Potentials
                    2. Symbolic Computation
                      1. Computer Algebra Systems
                        1. Exact Symbolic Integration
                      2. Markov Chain Monte Carlo Methods
                        1. Monte Carlo Fundamentals
                          1. Random Sampling Principles
                            1. Law of Large Numbers Application
                              1. Monte Carlo Integration
                                1. Variance Reduction Techniques
                                2. Markov Chain Theory
                                  1. State Space and Transitions
                                    1. Transition Kernels
                                      1. Stationary Distribution
                                        1. Ergodicity and Mixing
                                          1. Detailed Balance
                                          2. Metropolis-Hastings Algorithm
                                            1. Proposal Distribution
                                              1. Acceptance Probability
                                                1. Random Walk Metropolis
                                                  1. Independence Sampler
                                                    1. Tuning Parameters
                                                    2. Gibbs Sampling
                                                      1. Full Conditional Distributions
                                                        1. Systematic vs Random Scan
                                                          1. Block Gibbs Sampling
                                                            1. Collapsed Gibbs Sampling
                                                            2. Hamiltonian Monte Carlo
                                                              1. Hamiltonian Dynamics
                                                                1. Leapfrog Integration
                                                                  1. Momentum Variables
                                                                    1. Energy Conservation
                                                                      1. Tuning Mass Matrix
                                                                      2. No-U-Turn Sampler
                                                                        1. Adaptive Path Length
                                                                          1. Tree Building Algorithm
                                                                            1. Automatic Parameter Tuning
                                                                              1. Divergence Detection
                                                                              2. MCMC Diagnostics
                                                                                1. Trace Plots
                                                                                  1. Autocorrelation Function
                                                                                    1. Effective Sample Size
                                                                                      1. Potential Scale Reduction Factor
                                                                                        1. Convergence Assessment
                                                                                      2. Variational Inference
                                                                                        1. Variational Principle
                                                                                          1. Kullback-Leibler Divergence
                                                                                            1. Evidence Lower Bound
                                                                                              1. Optimization Objective
                                                                                              2. Mean-Field Variational Inference
                                                                                                1. Factorization Assumptions
                                                                                                  1. Coordinate Ascent Updates
                                                                                                    1. Convergence Criteria
                                                                                                    2. Structured Variational Inference
                                                                                                      1. Correlated Variational Families
                                                                                                        1. Normalizing Flows
                                                                                                          1. Variational Autoencoders
                                                                                                          2. Automatic Differentiation Variational Inference
                                                                                                            1. Gradient-Based Optimization
                                                                                                              1. Reparameterization Trick
                                                                                                                1. Stochastic Optimization
                                                                                                                2. Variational Message Passing
                                                                                                                  1. Factor Graphs
                                                                                                                    1. Message Updates
                                                                                                                      1. Exponential Family Distributions
                                                                                                                    2. Specialized Inference Techniques
                                                                                                                      1. Sequential Monte Carlo
                                                                                                                        1. Particle Filters
                                                                                                                          1. Importance Sampling
                                                                                                                            1. Resampling Strategies
                                                                                                                            2. Approximate Bayesian Computation
                                                                                                                              1. Likelihood-Free Inference
                                                                                                                                1. Summary Statistics
                                                                                                                                  1. Distance Functions
                                                                                                                                  2. Nested Sampling
                                                                                                                                    1. Evidence Computation
                                                                                                                                      1. Posterior Sampling
                                                                                                                                        1. Live Points Algorithm

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                                                                                                                                    2. Probabilistic Programming Foundations

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                                                                                                                                    4. Probabilistic Programming Languages and Tools