Probabilistic Graphical Models and Inference

Representation

1. Bayesian NetworksDirected graphs that factor a joint distribution into local conditionals.1–2 h
2. Conditional Independence and d-SeparationReading independence from graph structure: chains, forks, colliders, and explaining away.1–2 h
3. Markov Random FieldsUndirected models built from potentials over cliques; the partition function as the price of symmetry.1–2 h

Inference

1. Exact Inference: Variable Elimination and Belief PropagationPushing sums inside products; message passing on trees; why elimination order controls cost.1–2 h
2. Monte Carlo Estimation and Importance SamplingEstimating expectations by sampling, and reweighting samples drawn from the wrong distribution.1–2 h
3. Markov Chain Monte CarloSampling hard distributions by designing a Markov chain whose stationary distribution is the target.1–2 h
4. Variational Inference and the ELBOTurning inference into optimisation: fit a simple distribution by maximising a lower bound on the evidence.1–2 h
5. Probabilistic ProgrammingWriting models as programs and letting a general-purpose inference engine do the rest.1–2 h

Learning

1. Expectation-MaximizationMaximum likelihood with hidden variables: alternate guessing the hidden values and refitting the parameters.1–2 h

Temporal

1. Hidden Markov ModelsA hidden Markov chain emitting observations: filtering, smoothing, and Viterbi decoding.1–2 h
2. Kalman Filters and Linear-Gaussian State Space ModelsTracking a continuous hidden state: predict, then correct with a gain that weighs model against measurement.1–2 h
3. Conditional Random FieldsDiscriminative undirected models for structured outputs: logistic regression over whole label sequences.1–2 h