Probabilistic Reasoning, Decisions and Game Theory

Bayesian Networks

Graphs of conditional dependence and conditional probability tables

Code: build and query a network

P(x₁…xₙ) = Π P(xᵢ|parents(xᵢ))

Exact and Approximate Inference

Variable elimination, sampling and Gibbs sampling

Code: compare exact and sampled answers

Causal Models

Interventions, confounders and the do-operator

Code: a confounded example

P(Y|do(X))

Markov Chains

States, transition matrices and stationary distributions

Code: weather simulation

Hidden Markov Models

Forward-backward and Viterbi algorithms

Code: part-of-speech tagging

Kalman and Particle Filters

Tracking a moving object from noisy sensors

Code: track a moving point

x̂ = x̂⁻ + K(z − Hx̂⁻)

Utility Theory and Decision Networks

Expected utility, risk and the value of information

Code: an expected-utility decision

EU(a) = Σ P(s|a) U(s)

Sequential Decisions and POMDPs

Planning with uncertain outcomes and hidden states

Reading and demo

Game Theory

Normal-form games, dominant strategies and Nash equilibrium

Interactive: the prisoner's dilemma

Cooperative Games and the Shapley Value

Fair division of value, and its use in explaining models

Code: compute Shapley values

Mechanism Design and Auctions

Designing rules so agents behave well

Case study: ad auctions

Module Review and Assessment

Derivations and a scored quiz

Graded problem set