Intelligent Systems II · TEE · revision

Units 1 and 4 in one page

Last-day revision · TEE

Read the night before the TEE

Unit 1

• Logic fails under uncertainty (laziness, theoretical and practical ignorance) → degrees of belief. Decision theory = probability + utility; maximise expected utility.
• Full joint: add the cells where the statement is true; for “given”, divide by the evidence cells. Check the table sums to 1.
• Bayes: posterior = likelihood × prior ÷ evidence. A low prior can make the posterior surprisingly small even after positive evidence; calculate using the stated sensitivity and false-positive rate.
• Naive Bayes: prior × product of class-conditional likelihoods. Without smoothing, one zero likelihood makes the class score zero. Apply Laplace smoothing only when required or when you explicitly state that modelling choice.
• Bayesian network: DAG + CPTs; joint = Π P(node | parents); a node is independent of non-descendants given its parents; LaTeX: 2^k numbers per Boolean node.
• Query with evidence: sum over hidden variables, both query values, normalise (α). Sprinkler PYQ: P(W | ¬R) = 0.1919 / 0.5 = 0.3838. Flu PYQ: P(Fever | ¬Flu) = 0.2735 / 0.725 = 0.3772.
• Univariate GMM: LaTeX: p(x)=\sum_k\pi_k\mathcal N(x\mid\mu_k,\sigma_k^2). With K separate means, K variances and K weights summing to 1, there are 3K − 1 free parameters (K=5 → 14). Higher-dimensional covariance models have different counts. EM alternates responsibilities and weighted parameter updates.
• EM: E-step calculates responsibilities. M-step calculates weighted means and variances, with πₖ=Nₖ/n. GMM uses soft assignments and likelihood; k-means uses hard nearest-centroid assignments and squared distance. Elliptical covariance applies to a multivariate GMM with full covariance matrices.

Unit 4

• Agent, environment, state, action, reward, policy, value, model; exploration vs exploitation (ε-greedy).
• Markov chain: rows = from, columns = to; row sums 1; next = row vector × P; diagram with self-loops.
• Steady state: π = πP, Σπ = 1; compare with today's shares for gain/loss; diagonal = retention.
• MP ⟨S, P⟩ → MRP ⟨S, P, R, γ⟩ → MDP ⟨S, A, P, R, γ⟩.
• Bellman: value = immediate reward + γ × expected next value; optimality replaces Σπ by max.
• Applications: games, robotics, self-driving, recommendation, finance, healthcare, traffic signals, data-centre cooling, RLHF.