January 09 (Tue), 2024 Introduction to the Course: syllabus, objectives, course structure, and topics to be covered. Bayesian networks and decision graphs as a topic area within artificial intelligence. Example of plausible reasoning and causal graphs: icy roads (to be concluded).
January 11 (Thu), 2024 Examples of plausible reasoning and causal graphs: icy roads and wet grass. Networks drawn using Hugin; numbers entered for both examples. Reasoning in the evidential and causal direction. Intercausal reasoning and explaining away. Causal networks and d-separation.
January 16 (Tue), 2024 HW1 assigned: exercises 1.10, 1.11, 1.12 [J] due on Tuesday, 1-23. Note: these exercises are different from those announced in class. Details of submission will follow. Proof that the Classical and subjective interpretations of probability are models of the axioms. Conditional probability as a fourth axiom of probability. The fundamental rule and Bayes' rule. Computation of certainty factors in a compositional system. Problems with compositional system. The Chernobyl example with Naive Bayes and five-variable causal networks; the importance of structure in a causal model. A first look at Hugin. The (Kolmogorov) axioms of probability (with the "definition" of conditional probability as a fourth axiom). Proof that the classical model of probability satisfies the first three axioms.
January 18 (Thu), 2024 Probability prerequisites; potentials (Ch.1 [J]). An algebra of potentials.
January 23 (Tue), 2024 Ch.2 [J] ("Causal and Bayesian Networks") up to an example of the chain rule for Bayesian networks.
January 25 (Thu), 2024 HW2 assigned: exercises 1.13, 2.1 through 2.6 [J], due on 2024-02-01. Evidence, findings, probability of evidence. Bayesian rule with probability potentials: zeroing out and normalizing. Variable elimination. Munin. Probabilistic graphical models and their advantages. Ch.2 [J] slides from the authors completed.
January 30 (Tue), 2024 HW2 due date changed to 2024-02-06. Definition of Bayesian networks, accoring to [Neapolitan, 1990]. The local Markov condition. Theorem 3.7 in [Lauritzen, 1996]: equivalence of the (directed) recursive factorization, (directed) global Markov property, and (directed) local Markov property. Proof of the chain rule for Bayesian networks (i.e., recursive factorization) from Neapolitan's definition (i.e., the directed local Markov property). Lauritzen's algorithm for d-separation: ancestral sets, moralization, the (directed) global Markov property.
February 1 (Thu), 2024 Q&A on d-separation, with several examples. Observation that d-separation is non-monotonic.
February 6 (Tue), 2024 HW3 assigned: exercises 2.7, 2.8, 2.9, 2.10, and 2.12 assigned, due on 2024-02-13. The "Visit to Asia" (a.k.a. "Chest Clinic" example in detail. Bucket elimination for the belief update problem: a detailed example.
February 8 (Thu), 2024 More on variable elimination. Many questions. Questions on the exercises for HW3.
February 13 (Tue), 2024 HW4 assigned: exercises 2.17, 2.18, and 2.19 [J]. Please check dropbox (and/or the authors' errata page online) for details and an error in the statement of exercise 2.19. More on variable elimination. MPE and MAP. A detailed example of solving MPE with the bucket (variable) elimination. Axioms for local computation (Anders Madsen's formulation.
February 15 (Thu), 2024 Detailed discussion of exercise 1.13 (part of HW2). More on variable elimination: interaction graphs, fill-ins, with detailed illustration of the concepts in the visit-to-Asia example.
February 20 (Tue), 2024 HW5 assigned: exercise 2.23 [J], due 2024-02-27. The midterm exam will be on Thursday, March 14 (2024-03-14). The BOBLO network as an example. The coins and bells example. Causal and non-causal models. Intervention and the excision semantics for causality.
February 22 (Thu), 2024 Presentation by Prof. Alvaro Morales of the University of Wisconsin Madison: "Opportunities and Needs in AI and CI for Direct Market Farming and Farmers Markets." Ch.3 [J] ("Building Models") started: capturing the structures, with the one-day infection model and several variations on a 7-day model.
February 27 (Tue), 2024 HW6 assigned: exercises 3.3, 3.5, and 3.6 [J]. Discussion of HW5 in detail. No penalty will be given if HW5 is turned this coming Thursday. Using Hugin on the departmental Linux machines. Ch.3 [J] continued through section 3.1.4.
February 29 (Thu), 2024 HW5 is due on Tuesday, 2024-03-12. Reminder: the midterm exam will be on Thursday, 2024-03-14. Ch.3 [J] continued through section 3.2.2. (This is lecture 16. Next week is spring break.)
March 12 (Tue), 2024 Reminder: the midterm exam will be on Thursday, 2024-03-14. The exam will be closed book and notes. Simple non-programmable calculators are allowed. The stratum method for building Bayesian networks. Q&A on various topics.
March 14 (Thu), 2024 Midterm.
March 19 (Tue), 2024 Ch.3 continued through Noisy-Or.
March 21 (Thu), 2024 Midterm solutions with much discussion. Ch.3 [M]: overview of the next topics to be covered.
March 26 (Tue), 2024 HW7 assigned, due 2024-04-02: Exercises 3.8, 3.9, 3.10, 3.11, 3.12, 3.13 (parts i-iii only), 3.16 [J]; please read carefully the instruction in dropbox for HW7. Noisy-OR and its relationship to ICI explained. Divorcing. Undirected relations (constraints) and the socks example. Expert disagreement. Conflicts. Sensitity to evidence. Sensitivity to parameter values (conditional probability table entries). Slides for Ch.3 [J] provided by the authors completed.
March 28 (Thu), 2024 Continuous variables; Gaussian and conditional Gaussian distributions. The Angina example with two continuous variables (Fever and Therm) implemented in Hugin, in detail. Detailed example of sensitity to paramenter values. Ch.9 [J] ("Graphical Languages for Specification of Decision Problems") started: questions about the two lotteries involved in Allais paradox asked.
April 2 (Tue), 2024 Rubric (basic requirements) page on graduate student presentations added to main course website. Ch.9 [J] continued, up to a brief overview of the axioms of instrumental rationality.
April 4 (Thu), 2024 HW7 due date changed to April 9, 2024. More information on graduate student extra work added to the main course website (in a dedicated folder). Ch.9 [J] continued: decision trees, influence diagrams started.
April 9 (Tue), 2024 HW8 assigned: Exercise 9.8 [J], due on 2024-04-09. Ch.9 [J] completed: influence diagrams. POMDPs as a special case of influence diagrams and dynamic BNs. Ch.4 [J] ("Belief Updating in Bayesian Networks") started.
April 11 (Thu), 2024 The final exam will be a take-home exam. It will be due at the end of the scheduled time in the syllabus (and in the university final exam catalogs). Ch.4 [J]: The junction tree algorithm.
April 16 (Tue), 2024 Ch.4 [J] completed, including presentation of three approximate inference algorithms: forward sampling, likelihood weighting, and Gibbs sampling.
April 11 (Thu), 2024 Review of exercises 3.13, 3.16, and 3.12. The difference between the two questions in 3.13(iii) was emphasized; the second question requires the solution of the MPE problem, which in Hugin is done using the Max-Propagate method. The EM algorihm, from Ch.6 [M]. Very brief presentation of the PC algorithm from Ch.7 [M]. End of course.