January 10 (Tue), 2012 HW1 assigned: exercises 1.7, 1.11, 1.12, and 1.13 due Thursday, January 19, 2012 Introduction to the Course: Goals and Topics to Be Covered. The bulletin description, explained: "582 -- Bayesian Networks and Decision Graphs. {=STAT 582} (3) (Prereq: CSCE 350 and STAT 509) Normative approaches to uncertainty in artificial intelligence. Probabilistic and causal modeling with Bayesian networks and influence diagrams. Applications in decision analysis and support. Algorithms for probability update in graphical models." Examples of plausible reasoning and causal graphs: icy roads. Reasoning in the evidential and causal directions.
January 12 (Thu), 2012 More examples of plausible reasoning and causal graphs: wet grass, earthquake. Reasoning in the evidential and causal direction. Intercausal reasoning and explaining away. Serial, diverging, and converging connections. Uncertain reasoning is non-compositional.
January 17 (Tue), 2012 HW1 due no earlier than next Tuesday. Probability. The three axioms of Kolmogorov [1950]. Outcome space, event space, probability measure. Three historically important interpretations in which the axioms of Kolmogorov are true (i.e., three models of them): classical, frequentist, and subjective. Presentation of the classical approach, including sketch of the proof of the three properties that are the axioms of Kolmogorov. Brief presentation of the frequentist approach. Subjective probability defined from betting behavior: "[De Finetti] defines the probability P(E) of an event E as the fraction of a whole unit value which one would feel is the fair amount to exchange for the promise that one would receive a whole unit of value if E turns out to be true and zero units if E turns out to be false" [Neapolitan, 1990, p.56]. Similarly, subjective probability could be defined using the equivalent urn model. The probability P(E) of an event E is the fraction of red balls in an urn containing red and brown balls such that one would feel indifferent between the statement "E will occur" and "a red ball would be extracted from the urn." (I believe that this definition is due to D.V. Lindley.) Kolmogorov's axioms and the "definition" of conditional probability can be derived from the definition of subjective probability and the assumption of coherence in (betting) behavior, as explained on the slides. "Definition" of conditional probability derived in the classical approach, with the assumption that equiprobable outcomes remain equiprobable in a new state of knowledge. Definition of conditional probability as an additional axiom of probability, which is true in the three major models of probability (classical, frequentist, subjective). The fundamental rule, Bayes theorem, and conditional independence. Conditional independence implies multiplicative factorization.
January 19 (Thu), 2012 HW1 due no earlier than next Thursday. Potentials. Independence for variables. Conditional independence is symmetric. (Multiplicative) factorizaton implies independence (under a positivity condition). Table operations are pointwise. By convention, the row of conditional probability tables are indexed by the states of the variable on the left-hand side of a conditioning bar. Icy roads example in detail using table operations.
January 24 (Tue), 2012 HW1 is due on Tuesday, January 31. Wet grass and Athenian taxis examples in detail, using table operations. Transcript of notes placed in Lecture Notes area of the course web site.
January 26 (Thu), 2012 HW2 consists of exercises 2.1, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.12. Definition of d-separation in dags, decision algorithm for d-separation using ancestral graph and moralizaion, definition of Bayesian network, statement of theorem 2.1 [J07].
January 31 (Tue), 2012 HW1 collected and discussed. HW2 due date not yet determined. A generalization of the Athenian taxis example.
February 2, 2012 (Thu) HW1 returned. Neapolitan's definition of Bayesian network [Neapolitan, 1990; in ppt Intro slides]. Proof of the Chain Rule for BNs from Neapolitan's definition. Comments on the alternative definition of BN used in [J07]. Theorem 2.1 in [J07]: P(U) is a probability distribution. The visit to Asia example.
February 7, 2012 (Tue) Theorem 2.1 in [J07], continued. The proof that the conditional probability tables can be computed by marginalization and division from P(U) still needs to be completed. Proof that P(U) respects the d-separation properties using structural induction on the number of variables (nodes). Note that structural aspect of the induction is that the last node has no children.
February 9, 2012 (Thu) HW2: exercises 2.1, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.12, due 2012-02-16. Completion of the proof of Theorem 2.1 [J07]. Findings and evidence. Theorem 2.2 [J07] (statement and import). Variable elimination for computing posterior marginal probabilities.
February 14, 2012 (Thu) Reminder: HW2: exercises 2.1, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.12, due 2012-02-16. Midterm will be next week. Examples of construction of Bayesian network structures: visit to Asia (Lauritzen and Spiegelhalter and Neapolitan versions of the story), papilledema (Neapolitan), and Earthquake or Burglary with Mary and John. For the last one, we use the stratum method.
February 16, 2012 (Thu) MT1 will be on Tuesday, February 21, 2011. HW2 collected. HW2 corrected, in part. Sample midterm from spring 2009 discussed. This includes the coins and bell example.
February 21, 2012 (Thu) MT1.
February 23, 2012 (Thu) MT1 returned, with class discussion. Bucket elimination, with the visit to Asia example.
February 28, 2012 (Tue) HW3 assigned: exercises 2.13 and 2.14 [J07], due Tuesday, March 13. HW4 assigned: exercises 2.20 and 2.21 [J07], due Tuesday, March 13. HW_Extra (extra credit) assigned: exercise 2.16 [J07], due Thursday, March 15; this assignment can be done in teams of up to three students. Installing Hugin: example on my laptop; links, etc. are on blackboard. Building models: Chapter 3 through section 3.1.3 [J07]; the Chernobyl example.
March 1, 2012 (Thu) Catching the structure (section 3.1 [J07]) completed. Determining the conditional probabilities (or: Where do the numbers come from?): Section 3.2 through 3.2.3, without 3.2.2 [J07].
March 13, 2012 (Tue) HW3 and HW4 collected and corrected. HW5 assigned: exercises 3.5, 3.6, 3.8, 3.9, 3.12 (for 3.12iii only, students are allowed to work in pairs) [J07], due Thursday, March 22. Example 3.2.2 (stud farm) started.
March 15, 2012 (Thu) Ch.3 continued: section 3.2. completed.
March 20, 2012 (Tue) Discussion of issues related to HW5 (due on Thursday, March 22). Conflict measure (section 3.4.3 [J07]). Mr. James and Mr. Marwan will present a paper or two on conflicts.
March 22, 2012 (Thu) HW5 collected. HW6 assigned: exercises 3.13, 3.14, 3.15, 3.16 [J07], due Thursday, March 29, 2012. (Due date later changed to Tuesday, April 3, 2012.) Please use Hugin for 3.16. Please review the errata sheet for Exercise 3.15.
March 27, 2012 (Tue) HW6 discussed further. Due date for HW6 changed to Tuesday, April 3, 2012. Noisy or. Computing joint probabilities. Sensitivity to evidence. Sensitivity to parameter changes.
March 29, 2012 (Thu) Continuous Bayesian networks (Angina with continuous Fever and Temperature nodes). Object-oriented Bayesian networks (disease with multiple stages and car maintenance examples). Interventions (Sneezing example). Dynamic Bayesian networks (Section 3.37 [J07]): repetitive temporal models, DBNs, hidden Markov Models (HMMs), Kalman filters, Markov chains.
April 3, 2012 (Tue) Mr. Sharaf leads the class. HW6 collected. Videos from Dr. Koller on template models.
April 5, 2012 (Tue) HW7 assigned: exercises 9.3 and 9.11 due Tuesday, April 17. Graduate student presentationa assigned---see "Graduate Student Presentations" link on main course web site. Ch.9 ("Graphical Languages for Specification of Decision Problems") [J07]: test and decision actions, one-shot decision problems (including fold-or-call and mildew examples), utilities (9.2) including management of effort problem.
April 10, 2012 (Tue) Ch.9 ("Graphical Languages for Specification of Decision Problems") [J07] continued. Section 9.2.1 ("Instrumental Rationality"): von Neuman and Morgenstern's axioms of instrumentally rational choice, theorem 9.1 (existence of utility function and justification of MEU principle), Allais' paradox (students on 2012-04-05 had preferred lottery A to lottery B (7 to 4) and lottery D to lottery C (10 to 1). Section 9.3: Decision Trees, with a one-test milk example and the algorithm for solving decision trees.
April 12, 2012 (Tue) Change in due date of HW7, which is now Thursday, April 19. Ch.9 ("Graphical Languages for Specification of Decision Problems") [J07] continued. More examples of decision trees (section 9.3.1). Influence diagrams: section 9.4 (including the Fishing in the North Sea example and information blocking). Asymmetric decison problems, with the Test for Fever and Aspirin example, and how to convert such problems into ones without Test Decisions.
April 17, 2012 (Tue) Distinction between perfect-recall (or: no-forgetting) Influence Diagrams and LIMIDs. Most people call perfect-recall IDs simply IDs. LIMIDs are the only kind of IDs now supported in Hugin (now version 7.6). (Normal) IDs were the only kind supported before version 7.0. Example of LIMID: pig breeder network with four stages (Nilsson and Lauritzen, 2000 and 2001). Brief discussion of the LIMID for the oil wildcatter problem (ex. 9.11(ii)) and of the decision tree for the same (ex. 9.11(i)). Detailed discussion of the transformation of a test decision into an action decision with an additional chance vatiable with the additional "no-test" state.
April 19, 2012 (Thu) HW7 collected. Late homework will be accepted until midnight on Wednesday, April 25. Two graduate student presentations. See presentation site.