**August 21 (Thu), 2003**
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."
Questionnaire, wich discussion.
Examples of plausible reasoning and causal graphs: icy roads.

**August 26 (Tue), 2003**
Examples of plausible reasoning and causal graphs: wet grass, car start,
earthquake.
Reasoning in the evidential and causal
direction. Intercausal reasoning and explaining away. Uncertain
reasoning is non-functional.
Serial, diverging, and converging connections.
Paths as sequesnces of nodes or of edges.
Paths vs. walks, paths, simple paths.
Chains.

**August 28 (Thu), 2003**
Homework 1 (HW1) assigned, due Tuesday, September 2: Exercises 1.1, 1.2, 1.3,
1.4.
Definition of d-separation, with several examples.
Complexity of checking d-separation using the naive algorithm based on the
definition: list all chains, check every connection on each chain.
Lower bound on the
worst case is the number of paths between two nodes in a DAG. There are (n-2)!
paths between two nodes in a DAG in the worst case.
(There are c exp (n/c) paths in a staged network, a special case of DAG, in the
worst case; the worst value for c is 3.)
This motivates the search for more efficient algorithms for checking
d-separation. There are several of them. One of them is Bayes-ball [Shachter,
1998].
Basic Bayes-ball rules.

**September 2 (Tue), 2003**
HW1 collected.
Detailed discussion of Bayes-ball algorithm.
Powepoint presentation used is linked to course web site.
Two point of extra credit will be given for correctness proof, if done within a
week.

**September 4 (Thu), 2003**
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. Detailed presentation of the classical
approach, including proof of the three properties that are the axioms of
Kolmogorov. Brief presentation of the frequentist approach. Even briefer
presentation of the subjective approach.

**September 9 (Tue), 2003**
HW1 returned.
Guest lecture by Professor Juan E. Vargas: "Information as a Measure."
Notes from the lecture are posted under "Lecture Notes" on the course web
site.

**September 11 (Thu), 2003**
Handout: Ch. 2 of Neapolitan's 1990 book on the foundations of probability.
Continuation of the lecture of September 4.
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 pp.56-58 of the handout.
"Definition" of conditional
probability derived in the classical approach (Theorem 2.2), 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).
Bayes theorem (Bayes law, the inversion formula).

**September 16 (Tue), 2003**
Several questions answered on Neapolitan handout.
The theorem of total probability (case analysis).
Definition of Bayesian networks [Neapolitan, 1990].
The visit to Asia example.
The chain rule for Bayesian network: statement and example using "icy roads."

**September 18 (Thu), 2003**
HW2 reassigned and (finally!) due on Tuesday, September 23: exercises 1.5, 1.6,
1.7.
Marginalization (a.k.a. projection, in this course).
Computations with conditional probability tables, using the icy roads example.
Proof of the chain rule.
Bayesian networks admit d-separation.
Several questions answered.

**September 23 (Tue), 2003**
Midterm will be in one week.
Evidence. P(V,e). P(V|e). Normalization.

**September 25 (Thu), 2003**
Midterm exam will be on Tuesday, September 30.
HW3 assigned, due on Tuesday, September 30: exercises 1.8, 1.9, 1.10.
The variable elimination (Dechter's "bucket elimination" variant)
algorithm for computation of
posterior probabilities ("belief assessment"), with detailed example using
"Visit to Asia."

**September 30 (Tue), 2003**
Midterm (MT1).
HW3 collected.

**October 2 (Thu), 2003**
MT1 returned.
Introduction to Hugin.
Hypothesis variables.
Infected milk, one-day and seven-day versions.

**October 7 (Thu), 2003**
HW4 (exercises 1.11, 1.12, 1.13, 1.14, 1.15) is due on Thursday;
use departmental dropbox for submissions.
Milk test example, hidden Markov models. Many good questions.

**October 9 (Thu), 2003**
HW2 and HW3 returned. Students who answered question 1.9 by just giving the
final answer should resubmit their work.
HW5 (exercises 2.1-2.5) due Thursday, October 16.
Cold and angina. Independence relations in that model.
Bipartite graph models (hypotheses, observations) and their
limitations. Diagnostic bipartite graph models (diseases and symptoms) and
their limitations. Quadriparite graph models (setting factors, diseases,
pathophysiological states, and symptoms).
Family-out.
Many good questions.

**October 16 (Thu), 2003**
HW5 deadline extended to Tuesday, October 21.
Simple (naive, idiot) Bayes. Odds-likelihood formulation of simple Bayes, with
derivation of formula: posterior odds = prior odds times likelihood(s).
Poker example.
Pearl's coins and bells example: non-causally interpretable Bayesian networks,
faithfulness, stability.

**October 21 (Tue), 2003**
Much discussion of the coins and bells example, in full detail, with Q&A.

**October 23 (Thu), 2003**
HW6: Exercise 1.15, due Tuesday, October 28. (HW6 is only for students who
have not turned in Exercise 1.15 as part of HW4 or want to resubmit that
exercise. Submit using departmental dropbox should be used.)
HW7: Exercises 2.6, 2.7, 2.8, 2.9, due Thursday, October 30. Submit using
departmental dropbox.
The stratum method for constructing Bayesian networks (from independence
information derived from qualitative descriptions). The intervention-based
notion of causality, again. The telescopes example.
The Monty Hall puzzle. Bayesian net to represent it, with full numerical
specification.
Much good discussion involving students.

**October 28 (Tue), 2003**
HW7 changed: exercises 2.6, 2.7, 2.8 only (not 2.9), due Thursday, October 30.
Submit using departmental dropbox.
Assessment of prior and conditional probabilities: infected milk examples,
statistics
for reliability of information sources (after Vomlel): true positives, etc.
Stud farm example.

**October 30 (Thu), 2003**
Detailed discussion of issues related to questions 2.6 and 2.7, with good Q&A.
The transmission of symbol strings example (section 2.2.4).
Introduction to independence of causal influence, with Dog_out | Family_out,
Bowel_problems example.

**November 4 (Tue), 2003**
HW8 assigned: exercise 2.9.
Independence of causal influence and noisy-OR: the Family-out example, with and
without leak (background) probability. Representation of relations in Bayesian
networks.

**November 6 (Thu), 2003**
MT1 will be on Tuesday, November 11.
HW9 assigned: exercise 2.18, due Tuesday, 11/11
PR3 assigned: exercise 2.10, due Thursday, 11/13
PR4 assigned: exercise 2.22, due Tuesday, 11/18
Semester programming assignment (PR5) assigned, due Thursday, 11/20.
Chapter 2 concluded, with an overview of the remaining topics, and a discussion
of the tree-structured representation of CPTs.
NSDP.

**November 11 (Tue), 2003**
MT2 (proctored by Ravi Katpelly)

**November 13 (Thu), 2003**
Presentation by Hing Xi and Jingshan Huang of paper by
Y. Xiang and V. Lesser: "On the Role of Multiply
Sectioned Bayesian Networks to Cooperative Multiagent Systems." (Local copy
and PowerPoint linked to web site.)

**November 18 (Tue), 2003**
Programming assignment (PR5) due date changed to Tuesday, November 25.
Correction of MT2 (returned).
Discussion of exercise 2.22 (due today): review of conflict index and
sensitivity analysis.
Discussion of programming assignment.

**November 20 (Thu), 2003**
Stochastic simulation: forward sampling and evidence-based sampling (Gibbs
sampling).
Hypothesis-based influence diagrams (a.k.a. decision graphs). Utilities and
decisions (actions). Cow pregnancy example.

**November 25 (Tue), 2003**
PR5 due date changed to Tuesday, December 2.
Extra credit assignment (5% of total grade): add stochastic simulation to PR5.
Value of information: Section 4.3.1 completed.

**December 2 (Tue), 2003**
Graduate Student Presentations.

**December 6 (Tue), 2003**
Graduate Student Presentations.
Presentations are linked to the web site.
End of course.