**August 20 (Mon), 2010**
HW1 assigned: exercises 1.7, 1.11, 1.12, due date to be determined,
but not earlier than Friday, August 27.
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.

**August 23 (Mon), 2010**
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.
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.

**August 25 (Wed), 2010**
HW1 due no earlier than next Monday. Note corrected exercise numbers: 1.7,
1.11, 1.12.
Uncertain
reasoning is non-compositional.
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 pp.56-58 of the handout [to be provided] and on the slides.
"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).

**August, 27 (Fri), 2010**
HW1 assigned with changes:
exercises 1.7, 1.11, 1.12, 1.13 [J07], due September 1, 2010
(Wednesday).
The fundamental rule, Bayes theorem, conditional independence, factorization,
variables and their states (values) partition the outcome space, probability
of variables, probability tables, marginalization.
Potentials. Independence for variables. Conditional independence is
symmetric. (Bernardo Quibiana shows the latter in class.)

**August, 30 (Mon), 2010**
Review of causal networks: the car start example.
Neapolitan's definition of Bayesian
network [Neapolitan, 1990; in ppt Intro slides].
Comments on the alternative definition of BN used in [J07].
The visit to Asia example.

**September 1 (Wed), 2010**
HW2 assigned, with due date to be determined: exercises 2.1, 2.4, 2.5,
2.6, 2.7, 2.8, 2.9, 2.10.
HW1 collected and correction given in class.

**September 3 (Fri), 2010**
HW2 is due on Friday, September 10.
The Chain rule for Bayesian networks. Chapter 2 completed,
except for variable elimination.

**September 8 (Wed), 2010**
Belief Assessment, Most Probable Explanation (MPE), and
Maximum A Posteriori Hypothesis (MAP).
Variable elimination (in the bucket elimination format),
with the visit to Asia Example.

**September 10 (Fri), 2010**
Video camera failed (batteries ran out).
HW2 collected and corrected. Numbers for the visit to Asia example of
bucket elimination.

**September 13 (Mon), 2010**
HW1 returned.
Section 3.1 [J07]: Catching the structure.

**September 15 (Wed), 2010**
The stratum method for constructing Bayesian networks (from
independence information derived from qualitative descriptions),
with a detailed example (Alarm, Burglary, Earthquake, MaryCalls, JohnCalls)
from [Russell and Norvig 2003 after Pearl] with different
orders of variables.

**September 17 (Fri), 2010**
I forgot the video camera! Sorry!
HW3 assigned, due 2010-09-24 (Fri): Install Hugin on your computer.
(See blackboard for details.)
Do exercises
3.3, 3,5, 3.6, 3.8, 3.9, 3.10, all from [J07]
[Due date later changed to 2010-09-29].
Determining the conditional probabilities (or:
Where do the numbers come from?): Section 3.2 through 3.2.3 [J07].

**September 20 (Mon), 2010**
MT1 (Midterm exam) will be on Monday, September 27.
Determining the conditional probabilities: Section 3.2 through 3.2.5 [J07].

**September 22 (Wed), 2010**
HW3 is now due on Wednesday, September 29.
More modeling methods: noisy OR, divorcing, undirected relations, with
examples.

**September 24 (Fri), 2010**
Causality and Bayesian networks. Excision semantics. Intervention variables
and non-crisp intervention. Examples: Mary, John, Alarm, Earthquake, Burglary; Cold and Hay Fever.

**September 27 (Mon), 2010**
MT1.

**September 29 (Wed), 2010**
HW3 is now due Friday, October 1.
MT1 returned and corrected.
Coins and bells example from MT1 in Spring 2009 discussed in class, using
Hugin. See lecture notes entry.

**October 1 (Fri), 2010**
HW3 collected.
HW4 assigned: Exercises 3.11, 3.12, 3.13, 3.14 (use the numbers on the slides
for ch.3 [J07], *not* the numbers in [J07]!), and 3.15 [J07], due 2010-10-13.
HW5 assigned: Exercises 3.16 (use Hugin for this!), 3.19, 3.20, 3.21, 3.26, 3.27, and 3.28 (note: most of this is a paper-and-pencil exercise) [J07] due
2010-10-20.
Graduate student presentations assigned. There will be three presentations
by teams of two students each. See presentation page on the course web
site for links to the papers and some other details. Each student team must
turn in the presentation slides (ppt, preferred, or pdf) and a one-page
summary of the paper.
HW3 corrected, through exercise 3.9.
There will be no classes until Monday, October 11, 2010. Work on homework
and presentations!

**October 11 (Mon), 2010**
Presentation by Simin and Smith, with discussion. On Wednesday, we will have
a two-class period lesson; the first hour will consist of two graduate
student presentations. The second hour will be related to the AIM workshop
on parameter identification in graphical models that I recently attended.

**October 13 (Wed), 2010**
HW4 due date moved to Monday, October 18.
Presentation by Parsons and Tarter, with discussion.
Discussion of the HW3 exercises, in detail.
Second hour: presentation of the first part of my AIM workshop talk on
identifiability in causal Bayesian networks and the do-calculus.

**October 18 (Mon), 2010**
HW4 collected.
HW5 due date changed to Monday, October 25.
Presentation (on Vomlel and his students' work on assessing skills in
the arithmetic of fractions) by Quibiana and Roy Chowdhury started. Discussion of entropy
as a measure of ignorance (a kind of uncertainty).

**October 20 (Wed), 2010**
Presentation by Quibiana and Roy Chowdhury continued. Long detour on
entropy, decision-theoretic troubleshooting, myopic test selection.

**October 22 (Fri), 2010**
Presentation by Quibiana and Roy Chowdhury completed. Detours on learning
BNs with score-based and structure-based approaches.

**October 25 (Mon), 2010**
Discussion of the complexity of several related problems: PIBNET,
PIBNETD, and D-PR. Discussion of exercise 3.27 [J07].

**October 27 (Wed), 2010**
Discussion of exercises 3.28 (completed) and 3.26 (not completed) [J07].

**October 29 (Fri), 2010**
Belief Updating in Bayesian Networks (Ch. 4 [J07]) started. Video from
Spring 2009 was used.

**November 1 (Mon), 2010**
Belief updating through Section 4.2 and definition 4.4; video from Spring
2009 was used.

**November 3 (Wed), 2010**
Belief updating through Theorem 4.3, with examples; video from Spring
2009 was used.

**November 5 (Fri), 2010**
Jensen and Jensen's UAI 1994 result: a spanning tree of a join graph is a
join tree if and only if it is a maximal spanning tree of a join graph.

**November 8 (Mon), 2010**
Review of how to construct join trees of trinangulated graph.
Separators. Junction trees. Messages. Distribute and collect evidence.
Statement of the main theorem: Theorem 4.5 part 1 [J07].

**November 10 (Wed), 2010**
Conclusion of sections on propagation in junction trees: triangulation with
some heuristics. Brief discussion
of lazy propagation, using definition of marginalization from Madsen, which
is a notational variant of Definition 4.1 (Elimination) in [J07].

**November 12 (Fri), 2010**
Approximate belief updata: stochastic simulation, likelihood weighting, Gibbs
sampling (parts of 4.8 [J07]). Some slides from Thomas Nielsen are in
blackboard.

**November 15 (Mon), 2010**
Graphical Languages for Specification of Decision Problems (Ch.9 [J07]):
Introduction (test decisions, action decisions, causality), One-Shot Decision Problems, Utililies, including the management of effort example, instrumental rationality, and Allais' paradox.

**November 17 (Wed), 2010**
Decision Trees (9.3 [J07]).

**November 19 (Fri), 2010**
Influence diagrams: basics (from 9.4 [J07]),
Apple Jack example from Kjaerulff and Madsen,
worked out in Hugin. I note that Hugin uses LIMIDs instead of plain IDs.

**November 22 (Mon), 2010**
Influence diagrams: the pig breeding example by Madsen and Kjaerulff.
Solving influence diagrams: description of approach by conversion to symmetric
(full, complete) decision trees. Policy; strategy. The relevant past.

**November 29 (Mon), 2010**
HW6 assigned: Exercises 9.11 (both parts) and 9.12 (part (i) only) [J07].
The oil wildcatter example in detail, represented and solved both as an
influence diagram and as a decision tree.

**December 1 (Wed), 2010**
The used car buyer example in detail, represented as a decision tree.
Test decisions in influence diagrams (first part of section 9.5 [J07]).
Solutions to influence diagrams (section 10.1 [J07]) started.

**December 3 (Fri), 2010**
HW6 collected.
Solutions to influence diagrams; variable elimination and strong junction trees
(ch. 10 [J07] through p.358).
Student evaluations.