csce 582: bayesian networks paper presentation conducted by nick stiffler ben fine
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CSCE 582: Bayesian Networks
Paper Presentation conducted by
Nick StifflerBen Fine
Bayesian networks: A teacher’s view
Russel G Almond Valerie J Shute
Jody S. Underwood Juan-Diego Zapata-Rivera
ACED
A Computer-Based-Assessment-for-Learning system covering the topic of sequences
In this Paper it spans three sequence types
Arithmetic Geometric Recursive
ACED A Prototype that explores
Madigan and Almond Algorithms for selection of the next task in an assessment
The use of targeted diagnostic feedback
Tech solutions to make the assessment accessible to students with visual impairments
Geometric Sequence Model
Proficiency Levels available to each node
•Low .
•Medium
•High .
Bayesian Network (SS) Individual task outcome variables -are entered as findings in task specific nodes where the
results are propagated through the proficiency model
Posterior Proficiency Model -gives the belief about the proficiency state for a
particular student
Note: Any functional of the posterior distribution can be used as a sore
Terminology Si0, Si1,…,Sik – proficiency variables for
student i Si0 – special overall PV (Solve Geo.
Problems)
Xi – Body of evidence
P(Sik|Xi)
-conditional distribution of Sk given the observed outcomes
The Four Statistics (at least the ones we look at)
Margin
Cut
Mode
EAP
Margin The Marginal Distribution of Proficiency P(Sik|Xi)
expected numbers of students in each proficiency
Σi P(Sik|Xi)
Average proficiency for the class Σi P(Sik|Xi) class size
Cut Identifier for a special state Ex. students ≥ medium are proficient P(Sik ≥ medium |Xi)
Average cut score is the expected proportion of “proficient” students in the class
Mode The value of m the produces max{P(Sik = m |Xi)}
Improvements If student is within a threshold should be
identified as being on the boundary When the Marginal Distribution is evenly spread
out the system should identify students who have the greatest uncertainty
To get modal scores count the number of students assigned to each category
EAPExpected a Posteriori
Assign numbers to states to get an expectation over posterior
High : 1 Medium : 0 Low : -1
1*P(Sik = high |Xi) + 0 * P(Sik = med |Xi) -1*P(Sik = low|Xi)
Reduces to: P(Sik = high |Xi) - P(Sik = low |Xi)
EAP (cont.)
What it means The EAP would return the average ability
level for each class Standard Deviation variability of
proficiency
Scores coming out of the BN
Individual Level Plots
Comparing Groups
Comparing Groups
Reliability
Observed Score = True Score + Error Signal to noise ration in signal
processing Applying the Spearmen – Brown
formula
Spearmen – Brown formula
is the predicted reliability
N is the number of "tests" combined
is the reliability of the current "test"
predicts the reliability of a new test by replicating the current test N timescreating a test with N parallel forms of the current exam.
Thus N = 2 implies doubling the exam length by adding items with the same properties as those in the current exam.
Why BN Works Well Offers significant improvement over
number right scoring Bayes network estimates stabilize sub
scores by borrowing strength from the overall reliability
Differs from other methods b/c it starts with an expert constructed model of how the proficiencies interact
Other methods use observed correlations b/t the scores on subtest
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